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Last active September 21, 2017 16:29
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Background notions in linear algebra and shallow machine learning applied to electrophysiology
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{
"cells": [
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"source": [
"# Problem statement: why do we need machine learning in electrophysiology and neuroimaging?\n",
"\n",
"There are two central problems in neuroscience:\n",
"1. the mechanisms that drive neuronal activity are largely unknown.\n",
"2. the neuronal activity that we record is generally very noisy, partial, complex and difficult to interpret.\n",
"\n",
"Fortunately, our ability to collect a large amount of signals, and manipulate a large amount of experimental variables has dramatically increased over the last decades. Machine Learning (ML) now appears as a critical tool to find critical the mapping between neuronal activity and external variables.\n",
"\n",
"In practice, ML analyses have be used for a variety of purposes:\n",
"* **decoding**: estimating whether neuronal responses can discriminate different experimental conditions.\n",
"* **encoding**: estimating how different experimental conditions induce distinct neuronal responses.\n",
"* **denoising**: maximizing signal-to-noise ratio for subsequent analyses.\n",
"* **summarizing**: diminishing the number of multiple comparisons by fitting and evaluating a single model across many sensors and time samples.\n",
"\n",
"We will here review the motivation and background of these machine learning analyses.\n",
"\n",
"## Electrophysiology: source unmixing\n",
"\n",
"One of the main applications of machine-learning (ML) to electrophysiological recordings has been focusing on the unmixing of neural sources.\n",
"\n",
"Formally, electrophysiological recordings are multivariate time series of $c$ channels and $t$ time samples ($X \\in R^{c \\times t}$) which are believed to result from an instantaneous linear mixture ($A$, a.k.a *forward model*) of underlying electro-magnetic sources ($S \\in R^{s \\times t}$) added with some noise ($\\epsilon$):\n",
"$$X_t = \\sum_{i=0}^s a_i s_{it} + \\epsilon_t = A S_t + \\epsilon_t$$\n",
"\n",
"This equation captures four important notions:\n",
"* The forward model $A$ is not necessarily diagonal (or square): each sensor can be affected by multiple sources and each source can affect multiple sensors, but there can (and in practice) there are many more sources that we can record from.\n",
"* The mixture is linear: the electric and magnetic fields do not interact with one another but only sum one another in any point in space.\n",
"* There exists an irreducible noise at each time sample ($\\epsilon_t$).\n",
"* The projection of the sources to the sensor is independent of time ($t$) - assuming that the sensors do not move with regard to the sources.\n",
"\n",
"Source unmixing thus consists in finding an inverse estimate $W=\\hat{A^{-1}}$ to map sensors recordings $X$ into the sources $\\hat{S}$:\n",
"$$\\hat{S_t} = W X_t$$\n",
"\n",
"In practice, finding $W$ is not only challenging because the sources $S$ are much more numerous than the sensors, but also because they are not necessarily (and often not primarily) generated by neuronal activity. Indeed, physiological (e.g. eye movements, muscle tensions) and environmental artefacts (e.g. electric lines) generally account for most of the variance of temporally-resolved neuroimaging data [ref].\n",
"\n",
"Recently, a battery of supervised algorithms have been used to identify the sources that maximally discriminate the neuronal responses ($S=AX$) elicited in distinct experimental conditions ($Y$).\n",
"\n",
"This tutorial provides shows how such algorithms are tightly linked to the classic mass-univariate subtraction used in neuroimaging analyses.\n",
"\n",
"\n",
"# From mass-univariate subtraction to linear modeling\n",
"\n",
"Linear unmixing models are intimately linked to the traditional comparison by subtraction approach.\n",
"\n",
"To illustrate this tutorial, we will thus start with a common use-case: fitting a linear support vector classifier to decode from the neural responses a categorical (and balanced) stimulus. We will see how this method can be rooted back to a simple subtraction of average brain responses across conditions."
]
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"collapsed": true
},
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"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import mne\n",
"from mne.datasets import sample\n",
"\n",
"# Read continuous data\n",
"raw = mne.io.read_raw_fif(sample.data_path() + '/MEG/sample/sample_audvis_filt-0-40_raw.fif',\n",
" verbose=False)\n",
"\n",
"# Find stimulus trigger\n",
"events = mne.find_events(raw, verbose=False)\n",
"\n",
"# Analyze trials with a left and a right auditory stimulus\n",
"event_id = {'left_sound': 1, 'right_sound': 2}\n",
"\n",
"# Select magneto-meters\n",
"picks = mne.pick_types(raw.info, meg='mag')\n",
"\n",
"# Cut continuous data into discrete epochs\n",
"epochs = mne.Epochs(raw, events, event_id=event_id, tmin=.090, tmax=.090, picks=picks,\n",
" baseline=None, proj=False, preload=True, verbose=False)\n",
"\n",
"# Equalize conditions\n",
"epochs.equalize_event_counts(event_id)\n",
"\n",
"# Extract data with X y notation\n",
"X = epochs.get_data()[:, :, 0] # shape (n_epochs, n_channels, 1 time sample)\n",
"y = epochs.events[:, 2] # shape (n_epochs)\n",
"\n",
"X *= 1e12 # use fT to avoid numerical errors\n",
"\n",
"# Ensure y is in [-1, 1]\n",
"y = (y == max(y)) * 2 - 1"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
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4IzH7kR/nJAy1dYkFaHT5LLtZAHDG42CvBTXMwur0IYwrYPbn/glgEiL01DJc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\ncnkgrXk/q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"text/plain": [
"<matplotlib.figure.Figure at 0x7ff39d6a4a10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot X and y\n",
"fig, axes = plt.subplots(1, 2)\n",
"for category, ax in zip(set(y), axes):\n",
" im = ax.matshow(X[y==category], cmap='RdBu_r', origin='lower')\n",
" ax.set_xlabel('Channels')\n",
" ax.set_ylabel('Trials')\n",
" ax.set_title({-1:'Left trials', 1:'Right trials'}[category])\n",
" ax.set_xticks([])\n",
" ax.set_yticks([])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Electrophysiological recordings are traditionally analyzed in a mass-univariate approach (i.e. for each sensor ($c$) and at each time sample ($t$) separately). The recording pattern corresponding to the subtraction of two categorical conditions is thus equivalent to the dot product between $X$ and $y \\in [-1, 1]$:\n",
"$$A_{c, t} = X_{c, t} y$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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itAOrMJdmyXE0LR+DVZCLqet8eNcA0DQ03YaYDj5btYVXv1xC8/638c6TY0iv\nXJmy8THYdRAr+BttURa333KTTUcljh0/YYWINFJKnfi7tPnbHLKIiCMq5u20Wg2aiArZ06rWiDRD\nNI4fPsg3C+Yz+dExSHEuIZ+HSxrX5OL61fDnFwOQ4/NT7AtgczswXE4MtwMxDQr8fiylyC72sTcz\nhyKvn21HM9l6OJO9GdmcyCskv9iLFWlaPjF3OVEOO61rVeauS1oSFxeN92QemmHDX1B8KlLWDRu6\ny876o1napW1bxM9ftWGFiNRXSvn+Lo3+F0TTuhnOqGc6jXndGZsQS37GYVKrVMdu08g8vJ8Z095k\n4/yPsIqyqJKUSN3ksjgMGx6gKBgkNxgAu4bDZUc3tFMtCQBLKXbnF1C7XCy6TUczbOgOE5vDxBI4\nlp3Pwc0B1gaClLVCVE6IZnS3CyjOzKUooxibwxbJ51vhFoihY4+xcxQfNVOTjN3Hs2aLSCul1MaS\nU/D3EZFEtztqiSsqylkpPR2AkBV2xoGQQhMBLew8Fn40k07dLiepfBK6BgvnfUlCQgJ2Xfj663ms\nWreJ5ZPuRyvKI1RcTNDrZ9eRE5SPiSLa8csvv2bYsDlMTBXijsvbs+VIJl2GjGLB1KcpXyEZgt7T\nhmxF7ldkIT6n3c6c96a7L7zk8t6Hjx7bBzz0jwn2F4mNjZsWl5DYtHbDxoau64SCwTNqu3PtKrKO\nH6Vdxy7oGniLCli3di13DbuVwuwsbh3zOO+OvYU0p0YoP5eg109OXiE5xV4ql4n7xTl/1tZflE+T\nKimMuuoyBox8jOmPj2LiyFvAEFQwcEZtRSmG3jhIzzh6qMzL09/9VkSa/l1jwf++CFlkiDsmrnta\njTrOQzs20XPwraz/dh6T5nxIqwta0advHxJi3JCbj8PhwOsPIJp2Kt1wXcu6YSfpsHPY52f4lI9Y\nt+8oDtNA1wSPP4ip63RsXIu6VdJITbPToF4d7hzUh9goN4bNFo4mlOLEiSzmfreCqye/x5Qbu9O2\nXCKWP4gVCAJ+nl27HbfTTtfGNVCa8OKDd9tqdx9czbTbpwA3/W0a/R8RkXSb6ZjVaeTzzrKpFTm6\nah4V6zVh6pihXD/0DijMon27dpQrk4h1NIegZWHTwpVMdI0GFRKoVy4eTRdsDoM8pZi4ajPDW9Wn\ngtvJumNZ3L9qM6/1ak96UgIzN/7E26u3Yik4kpNPjMtBUlwUs3fsx1KKbYcyaJRWnmc6Nsfhtwj5\nQ5HO1SDN+2YPAAAgAElEQVTLCnOZn3GSyVVb8tWWvdxzVXc+27DfMf/bJQtEpKZSKrdk1fwlIqK5\n3e7PBw66LmH9ho3k5eQQXRFmvfQk6Da6XH8nuiaARshSHNi1nWr3jDk1HGvunE95ZNw4urRrwyWX\n9+ShG/vx8sdfUTHKpHvtdIJeP6M+WMgF6Snc2b4JhR4vD8xdxlVNatGqekUst4MHL2+DHhUFhh3T\nZuPSW8ewYOpTJCalIJHxs4hGQbGXfoNvYeQdw+jUrjXRToN5777mqtn20tEiskwptaCk9fw1InJD\nalrF3gMG32Bs274TgDVLFvLtJ+9w3aNTsDsc/Kzt/p3bqFa73iltFyyaR/u2bXlk9EjefG0KrerV\nIC8nh3HffM/oS1oR9Pp54euV7D6Rw7SBXVGWxZSl6zFsGre2b4rldnBFg6r0bd0QMR3MGnc7/cc+\nzfvPGFzU7sJfaItm44FxT2AYNsaNHoGE/IwfMcyY/8131Xfs2T+V8GJnZ52/xSGHxxM6nusz8lF3\n8clMug68CYfdTo269QnmZeLJzaJcmTJ8s3Q5HeuG80P+UDhS1XQN3WEPb6aNRXuPMHzGXLo1r0eb\nRnV47Ob+AOQWFpNXVEzltFQ0p5u35y/DH1KUS68eScpHHBBQIaECQ6rVoF7tGvS642Hm33cN+7Lz\nqGo3cRg2WqaUxe2wk5FfROVyCfi8PkQTiYqO7iciX6jwehjnBCKi66b9k/o9BttjyqWga0JavWZU\nq1ufvB2rqVajJsd2eMnMPMHxE1mUAwRBoU6NUPk5Gv45avAFg5gOO45YN87YKFrGunmlTCyZXj/D\n3voSw7CRXCaeZ2+5ktpVKmE6nYjNAE0HK4SvqJCxr7zLTXOWMqP7hZw4mU+h8pPiMKkl0eTbFLql\nOFlUTEpiHOXKxJNepVr8Tz/tfh3oV6KC/pa70ypWrN9v4LWG14LEpGQCIYvK9ZsRQMPjD+HJz8GT\nfYzqNepw8vhR0qtURdcg4PPx/ZIlvPHyZHzFBaxav5lPx9/BlF07kJAVCQDgyZ7tKetysuv4Sa6d\nOZfMQg+bjmQy8+qupCYlAiCahuaweLh/Z4q8PvrfM565rz2FFQyyctNaOlzUAbfTQdfOF1GnVs2w\n5ZZF0OfFsOmGUsYHIlLjXEq7iUhN0zQnP/PiS86jWbkEdCeBkEW59JqkN26NX+kEvQEOb/6Rxi3b\ncPCnHXTv0w9dC3cSL/j6K3pc3h1Cfr75/gd6XtgM3fIiSp3S9vYOTcgt9BAMBrnl/QV8t+cwAlSL\nj6Fzg+phOzQNzbJolV6emWNv5epRE1j05rPUbdiA5Ws3Ua9+A2LiE2nXphWGEWnFWBYBr4cKZRKM\n/YeO9BaRz/6ODuqzPjFERHSbaf+gy82jjEVvv0zW8cPYTDuWgqTUilx7061s27yZ+LgY7nngETZu\n24EG5BYVc+VLH3IorxDD7cCMcfHFzgPcNfNrPnnwZqbeN4THh16D5nCjOdwklCtPetVqaNFxaFFx\nDL76SoYMvgbLHo3ljMVyxWO5E7HciQSdcfS/5xEO5hUz+oZ+3D5zPuMX/ciiIyewuR10rJpKq7Ty\n1IqPYc3ugyxfsQqf18ddd4+INk37NBFJPNs6/Q/cE5NSNb24sMBcOeNZ/EELzRWD6Y7mskG3kJqS\nwvEjhzh48BCvvv0+BAPYdY1dGdm8s35nWNtoF/a4KOxxUZgxbsqVieferhcwb+8RHly4iocXr2Hs\nvJXcP3c54666mB9eGMXC50bTqHEjnEmp2MpX/MU2Zf4qDFc0FcrGMXXrXj48cpRZJ45jRhmkxrnp\nXaEC/oIADcvE8dWSFSz/YRWHDx0wYuPiLhGR3iUt6M+ISC3TNB+75977Ym694Tp6D7yBmAoVKfSH\nqNS0Lcn1W+ELWqz47D2+fuNFRGDMpGl8OWsmj40ewfrVP1CnTh0S42LYu3cvaUnlcNqEuy5vS/eG\nYWeg6RpVyicQ5bLz2eafuLhmJbaNGEjH9BRu/nAR/mIPQa+fQLEXy+tl7bbd7DpwCE0pxjz7Cgu/\n/Z4RjzxFTmYmmsCdt91MhfJlwxegaTz/xjsUeXwMurSDYTdsr5egnL9ARDS73f7x/Q8+rL/0wvPs\n2b2bdr0GUOgPYcaXp0mPa/GHFEf372X2i+M5uGsrvW8cRnJKGrdc3YcDe3ez5Nvv6NKxA2IF2bln\nP3UqJdGpQTVGX9YGCGsb63ZSsUwcP53MY/OxLDbcOYC3+nbkzk+/Y8eh47/QVnmLeevLxXRv3Ygr\n7x5HzokM7h3/NB9/9gUoi0s6XUTHduFjo2ksWr6K5eu3cG23Di67YXtDRMqebZ3+hpl6MiQhNb1S\no279zUtuG0veyUwWvPvGqYS9KMW6Navp26M7X739Co2qpnHo+AkqlomjVfU0yiXEoDtMhr87j5Hv\nzmPOI0NpWb82YjPD4wntDsTpJmS6KMKG5ooBhxtluFB2N8p0YZluVmzYxtBRD3IgKx9ccVxwQWvq\nNWzC8CHXEVBwVbtGXNW6AYbbgS0SNZY3DVpWrMDxwwcZM/R61q3+gSv6DTBNu+PJs6/TX0dE0jTD\nHNf0pvFx6V0GUqPHLRR6g+xc8Q3fvPEshiaYusa2LZsYOuR67r9lIJa3CCsYwG03aVKxAjaHydbc\nAl5atRWbw05IE2as3U6nSR+wMzOXWmnlaVgtleE92rF20ih6dmqLHhOPFhWH5o5Bi4rDZzgZ9cI0\n9mV7UO54mrdoTvOmDXnx7uuZuWY7A5vXYcwF9TDcJjaHDU0Xgt4AvSsk8fY3q3nnodtp37oll17W\nPcbucLwaWViqpLUVp9M586677tIu7XEFcYll2HfoMIX+EAW+IAXeIP5gCI8/SIs+N9B/zFP4vcXU\na9Kceo0a07BJU5YuXkTbC9syesz9/Lh2PZWSy4NlhTfCkZloGkXBENg0ThR6qJoYh1iKu1vVw6Fr\nvPjdOt5bsYnPf9xGoNhLqttO6+qpvDF8AHOWrCI/O5uvXn+ahBhXeBGd0xbQARgz/GZsusZTtw+K\ninE7u4hI55LQ8wzcULZs2SpDhg43m7duy5GjR8+obWxyZW5+9i0q1axDUnIK1WvWpFmLVmRnZpCQ\nEM/ibxYxe85c9h85RqVyCb/R1tIEj2VxoshDxfhoTBGalU/k7tYNuP3jxazZfZgJny3BX+QhVFxM\ni/QkhnVrTdv61blh9ARmvzie6/t2P6O23Tq2o3m9mrRpWJtBl1xoOO3GM2dbpLPqkEUkxmban+40\nbHyspRTl02tQv+PlbF7+DSFLYWgahw/sJSo6iuSyCaSVS0B5iliyfjsdaldmVI+2xES7mLFsI3PX\n72Jo93Y0qFYZMR28MHshY159H3G40VzRjJ/2Ibc+/hLKFYdlj2bKu7MZOf4Z8n0W4595gR59+jH7\ns89p1aYdt905ghuG3EzNug3QouJ55ZERTPxyBScFzGg3NrcD3bChQhY3NqrBy18sYVjPjiz5bgm3\n3nZrlGkaA0Wk7tnU6v+CzRX9YqWOAwwjvgLijEWPT8YftEDTsUJBDF1D12DT+vV0uKA5ZtCH8hSR\nmZ1PzfIJNEwrj2YYHC70sOrwcR78ejlNn5jBx+t2UCO5DOOv7cbtfS+mSb0aPPn59xwL6OixiezK\n9dF77PMcKQqAMxqPMjialUOOx48ynXRo15b+fXqSml6Fe67owNMrN5GYFI8z3oEZZaIZOlZIUSag\n0Sk9mU/nLuTpUcOYO+dTLmzXPsodFXV/SWsLXGYYRsN7R99vZmSeZOfWzVSsXZ9C/+kOI0TIUuiG\nSXR8InOnTebrD6bTpGlzuvfoyUcfvEfPyy8lIyODPXv3UTklCWWFGDLlIz78cdupVNEtM79i8uI1\nrDl4jJplYxk7byUfbvyJpzu34J21O1i66yDHsnIJFHmJQbizQ1PKGhaz7hvMvc+/wfEjh5GQHyLT\nhf+zWWScOEHVtGRchs7kO6+NinE5pkYWmSoxRCTKNI1Jr7421RVUwg/LllK3ReszagsQV64Ch3ds\n4dFh1xEfG8vd947mg3dmclX/fmRmZLD/wAFsuk6sy8Hkuct4cPa3p7SduHAVd85ayOp9x6hZNo6Z\na7bzyDer6V87nZRoN08u+IEjWbn4C73484u5vmVdasY5eHbQZZzMzuHNWZ9iI3RGbTUUh49nUrVC\nGcZff4XbtNn6iUiDs6nV2XXIuu2uik3a2sqmh3NaIUuRUCGNvMzj6JqgacLOrZtp1KgRWEEkFCAz\nM5PVu/ZzUe10LGDKoh95+ovvWTZxJA9c1xuxO8Bm0LReLZrUr4O4Y1DueK6/9hqGD70Njy2KpRt3\nsfvQcbb/tI8GLVqzZ98Bvlu2gl37D7Fm42Zy8vLp1XcAPjFQdjeNmzVj5KDeDHlrLlqME8PlPDVm\nuVH5BJw2nW1btjLoyp588cnHDL/nXrs7Kuqps6nVX9ZWpJYKhbqmd7nGCFmKkKUIhCz8IQtvQQ7u\n2HgMTfAWFXD48CHqpadieYpQfi8HTuSQEh+NZtpYsOsAD3yxlBing3KxUXx17zV8eNcAOjWqRUJS\nMnpiEk1btOCRO26gasPG2JIqklytJo0b1Se+XAUs001MmfLMeP0VGjZqEh5YbzpRNjtadDx3XNWD\nopDFuz8dwh7nxnQbGM7/RMlXpCXxwbc/Uj3RxZU9L6dMQoIzFAzeKSLxJaituF2ulwb072eg21i0\nYB4t216EZbPjDVr4I9vPuuuRTqYN3y/ignYXYdOEqZNfoHPnLrRoWI8ZLz2NhkWFxPAlNa2eRqMq\nyYiuoZk2hnduQZEvgNuw0TAuhuoxbmrEuChrs/Fy19b8cOAYC7ft4+kvl7Fu+358OYX4cgupHe9i\n3MBLGfboi4SK8pGgDwn6ESsY/hsKsHHrdupVqwzBAN2b1KJi2fgylHCeXtf1O8qUKWu2vLAtOXm5\nbF6/ljqtOvyutqauseH7hbRoG9Z297YtLP5mEbcPuYH7br+JSy5sSYWyCQA0qppKkyopp7S95oL6\ndK2dzls/bKZ/rXSqRbuoERuF5Qvw1EXNwi30gxk8OHsxn63cRGFWHr7cQnRPIdPvuprJ733O9q3b\nzqhtYUE+B49lUL1CGWINjfv7XeyIdtrPapR81hyyiDhF00a0GDDUqWuCHunV1w07jTpehqYsHLrG\nvt07qVOrFhLyY/k8fLtmE23rpOO2G9z25hy+WLuTrx8bTrUqlcIpCpuB2Aw6XNCcAb27n8oRZ3kV\nU2bMIq12Q0aOfZgCj5emLVry/sef8tJrU0mplI4/pLC7o5kydRpOl4v7xz2GZbpR9hjuufV6EuLj\neGTuCswYF4bbGW7OZ+XSsnIFVqzfzA19LuWjj2Zx05CbNcuyLhKR6mdLr7+sr824v2LH/prN4QLC\nkxOUpfBmHCQ6oSyN2l+M3aaxbeN6GjSojykhlDfskD1eP19t3kPrp99m7JylfHBHf94d3o9RvdpT\nI60c5ZPKMvb6vriS0tDLpuBMq0avvv3QylQkGJNETEpVHnzgAZwJ5VGmC2Wzhzcj8lc3UTYH4orC\nnlCeGffdwMvLN7Ld68WMcYbTFobOca+XeKVT6PGxffNmxt11Cwvmz6Ndh44WIreWlLbAxZquVRg8\n+HoUoOk6F3XvTW5uDvu3byFk/afpato07DaNA5t+xLTbadSoMd6CHGa8+QbjHhwTXgbS7+GHtRup\nl54CVohbu7ambsUkNCPch+7x+fngx21MuuQCAgUe+lZKoVZUFFYgSL2EGL7sfzG9a1Yiv7CY696d\nx6C35rB37xG82fkMbFoDHcXL0z9AC3jCjiPgw1eYz4aNG5j91SI6Na2H8nshFGT8gIujXHbjkZJ6\neriI2HVdH92lSxddAVmZmfQaOBgxTHatX00g4P+Ntjohvv/yE3r27Y/DJjz/zBPcO+JuYp22sLar\n11KvakWwQlxYpwr9Wjc4pW2MafLkvBU80K4xlQyD+lFR9KyYjBUI4gSmXtqGh9o1JtFm47XvN9J2\n4rt8/cMWvNn5JNksRve7hKEPPQ2+olPaStDH+g0bmP3lfC5oUAuTECoY4IaLmohSqo2I1Dpbep3N\nURZXl6taN5iYmh4ZFgS6JuRlHeOn9T9wYNsGanVox+YN67HrghXwowcDrNy8i22HMpi88Ee2Hs7k\ny0eH4dcMxOEOD5S3GYjdgeaOwTKjyPXD7XePYNnyFQwZOpwR4yYQl1AGi3BPrKEJ3qDi5zHmufm5\nBH0BnpvyKp0ubEX2ySya1a/D8Kt78PbTY6nX6yZQivHdWlPg9XPv/JU0rVyBPYePU6dSMijFieNH\nufq6G9T011+5Axh+FjX7U4hIWbEZfSq172P/WdtQSCGasPerNymfkkqzAY9gUyFefv4ZqlWuDCE/\nBQUFDH1pFh2rV6RmUiL3dW9D2fhYalUqz8/fT7E70FwxaDEJ6PHlUK44Qo5o9h/L4vN5X7N9xw5E\nhAb169H14s5UTktFiUZefgF5+QUEfF6qVUxGWUG+mPcDn8/9mlfvGMiLN/fm1jc+o2/ddG6rUZlQ\nwGL6zl2YJ3TaVq7AomWruKNNB/r0vBxlOKLtpnmPiDxTErPMnA7HvSJiT05JwVJwed8BHCv08+qk\n51jz/bf0f3wapk2xfclc7HaTdpf2xJmcTP0mzfh4+mvkZ2XQ64pe2IJ+inOz+O7bxew7eJgujWuh\n/OFx9aJrEIDs/CLufn8BE7tdQBkEX76XUMBCNMEKKfSQhduw0aVCWepEu7mldhVm7txP11dnU7VM\nLI/37cTk6y/l4sems2zjdiY+OILU1GTeeu8jHp88DYdp460Rg7B8HpS3iIuqpxLjtJcv9gXaAUv+\naW2B/knlymoNGjTAUpBauSpDRj3Muu27+GTiA3S+7UEq1G5C1sE9bFj2NX2GjsSlKTpf3pv3pk7G\neeNNrFuzmtcnTuDw/j1EawEef/kt3hxzKyoQ+IW2KmQx5qNvaFcpmW7J5c6orW7YaBoXQw2Xk8sr\nJrEzv5D75izlhSXr6NGkJnf2uYg5P27mkmuGMvS6/vTq2pHc3Dz63jKC/MJC3n1w2CltzWCAIR2b\nyUvzfrgLOCsBxVmLkA2Ha2iL3oMTnKaOadMxbRqiQsx67G76Dx9Nw2YtMXWNw4cOEAz4UaHwIkBt\nGtTkRF4hry5YxYdjbuSVeSu565UPw6MnYhOZv34Hr81ZjGW6KVIGTdp1YfvOXXy7aj39bxzKhx9+\nxP2jRpJdHCTfF+KzOXOY/tY0PEELT9Di2QmPM/6h+3HGxDFx0svMm7+A8smpKLubhJSK9O50Ie8t\n28jLq7aSkFqWGbdcQXLZeGKiXBAK0Kh+PXbt2MG1N97i1nXbdSJi/oEUfwcDKtRv7Y9NSMS0aaea\ndQ5Dp/6lV3NowzKctvD6u0cOHaJC+TIQDGLXhbSEWFpUS+XTuwYQE+Nm0Guz2XqyGC06jkzLYMz7\nCynUnWixiazfd5xeQ+7mnnFP0apDF5YsX8GyFStJTEpmxY9raNWmHbFlK1A+pSLVatamectWNGvV\nmm9XrkEZLtIqpVOtSjp6VCxXXNSaehXL89n2AxiJMbgSXYxoUYd7WtWhapk49h/NAL+XSzp24NCB\nA6RWrKQDXf5pYUUkWSnVxqbr/BxC3nnTILIzM+h69Y1c88AzRDtsxLlMgvknsQpOcmLHBlLLl+HC\ndh1w2k1mvfsOD40eyR0j72X0IxO4efRjTH9gGFM+mMP36zZDMIAVCHL7tC8YPPVzulRPo1lCLGO/\nXcusbfvx5fkIFAV4beMu1h7Owl/kx1foY8Q3q/l46z6GVK/MxHaN2XY8m+mL15LoD/HKDZcz9/sf\nuWTQ7TTtNoAHnn2ZxtXSWPj0SJxBD6q4AH9+ESGPj1vbNXE6DNvN/7S2AFEu17BaNWuc6rR9762p\nLP7yU8qnVGTIU69Tt1kr4lwmmjcff+4JKDhJ9r6d9B94LRXT0pgw7gEevP8+XnntNYaOHEv/offR\nr+MFeAvyeHn2/FPavrpgFddP/YwVew4zslltZqzbxWOrtpzSdvH+Y7y/ZR/+Ij/+Ij+TftzGE8s3\n0TI2lo8va0uRx8fbyzayc+t+3rmlJ3sPHWHImMdp1/s6qrTvRZzL5I2Rg+lQI/mUtoEiL4Nb1HVp\nmgwUEcfZ0OusRMgiUtl0uurUbtke07Sha4LdpjF/6kQSk5K54KKLcZs2bJpQXFTECxOfwRZJwvfp\n0IquDaoRCgWJjo3jjqsrkxUUtLhyKJuDjGKL43keLGcso8Y8QqXK6fS7ZhDKcFDgC5Jcox5+w0VG\nkQ+XoXPo6HHys7PI84UDratvHk7I78MXVFzQoSOX9ejJVwsX06fHpRAKMuWJB7ln8JUMe+Q5Xl+4\niiZVUli+bR/znr8fze7EZrMRDAZJSatIleo11I6tmy8Bvjgbuv1ZTFf0rXUv7hsX5bCdyrVBuIm3\nYdXXNGzXhWi7QWy0izJly9CtUwdU0I+haTwyoAtBrx9N12hYozKv3DmIxk2bojmceIJHOVEcxO+I\nQlwxJKVF4/H7WbZiBd/+sIaQ6Lw19TUG3DiM2Gg3Nw3dzgtPT2DsI49SqVJlgoEAkyY+xTXXDWbW\nuzNp26QJjWqmQ0EWWnQcsx66jf6PvsqweSt5vltr0mJciKZxZP9RqiWHF2ePjYmmsKiIQTcMiX1m\nwvghwD86pVrXtQG9unay1mzeTk5ODklxZdi2eSPFRYW4ysSRkpqGL2ihidDnpmEc3bmZ5+8azEvT\nZ3F59+4MvrIno+4dQUp8FPfefC3XDr+PJ24bSMv08nzydRbHHRreeDc/HT7BgYxsdmVkM+XilgQK\nvdRyu6miO05NM88s8pJZ4CEYE0SFLO6tU4OK0W78RQEaR8cy9/L2jFu1mW7Pv8eUfp3ZP/EOtmQX\nYjNs1E8rH255+ovwHc/BCgTJyykg4AvQo1Yl84mvll8hIo5/8mkjIpLqcjobNKxbm5zs8CKKx48d\nJWQ7ST1NqFi5yiltW7VtR6uWzZk4bCBtO3Sk14MPsWbx16As/h9v7x0nRZXu/79PVXXu6cmJzAw5\nDhKUqICCipjFVXFXMKc1ou66rmu+q+7qmhMYVsEsZgVBVJSoJMlphmGYPNM5VDq/P6pn1Ht37/f+\nUPe8XvXqmpkOVe/p+pynnvOEC848mVhjLZdu2oBmqdx53oks/GQFjc1tpFsjtIdj1DW08sXOA/z9\n+LG4dJN+Pj+K1+xk2xJL0Ww6BcakZTO7RzdS0kZPGPhdCq9NG8eL2/dz/COvcvv0say/bQ7VaYOW\nWJIBXYopCnqxdYNMQwO2YZKOJWmJxCkO+hncpcjecKDxBOCdn83sl0h5F0JcNXzqzAfP+sODnvo9\n21n9zotUDBvJl68v4PYFb9O9rJQiv5sCv0ZVrzJqd28nVyYh0oDd3oydTjjv4/ZmLeMibH8+TQmT\n73fupr6xiZUrv+HrVat49+OlqP4Q0YxFS1InkjGJpQ2EcCaBjipRavaWvKPYjrMpWKkEJx93NPNu\nuJ45s05FpKMoegJSMTZv2sSGLds5dkwVXXr1gvxyuoycwsVXXMXvrryOZx9/lGf+8eDCSLj9vJ8N\n7f/OtlRzew5c9NJKt2kLvpp/Hz1HT6Zn1TjqN33FV/P/yl9e/ojBPcvpkethTL8e7Fi1jGIrglm3\nFyvSijR0hMuN4s9ByS1ELSyDYMEP3RMAqbpoNwQDR47lo89WUNilB0lTksyWM/VoCpoiUBUn0QTA\npYBbVVj95XKuvOQiVi77lIqSHJRkO3akBTsWRo+Guebh5/li825unT4WKQS3LF7B2mfv5quDEd7/\neiPRZIa7HniYSWOqkpl0Ovc/6bYoLsj77tkH7xrx8IKFDKs6gtyiUj5fsYKTZ19E/7GTiWZMLFvi\n0RT2b17PA9dfzJ/vf4SjJ47n8vPPZmD/vjz1wN3IeBsnzb6II/r04K5zj8eKtWNEouzcX89Nry1l\na30z0yu7cenQvhSqKnrc6cSSiTqZ+apb/Un5U3DiaoX6g+tXWhIzY/J+cxNP793PRaMHMWlQb7xu\nFyW5Aapbo2ypbaS2LcKq6kNsbWgj6Hbx4MwJPLJqS3xLXfOZUspP/1NshRCXnXXS9IcnTpzoWf7N\nOlw+P/2HjWDd2nVcfvc/fsJWj4X52w2X0Luiggf/8Tjz//EAb73xKkveXkT3PD9PPbeAp15+kxUP\n3oDPTGFEosTaY9z77pcsXL+dEWWFzBlcyajC3MNma+kWezMp/rJtO/1KCpg7cTg5Xg8luUGiaZ0N\nNfXUtITZ1dTOZ7sPIBCcOawPg3uV8+DSNW+0xpI/e/H0F7GQPf7gaUMmHOtxawrBnCD+YIixx81k\nyoknU1pU5IihW0UTkEqlCOTkIGMpVI8P6fE6fhNFQfgCqDn5WJ4c7nj4GR57+lkGDhxEcWkZFZV9\neOn1xaj+ECnTJq6bRFI6L/zjr+imxfEX38Cbf/szobwCuvSupLR7L/oPOwKPppDj1jBsCWj4fQGe\nfmkh5552EtFYjMsumI3H7Ue4Aww7KodhI47oOCkORdPE4nGGDB+BlDBx6jQee+Ceab8Es/8f4zhv\nMIRXE1hCIyevgLz8fIIu6N2vPwPvfYIuJUXkuDXi4TYURaGoIA+aI47/vWNh1O344dXcQshxJrya\npnYOHqpzCqULwaNPPMUJJ86gvHsvIhmLSNogplvYWYvcKQyldO77XSo+l2TMpMlcdtXVXPr76/jk\njZcR7iBKyEa4vXgDIZ780+9Z/OnnPP7ucjKGyTPXnEfX7t3JTznNREpKS+narSvFxSXGwdoDo4FV\n/wmwQoiAS9MGTzlqJO8tW0kimaSisJAxY8fTcLCG4ZqCLTXCLc3kl5Wws72Zex5+kjGjRnL+aScy\n9Zijuf9PN0C8lctv/BNuAX85xxHjTGs7zy1dy18/WcWVowfx6IQqSFuYCZOk7jSONdMmdrbAlbSk\nU/laSTAAACAASURBVPfDkiiqQCgKZPXD0i1sw6K+PcGO9ihHBoIMGziYl6sb+Hj7ftKWTWs6Q5cc\nP0MK8+ji93Jenx5sys2hb3Eer23cxYxhfX3b6ltnAP8xQc4J+E+dOXWip7C8G6+89S5HjD6SMUeO\n4/133sabZWsaBqRjeFTJkUeN4+Zb/8Tf7ryV1V9/xbJ3FtEl5OW9997j7scWsOzBefjMFHpbmPXb\nq7nylU/omx/i/dOOIU+qmGmTZEvqsNjGoxk2t4YpcLt5qv9g3og0c98HX5MyLZpTaQIujcGFefTI\n8TOxKI8eHjfDywu5ZukaLjluDHd+sPI4IYT4uUWdfrYgCyGE6nKN6TN8NKoiSLY3U7P1O0K5ueR4\nNPwux0LVsumPiqJgWDaq5tQhVYJ5SHcaNKdGaWvK5u2PPuL1d97l89Xf4QkVYEowsqnV7334EfFE\ngqpjTuCxv9zE7q2b6DtuGgfbkhQMGE3L/h3ULPuUUEExub0H07RrE70qKulWVoptS2yp0aV3PxYu\n/pC7/3QLDz30EHPmzuXyC39HSU4xwuusTqO5efP11zj5lFOZcMwUkoZNZd++CCH8QohuUsqDP5fd\n/4mvokwM5he5qtd9QZ/x0zj6t1fz2RN3UvfdCs66+hZyPRpBj4bfrVK77yA9und3XtcpwjlgO+KY\nVD14PUFszc9FV89j6dKl9OpdkeVi06//APIKi4mldRIGNLZFWfjMo0yaNQdfTsgp/GJZeD0uPKrz\nf/UKkwKfmzmXXc2nH33I3595gRsvvQChqAiXH8WvI7x+Tpt5AqdMnYDMpFF8AZRAiBOOHczX22pA\n8yCAcRMn8frCl8fyHxJkYHRF9/JYwOcpHNC3gpr6VubMmUNryiSSsWloC/PFu2/y4sN/5YlXFzPr\n7FlEWxo479QTOW3mDO684XLq9+3g4nm3Yxs6T11zHiIZJdrSxsVPvkV1UzuvnHI03YRKpj3N89v2\nMjYnj67CjbQlHzU1UqZ6GOoPOkLhUrCkxO3RUBWQUhLPmPhswccH6nnkQDVdVTcHzAxTfHlcUN6N\nsm5BNK+G6nYUxs5eJ6pb5biiYr6NR0gZJuP6dVc9y9cf/x/iihBCeNyuoyaMqgJ/iP37q/nks89p\nS1sseOsj2hJpqjev5+n/up2jjzuea+bdTNVtt3HXH27k+w3f8elrLxASOvc++BBPLVrMCzfNpXfI\njd7ezoIla7jvk1X8YdwwphUXYiRNltccJJrSmRTIQ9qSHZEYWxNxTs4v7qyPbkqJJ8sWIJYx8FpQ\n0xrjpp078CBotQx61nqZW9aN2RUD/i1brbgEb64Hr6ZRnp+DoigeoCdQ/XO4/SxBFkJ0AYpdHp/M\nL3F8gp8vepZjzjzfidXMVndzqSIrxoKS0lIO1TfQuySPL77bxgOPPc0rD99DbiBEdWMb08+9mKaW\nVt5fshxvbiHXXHYhPfoNZsZvLwXgu02bSSUTtGQEe7dvYeCU0zi4Zwf14TSevmNRU5KmdSsZNvtm\nqpvjLHv+Sao3fM2pl93AWXOvwLBtnrh9HsOqRvDUK2+xb+c2XlnwDMNHjeXCiy7k2isvpzAnB1vC\nSwtf4w9/viNboxUUoTBwyNDEd2vXjBNCrAOqf60yh0KIIJDv9vknnnj5H0WXQUewbeVSNn76Jolw\nK1c/9ipeTSHo0chxOxNeLNxOYVERCAVL1fjNHY/xmyljOW3yUQiPj6vufJTyrt0IFpZS39DI3Mt/\nz/ZtW7n30WcQAjauW82CJx6hsT1KWvNR09DIju83ohR9RjwaYdAxM1j0x7n0GDyKEy64gvKyEt58\n8DaCXjd33f93Hn56ATMmT2Dx4ndZ9uFiPJ6g08NM86J6/SjxCHYq4ZSa9AawNRe7du/hhJmnADB+\n4qTQ4rfeGC+EWAzU/VqV9rKJEhXAmIkjBmtImxGDBvDOx493fm/37djM2ccfw8hxk3j85TepGjqU\nZHsL5506gznnn4dMxzn9vAtY891mLjt1Kjmawtx7n+KfF5/K7MfeQLMlwrZJtSdICTfJSJqtzWHi\n4QzYkkN6mi3pBKWai1tLehNyu5jfdBBdwE0D+yJUwWdNzby8/wA39q7g0doaLg+W836yjQu95Wwy\n48zZ9z1H1YUYFsyh0OUm5NLo6vWS63HhDrjx5nuJpHVCXg/DK7uR1o0KIUQZYP6aNS6EEOVAgVvT\n1O7lxdieHKS0aWw4hL+wHFWYXDhjElJK5l55HbPOnU1AU7jtxt+zf88u7rzpas6YPZdIJExZXg6v\n/fFiLnvoRe45/Rg27K5lwdebqCrOo645QtoVJBPNsL0pzKFUikY1wYFMih2ZJHHbYoDmpa8/yLfJ\nKC80H+KhYUPIUzUy2FyxbgPnlHfh5ZpapnhyqTYyDFOC+FSF22v30rPhIEcGcyn3eAlpGsUeN+Ve\nD56gB2++F8OvkdAN8vJyKM4L2TWNLeOy4YWHrQuHLchCiNuAeUCqoGsvQzdtFNtg13erufDOh1EV\nQSad4ovly5l5ymkIobLx2/WYpskbby9m3tWXU9l/EBPGj8NfVIbl9tGqtxONJ/jT7XfQvbIfbSmT\nI46eRixj8eCt15NJJTENgxHHziRv8FHMvO0porYH93Cdxkga27SxCyspHH0SDTEIG0mGX3wP/rcf\n5aMXniSvrDuTps+g+6DhdBs4nPaUSdc+A8kYFrPnXkxdQwNDR4ziuOOOxaVpeP1+xh89mbQNtgRF\nwJDhIwLfrV1zF9AN+EgIMeuXFmUhxBHAMsBnZNKipHIAmqaSX9qFwZOOZ8C4qfgCAXavW4lr0CC6\n5fRCFYJHH3qQpoZ6JybYG2Li2DFUjTwCtbAcXG6uuuRChD+XmbNm89aHn9CW1AmWduVQzFnnKe5f\nxc3/WEDEsInEMzS0RWltbGTZi49S1K8K/5Ap5A0cx/6dG7n33Kn0HH4UU886n15dy2mK65SUduX+\nR5/gofvuZtDIozh/9mxcqqC2upqn7/8LiqKx71ALkXicUaO6IlU3u/fs4crKPihCUNlvgAAmAFuB\ncLbM4aFfmK0L+AYYBNR2K8rPxdAZOWQAm7//Hts0UIVCIBDgyUWLOXL8RFyKYP4j9/Pic89w6UUX\nctPlc7jsqmtYv/F7PrjveoYWB2g41EBIT3HiX19iRGkh11f157WNu8lPQzqdZmV9E9sTCWpFiqGu\nAH1VL0cEAqzVY9zfVMPd3fpwTG4BdrbmtMunMaFrMT5F4bOGZk4IFtBb8dFT8ZEr3RyvFTNcDbIo\n00RLxMDCaT7bYOlM8eVxfe8KNK/GoUSKLrlBGuJJ3G6Xmc7oewBLCHGllPLlX5Jtlu8fgVuATGFu\nUArTQHHbjKwazoZvv2XS9JPAsrjs+luYPvNUfG4X+7Zu4sqLfktOMMCX773O6i+Xs2HrDu6+8Awu\nPno4VjzGvOlH8tY3W1i7v45/njiBb/c3UGprpNvT1LbH+K49zN5MipQ7SC+XhwG+AiLS4paGfczv\nMZD+/gCnlZaT6/Pg8mm4VYWLK3ujZSxSlsUUfz4fm2EK0OghfFQFcliQOsTySDtBRSEhbeotnXxF\n5cHKAXT3akRSaYoCPnxBHxnT9OGUPO0OLBVCnHY4unBYgpy1jK8F+gMfS2kP1k0bTUqmnnsxvkAO\nANU7tvLyEw8xZvQYcip60aNXb2aechqPPPIIAwcO5ITjpnDjvJs5UHeIR598jIWvvsrtd93LiWf8\nhrhuE9Mthk8+gQNNrVTX1YPbh43AKOhFdUuSeNqBkkkZGBkTU7exLBf+iklE21KkPDopv5vep15N\n/xPOw1cQYtuuvZT0ryLUs58TmaGrDBp5FEOGDOaIESO48prrOP3EafTqXcGCf76MLRSsH+W0m5bt\nF0KUSSmLgW+BKTji+UuOB4AbAFVK+bSdXUTr0n8oXfoPdYLnFcGShc/RPuEYhlz1e4SAqdOO56H7\n78NSXKi+EFdffinCtpBCwXb7yOsK5865hFnnnEvX3n0JpE3cZb1pSxlkTBsjW/M3mTFoCcc5UN9M\nj0mnkj/yRHTdoqHdJHf0WeSOPgtVmLR9+wFmfk/swjLqYmksKTlyygm8N+1E9mz/njcX/pM3X1vE\nOWfPcmqMSJun3/qYtnCY+UeNJ2nY7N27l74DBmBLSVFpGXomUwKMAs4A/gL80uFac4E2oAfQsGHH\nHqSpEwoG6dGtK1u3bKLP0CN4/41F7N+/jwkTJ+HVBN9v3EC/vn257fqreO/tN1i+cg1rnr6DIpki\n2dTMq8vX87cla7hi1EDOrexOOpzm1PwSItEUj+/bz9pYhKtCXRig+elo7agK6O/ycW3bPgAG5YZw\nB7OZjS6VECoTy4pZtO8AJ2n5qJbCJC2flGWTsmxycFOl5DDRlUdAUdlvp3gr1cjaTIwt7RGOLPJR\nE00wcmAvdjdHEOAC3gPuA5YIIV79JRdQhRClwI04k93i5nD0CJlNQR49Yjjr1q5h6okz2bvje154\n/O8cMXIk/fpU0nToAO1tbSx/93XS4WYuufkOFtxyMTMGdkVvbeObLXt54P2VlPm9/HP6eFxJk3He\nXDLxDB/WHuKpxlpm+gu5vqBr54KzKpy+jt+ko1TraY4sKOSkoiBuv6tzcW9SeTFv7qxhgNuPIaFK\nzelkq9qCIUoO5aqbXpoPtyJ4JH4AVQgWNRxiXlmI/ZE4FUW52KpGU3tUEUJ0zerCWmAah+GvP1wL\nORdoklLWCyG+6jl83PCMaaO6XUyf83t03cSjKvSvGsUjr35AWaFTLDq3oIB7H/g7M08+mT/dchMX\nX3IJoVCIaCTKrHPO4eMV35BbXEo4bdKWMqiuO8T9113MefctoP+xZ9Ia14mnTdp0i3RrEiNjYmRM\n0okMiZZ62jYtJXloB9IyKZl0CYHy3piGjZQSvz8Xt+Wh5vtv+OyJvzB+5tmccuHVFOfnMm7G6eT7\nXOiWpEvP3ixfvZ68UC4IQcZykkwkEkvCyLET+eDtN/ZF2tuSQojNQNFhMvzfRjGwHlDdvoDx/HXn\nus+87RGKuvb8yZOu/OtTlOeHOn++7Krf88qLC1i9YTPjRlaB6kZKm4xp8cyLi7jvrw9w9fU3cu6F\nl5E0nAkvaVikDJuYbrJn1y5Wv7uIbV9+zJCZF1Ay7jT8g7sQDadIJwwyKQMzG2jv8WnkjTyNQykX\ny265lGPOPJ8px03DlpJ8n4se/Qdz6z33c87s3zLrtJn84YZrKMsLcPet8zANA+n28cVXaxk+vAqP\n10fGlOQVlaJpmmma5k6cye7cX4FtEbBeStkqhKjfVX2wu9TTKLbJ+NEj+WblSgYMH8mNt9xKLJXG\npcD3G9azZdNGNq7+mlhLA1f/6W5ev+tailWL1rpmzvrbIrAsXj75aHp53aTaUmQiGXY3hfnj7p30\nc/l4ML8CFwqpHzXaFUjapUlAUVHdiuOb9DqCobpVZNZn2a4bFHg0sMi2OfrhsYpckoYkIyyKFQ+X\n+rqxygqzIRnjSMqojiX4TWkhO1sidCspkrtrD62QUm74lVLVc4A2KeVBIcSX0pYjd+/ZR79hIcaP\nruIvDz6GpghGjRrNqx8uJScQRJEWd99xO/+c/wzdi3KZe8VtnHHMkZw0tDd6awsPvLOC+V9v4pax\nw5jepZh0OEM6kiEWTnH/3j3sSiW5NbcH3VUvui0Bh29HAEXUtsj1uP4t29aMTr7qLC7/lK2kNwFU\nC9psC7cimO0tJy0sFqachiEH4kkqSwqojyTJDfoQilrd2h5JCiE2cZi6cLiCnAY6AqE9voISdNNC\nVQRfvf4cmWiYc6+9FcOy8fv8GJZzglIKLCkZN+kYVqxaS0NDI7FYjNKu3UF1kTJtmhMG7SmD775d\nx9N3zKPH0DHUN7WS1nKIJA02vP4YlmnTZfIFGBmL+q9eJVqzhdDgk8jEInh6jMFKRsjoJpmd6/Hk\nhJB9h2CZNpaUFPcfy6wHXuPbVx/lvy47m9tffB+XquDRbLyaRDHBE8hFl4CUGLbMtu5x3Bb5RcX8\n6Ny9WRa/9Ojgm5NX3iM1cPLJ7heuP5fZ9/+T4u69MbOxyC6vHwuBbZOdNOD6G+dx+ZVXccN11xEK\n5bBz5y6emz+fPv36s+i9j+ha0Y/2jEUkbdISjrFn7x5CPfpy4GA98687D8XtZeQVD6IW9aK++gDb\nX/ozxRPnInIqyMTbyDTuxlXQA29uCVa2qWnZ0efw6r3z8AdzOGrsWCzpFOESXkG/wUM54YQTWfTW\nYq67ZA6uYB4uQKpu/vnq65x25lmYtkS3bHRL4g/mZKLh9sJfmW1Bdj/Q0BahpqaWipx8jh47mtc/\nXMqlV1+Lx6UiVCdN/dknHuWGG24g1+/m3ofmM23sEYzuXYbeUMvvHnuTirwgt48dhhlPkWpPk4lk\n2NMU5qodWzk/WMIxnjwipsVfYzVM9uQz3BVEFfBSsoFW22CEN4jqVmmUBkFUuri9KKogmzuFJbOd\nNCAbzinRbWez5E+byvpUQZ5w0ag77vcDsSR9ygv57NuddCktZHftoaAQQgP4FcILf6wL3uGV3Xn3\nsy+5afBgjhoxlO+3bSOdiKO5/eSHnLvozz78kLLSUo6fPJEdG9ewdOVatjx3J3a8lRc/W8er67bx\n9hlTybMl6XCGTCRDMpLmxp3b8dpwX14vLFvwcrwRS8IZvmJUAV9mInyTiRC1TfqEgpguwYFMkqH5\nBT9ha0vZEXDxf2PrdtFkOunetYkUfSq6UNMWo2tJMXXNbT9bFw43Uy/Dj8DbqpuUbqGbNgMnTGfV\nB6/T1tqMYUvSpk3asjFtHHGzwbSddi15RSWU9qhARyOasWiK6zz1j7/xxsKXeOSWqxh56hxampv5\nYuHTtMV1Igkdf7eh+LsOJRGOc3D5yzSveQtXXg8IlOCtnEymrY7kvq/Rk3Ey4UYOvvsX9iy6nWQs\nSTKWoTmWIe3OY9IVd/GbO59GtyFtWhiWTdq00C2JbkkyprOZ2WM2LEnatIjGk0TD7R2567+WaHTw\n9SpuLwOnnc1ptz+Nv6gL1ZvX0d7UgG7aDlvTIm05k41lw1nnnMfVv7+GJZ99xksvL6S2voGnXniZ\nZxa+xe59Ndx9+5+pi2ZoiGd49/WXefaOeSxb/CYJ4WfyrQvodvRZ2KFuJKJpDNtPTv9jsdQCkq2H\niOxZTduXj9G26gUSzQdItEXZ8dr9xJM6VRfcxgt/uoIDDS1E0gZJw3LYScmMmafw+ptvY6vubA0M\nH9v317L888857azfOMxtScq0iIbbAzj+eW+Ww6/FFsA7tao/H321BjuT4rjxo/nq61VOkffsQrSQ\nkhXLl3HWGaeDpbNo8YdcdupxyEyaF5etJ5xI8ZdJI2gPx/jTlxupbo1hpAxu27sLlxCE0EhZzv9m\nkBagXHHT4QA70h3CBob6gghF8PyBAzy/p7rzQBfurmHR/lp8qkLatvlR2CyWBEOCjfOYtiVR0yZl\nSTSpOEkPEsJpnfL8HGpbIrRF4iqOi+0/wnZERVc++moddiZFwK0xZuQRfLF8WSdbVQiWL13CmVm2\nr737EedOn0RQhbrGNu54/yuenDGBAiF49rtdfLDvIGba5JWDB6nT0+QLDcsWpG1Jpeqnj+rrZDvU\nFaCXy8tgbxBNVVja0szdm7ZhZuuSbG4Nc9fm7U6pBfl/Z6vYgpS0QQgOJlL0KMylri1GcUEu7ZFo\nn45zP1y+hyvIFj9Y18K0nIpNKd3EV1hOeZ+BvDf/UTKmTca0SRoWSd25QI3sptuO8M1/+gkWvfwi\n7SmDPQdqWbfyC1LCw6yH3iE0fCq9Tr6C4snnE4llSMUz+LoNRy3sy54XryNxaBclJ96Or9+xGIkI\nmVgb5PZGq5iCHg9DTjmBfseROLiFZHsUPWXSsOkbVj3/VxIZE1uovPf0g9jSmSwyplM9zbA7RNlm\nyUcfEk0kOs8lres/5qAC9v+g8/NHB18hJWRMm1C3PphSsGX5+7z8hwtpbW0jbTruhqRhkTEdrqYN\ns847nyeee56Lr7waw5b0HjiMSMYiZkpSUlAXTbN67bfs2rGD5vqDbP5yCY3tCTK+QorHnEImaZKK\n6yTjJp6e48jEwyQbd2PbAqVkMGa0kfCq+aSizaD4sW033t4jmXzzE7z+0J3s2LY1Owk7QjRl2jQM\nw+CFRa8jXV72H2ri9Fm/4YK5F3KoobFzAkwanSjd/wG2AGJaVT8+WrkeTAMsk+5dy1m+bGln26C2\n5ia8Hg/FRYVEwmEONbUwom9PkokEd72zgjOGVCJMG9uwHQvLsNkRi2HZkrsLezHUFUC3JYaE8a48\nAmidUTtVniD1ls6gYA5CFVzVp4LL+1c6DVAtSY6mEdI0TNvp4v1Juo31ZuR/PbmoaQOSjLRZ3tpM\nScCLy+vmUGu4oyZ53n+Kbf/yIjbu3u9k6VkGvXt05e233+pkqwrYv28vgwcOREibdRu/Z2LVQKRp\nMO+VT6gsDFGRE8DSLSdKy3JCzz4Jt3JdfjfO8pd0WrMVio8+qr+TbanmxqUIBvgDCFVwYlkp948a\njirBtiR+RSWkadi2REWwzUjwnt7E/7YOFzVtOv76VVsr9fEk3YrzqWuLUJj3kx5+h833cAW5AGjN\n7qczmYwjZqZNa1MjkZYmXF6/I8Q/2lKGTVI3aGlrdy5CywZFw0SlKRLjrstm02vEUZRUHcOhiE5d\na5KE5Seja8QjaZIxnVhjPaapUjDuQvInXIot3BiJCEYqjqWnsE0dKdwYyShmKo67+2hyhswkE2lD\nz5hIxQseP7ppYysany18hng0krWQf5g8UqbFwUOHeOz+e1i3ejXp7N9dgRDB3Lyd2XNv44fb319y\nFGb5pg09jZ6dDHTTRtczKJqLl266gLqDdSQNJ4EjrptkLJuG5hbSpiRtSmyhguIirlu0pQx6VI2l\nasY57G2KsWnLNtJaiNHXPU7FebfTnrBIxjKdvuJMykRPJsnE24lufJP03i+xbFBLh6NWHIutBTET\nYUIjzkIJdUXPmIicElrqqgm3tWFYNqZl0dzYiEThyWef4+577mXGKaczftLRXHrFVdQePMhLz89H\nt2R2UrHIySuIA/v/A2wB0kf16cbXW3aSikVZ/MlSorEYS5cscaxjAbFohNw8x91aU3uQovzczkSa\neFqnojAXgJDbxR+HD6Tc5yWmmxS6XPRw+zpdDT/4J+m8HQ7bJoaUlGbbBOWpLgIoWIaNmTaZXlLC\n9KJiWgyDPFS8QsEn1OxtNCSxkPxPATGlpN02WXiglpKgD6Eo1LdFGHfEUBMnvTcGeH+Fuiw/YWtZ\nJuMG9+GzlWtpbWnm69XrWLJkKQogBChCEImEycvPw7IsGppbKC1weIYTacpzgp1vfF5lT6aWFCMt\nSdwyqXD5CCrqv2ULsNdI0zdbHVGVgjKXu5NtD7eXK3v3plU3yBf/k62Ojf4vNNXMujie219DfSxF\nWV6Q+vYoXcuKycsN7c0+7bC/u4frQy4GmrP74XQsim7aaIrAl1PA7AdfIS8vjy/fe43e/QYxpGoE\nsWw95MXPP8Har1bwzKvvYEuYcc4FRDImT91/F4XdejH8lDkcaE3RFkmTjGbQMyaRfZuI7v2W9KGt\nGNFGio65GjW/B2YqgRFtIt2wFSW/0hHjH5VK1OPtqB4fvspJ4MnHNAwC5QMoGViFLUFzexBC4Z8P\n3M619z2CYUtUSwI2ihTkFpXyj4WL8eXkkTEtDEvS3t6OqmodZkozv86iXlH2vV16Iq7oWV+tpQjG\nzf0Dqqqya/k7hGNJWhM6Hk0hkjZpa6hj3oXncuf9f2fUkWMZWDWa3kNG0p4yiGRMDrW089ClZ1I1\n589olePJ63YkacPCbkliS0m6rYlo9WaClRMx0gZ6KkZs2ydkDm3GM/Qcsgl7CEVFLRuOkWjD1FOY\nehDLsNDxECgoo6XhILaEjxe/yWvzn2DxJ8voN3AwX3y9irWrV9N/4CC69OjFjDN/g4lGyrSyd1I2\n6VTCDbT/ymxrsvvttqnnD+rRhW82bOGiM2ZQ2ac/193x184LE2RnZbx7Hnqc+qZW0Fz4/H6G9ihD\nqiqq20keUHULoQq6+X3UZNJI5YfFJQGsMSIMVgPkqs5l920mRq6qIYRwUncN5/Uyqyi2ZZPOGMQs\nkzxFY6o3n6hpEzEshJB8TCPDyaUPP224EsNiqC+H4ZUlrIxFkELQGk2QyugW0C6ltIUQrTgCWv8L\ns+3QhfZwLM7UqgEsW/Mds04/ma/fXcSI6aeze+cOevXtj4WT/CKE4PEFL3PgUCPtiTSiJMiMkQPY\nsLPmf7AVqqCrx0uNnaGP8ACOj3enkUBDUOnyARCxTWrNDGUuz79laxkWzXqGfmqQvoqfUuElYlgY\n0mad1Y4FTOKn3dsSwqRAdfHUhFGcuPQrivNyaA7HqSgux6W5otmnHfZ393At5CKgI7C8Id7aaPzY\nihNuxwJ1+UM8Oe8i1nyxnJZonEjaYMKMM5h9+XWdlmiHK8DlDzL9sj8QTZm0xXVSiQyNG78g1p4i\nXl+NZRr4B0zHVTaQ2L7VGIkoZjpOumEbmdr1WHrqXx6obejYhk7jR3eROLgDaf/UovAGcpgwcxa2\nLbEsm727d2BYP7hW3MHcTus4bdm0NDZgWWZHll4LzuT0i41sYHkRjqXRkI62aZYtfyjkrbixhEbl\n1LPAn8/bf7uN7du205LUUfNKuPj6P9JnyAhSpuO/j+smMd0kmjZ58/EHKB00ClHan3g4TaQ1SbQl\nRaQ1SawtReuOdbRu/JRkNEYm3oYRayO1byVqTjnC9dNiVlJK4muexYy3Im2wTMdf7C8oIdragiUl\n46cez02334PH48WyIRyJMuGYyXTt2QvDlrh8AYTL3enWisTiWKapANFfg212FPOj7+6h5jBHD+3D\n5+s2g2UwaUwVTc3NHDxQDVLS2tpCW2srCIV511xJUUEe22sbEL4Av506midXbUb1e1C9bkc4TDDC\nrgAAIABJREFU3Cpdc/zkahp77AxuxVkQymCz2ohQb+uddVa2GQnCltkpGJZuYaZNzLSR3Uzakxly\nFLVzYclZXFIIaRrHqoX0xBEgHZs4zhrdQTvNoNwc4tKiPDdI1DAIeD0cbGzRgcbsuf8afH/CtrY5\nrE8aXMGK9Vuc0MKA05R1yScfowjB/n17CeXm0traxtlnnMa0o8ex6vvdCF+As44eyac7qmkwzZ+w\nVd0qR+bmsS4d6+ShCthsxfneSnSy3WEkSds2Ud34t2wt3SJsmOQq2k/Y+lSFsVouw3AimCSSdpxS\nn/UyQ/9AANwKQY+LgN9LSzSWXfi3634u219CkPdFDu6JdQhGprP6v03lkVOYOvd6nrrpYt5+7jGi\nGRM1p4DKEWOIZxw3RtqyiSYSTD3vMrRQkSPSGZOmb5dSv+xpwluXoBYNwN1jHPhL8PU/AXfP8Y5g\npOKohX3xDf8NiuZ26icDMtWG1fR958FK20INFmJEGhA/qtWsKoJ5z79Pv6rRAGxet4q7f38RtQf2\nY1i2s2U7c3Q81u7bnY5Hwpuzb93CL2/F5QKpbJZavZVJasl4vLOrwo87LBio1G79jufmXUBrUqc9\nbTJw/FTitkI0YxLXzU53UX19PRuWLqbipEtIxTOEa/dz6POXibe1kAy3kgy3opUNJ2/CFeiJMEYi\nipSSnNFz8PY//ge2toVVvwHMFELzYenJzn6JAKrLjWk4ohMI5jBm/KTOMKJrr76Sp598MhtV4SyY\npk2rc7Kr2b8Pl8d7KBtQ/2uwhZ9+d/fvq29lbL8erPl+F5gGmpAcd8xElnz6CSu/+Jxbrr8W27ao\nrTvEyFGjOfWEabyx7BsUb4Dzp0+gLZnm/b11uPxeNK/LKcbvUSlwu3k32ozmUnErgnxV44ZADwa7\nA50xslfmdEEAh9IppCWxDZtP6hpY1dSGpdtYuoU0JaZ0al+7FYFXEQQ1hVyXwnBPkG4eFyFNYTMR\n1tJOqVdhj5XiyPIi9iYSDOhSTDStk5fjZ9f+AzawL3vuvwbfn7DdeqAxPrhLIS3hGC3NLQjbZPrk\nSXz66SeoAq698jKQkg2bNlNcVs4Vc3/Lm5+tBLePsrJSLp06mjuWrUPzeTrZal6NXJeLJbE2pOYw\ncQnBLG8Jp3qLOtmO84aY5MtlYzLWyXZ3W5SXq2s72dqGjQLY/4JthdtHf4+XkKbQLnSW0YzPY7Pd\nSjC2uJD9qST9SwoQqkIknqIlHDHa2sMbfy7bwxXkfCCe3d8Rr9+v/lgoOvZ102LQlFOYeuENjDhx\nFtG0SSRtEEmbTpU23SSeMXnw2otY9/kntDbUkcyYGIZF0+q38XYZihGpx0zH0RMR9EQEIxnDSEax\nMiksPYW0LYRQUDQ3iuZGdXuR6Qgy1YaWLXLfISa2mUEooGoKbk3BSsVor6vGle020H/EGK65+2GK\nuvTAzoa8OXUenFoaGdNm77bNMWBH9tzjWRa/5MgD4tlCJZaieQ6011V3lt3s2HTTxrAkE657CHcw\nj7eeeJDmhE5TQqclqTtuirRJJG2SMmxSpuTEW5/AcOegZyySLfWkW/aTibSSibR0bkYigpGIdN5x\naMEiyIQRVhqXP4SqqpAJo2AijSSqN4SVSWKmnIp9I0+bw+Sz53aejMThZ9lwx30PcO4FF2YXH50F\nyI47pIxpU7NnF5Zpdkx2cSD/V+h0kccP393tm2rqYwO7FLKjpg5pWyBtTjn+WN588y2mTJ7Mk8/M\nZ9z4CaxavQY0N5fO/S3Pvv4BSVTcwRDPXnU2t3+wkn2pFFrAizvoAo+CX1NZE4+gq7IzZMqvKp0C\nogpwKQrH+vJ4LdzUKRLVqSR7Y3Fsy0ZakjxVJaiqfJBpR3M5YpHvUsh3qRS4VXJdKrkuhcnufE5w\nF7JHJBjmC1JSEGBdYxtH9elOzJTkBPw0trT5gd0/5vsLs/2xLmzf1dCqCduif49ytu+tBmlz7ISj\n2Lx5C82N9fz94Uc4/4I5rF7jsB171JH4fF4+/nYbii/AzWdPoz6W5OXt+1H9ns6kmbQiCakqa434\nT9h6VaWTLcAJvnzei7YQSxtYusWBVIrdsTiWaXW6Lvr4/LyTaMHQ+LdsB7h8nO4uodSlscVIMq1X\nF9a1RBhT0RXh8RJJpthbczAmpfzZunC4grwCmJm9WHYZqbgnEW3/l6KhmxYjZs5G+PN56KpzWfnp\nB0Sy1ls0Y/L9xu84sHsbweKuvHH7pTTu/h5L10m31pJ/1O/wVUzCMnVsU8fSU5hpZ/GuQzA6BFdx\nuVHdPlS3D2/3I/APPgXV7UPz+BCKINO4AzPeipItzakpgqZ9O/hw/j+c45USVVWpHFqFzC4Q2B1R\nIZaNLcG0bPZv2xjASdoAODnL4pccB3BCZo4AsEx9Y+uejfZ/Z9vB15VbwsTr/4EWKqYpmqY1qWet\nZYP2tEFct4ikMiz4w8Xs+uYzLNPGNm08ZUPIO+oCbNsisWs54a+fIrL2JZI16zEyScxE6w98bYvU\npkVYLdvRvAF8Q8/EU9gLf9+paP5cWlf9k4NLnY7zkYZaUtEwQGcoXoeFXNF/AL5gDnrWJZTO+uU7\nIly2rFoRN/VMh5UxE1jxK9QKWZF9b4CNn2/fb5TneGmLJcikM2CbzJgykT179rJr+1ZGjTyC4uJi\nWlsdw6//gIFMPHIUTy1eiuIPMWJwfwZ0LWb2K5+ied2oLg2v28UDw4dSFQzxTSqKS/3B3eDNPnaM\nMwJFrEpGqEunsC3JnJKuzCotd9irgq9jETQhWJFo5/yG7TyaamC7kqbAp5HvUghpCrkulXK3m75e\nL5/rYc7u3pVqdKQQDOvTlYZYGp/Hjdul1Ukp00KIEDAe+PpXYHtStlbIvng6ozW2tNGrtJDqugaw\nTXxujbPPOI3nnnmaIYMH071bN9qytZLRPNx81aXcM/918AbxhvK5+dSjuXPJalY3tqK6nL6XF/Tu\nyZwu3VkWb/9f2Va6fAxx+3mvvQnbkkzIyePW3n0QwvFFW0KyJRnDUmBuww5ujx1ghR3F51V+wjbP\nrTHCF2CtHWVKYSGlJUGWVNcxY9RAcHlobAuzaftuDz/owkzg88MBeLiCvBZI4bQzugnbEq071v/k\nCf9dONKmzbjZ17D4yQf429Xns23LFtrCER658SJOu+Z28rpVMu5388jp3g+havS/7MVON0SnhWsZ\nGDUrsRLNnZ8jTZ3M3uVIPYHicqP5gp2byxdE8wZRPX4KJ1xG4ejTEUJ0dt1QFQE/ut47QmYs6VjG\nHULi+Icknyx8lkwq5QH+JIQ4CTgGePUwGf7LIaW0gfnAn4UQJ2FbxzZ9tzz5v7GV3lzKxs5k08rP\neffpv9Maz9CWtZDDaYOv3nsDy7LoM3UWlulk2olsGU2pJ7DiTbi6jUIqLoxwHUbTDlI7nDrx6QNr\nUTwBcsdegow3kFz3HKn1z+EKFpAz5ERUzU3usJMoPvJ0ALYufYstXy/HkvJHlrBzrKb1w+8MK7vZ\njmvIkpLtq1cowO+EEFOB64Fnf0m22TE/+xlTgBv2NofzTMumvCCX2vpGhJR4NJUrL7qAG264geb6\nOjZ89y19KyudVwuF22+6hr8teI2IKRG+AE9eOYukYVKX0R1/p8uptXtsURGfJ8KobpV6O8MbqabO\nW2q3Ithjpvgw2UZfl4+9WQOjo06vojqZe+NKC7m+spJnh1exYFgVQwtyeSHawF2RA9geQYFbJaQp\nFLoUPjZa6ebzMq53Ga/sq2X2mMG4Az421tSjqKpMpTNlQoi5wG3A51LKhl8SrJTyW5wIg2uAGy1b\nqsu27KF7cX4nW2FbXH3JBTz33HzWrvqab9etpU9FRSfb0046HqEovP3NRoQvwCkTj2BMRVe2t8d+\nwnZCYQFb0wniqhMS+Gaqifof+ewNJAtiDVS6fOz5N2y9fjdXV1Rw38CBLB45mlnduvG9neKq5j1U\nK3on2yK3SpPI8HkmwsWD+7AqEsXvcXPkwF7saY4SCviJJZJe4FYhxAk4adMLD4fhYQly1mq5HDgB\nOBF4oH3XtwY4YmH+DyvZJqVb5PcexPmPvEW/8dNpbm7i3QWPM2jCcfQ+6ljSpk3xoDFIoSKEIFW/\nHWkZjuXbIcxCQVo6WMaPhFoijSTS0lE1N5rbh8sbxOV1xFjJhhQZkXoi21cipeTQd1+w5O83kVPc\nlaba6s4sPPjhsSM7r2NYtuTbzz7CG8hZAviBPwKXSSljh8Pw/zEex1l8eQC4PtFQrUn7hzbpPz6m\nDsbxtImrtJI9337DU9f/jnfnP8Ezf/o9u7ZuZcmChxh/4R9Rcwo74yxVzXHzaIECgsNOR83vjRoo\nRHH7nDS7jkkwE8POxHAX9CR/3MWUnPoAhdP/jMsfQtFcSNtC8Zeghbpg6haK28sXb7zAprWrnMgU\n23YSa7Lbf3dVpLM1NNpaWkjHYxrwIPAoTv+3n92B4b8PKeUu4J7s52zJ9Xp2frOzhu7FBdTWNzqt\nxaTNNZf8juFDBjG8qoqcYJApx0zqfI+ykhJ8Pi+3PvkKijdA3949uXDySF78bqdjJWcXnyaVFHFA\nT/FVOoqhQQYbn8u5xfZqCkls6myd3UaK4TkhVLeCUDoEQ0F1qQS8bo4sLcIVcNG9OEREsZlaXkLv\nUJAbmvZSrepENJOn0vXskmnuOWIoBzSTVXXNXHLcGNRgDh+u+Z5k2kgDN+MYUb2AW39pttlxJXAs\ncLKE//pyW7XevaSA2obmTrb9enXnyYcf5IILfsdjjz7ClZf/0I5OUTUqe/Xghr89i/D4UX1B7j//\nBF5avw06Ii7cKjk+N5PzCng6fAjpUchgg0onWxRJWFp8lmpnbE7ev2SrulRGlRSSl+sjN9+PN+BC\n1RSuq6zg3pYaPrMi4IHPrHYeitVx17BBdO+ez9/WbeWWkyag5YT4cP02Knp0Iy83tAQnau3PwBVS\nyv89YPzfjMPuqSelXCmlPEFKORF4pWnjCkPaVuffLVuSTiap3riqUzRSukXaUug9cSZFA0cT6lpJ\nz5FHk9LNTv9zx2he9RpG615Ut9fxDXscd4Snz3Foed07BVloHjz9TkC4Q3R8vlBUkBZCc3LUbdPA\nlpJEzQYsU+Ip7UFh5WD8hWXMuGxeZ/ZOx9i+YT3NDfWdlnLHYbU2HDTS8eiLUsqzpZTjpJSvHS6/\n/wfbdinlJVLKgVLKBQhR375vS2fz2A6+LTu/xUjFs2nHNhlXiLE3PE7Z8InsWvcVoW59WPvRG4yd\nfS05PQbSET4HIM00quZGcblJ71+JeXAN7m6jcHcbhZ1qQ/HlIW0LT68JuMqGOiGFloVQFFSXC4FE\n2pYT9paOO3VFDItQ7yGYpkleWXeMbHKN+SNL+eDBQ6xdvcqxjG07OxlKtqxcJjW352sp5SNSykFS\nynlSSv1f8fkF+D4ipTxCSnlNUjcXvbN2W7pbUR619U3IbOv3AzU1zD13Fm0H9vDZh++i2qZTJxsI\nBAMcP3kC73/+DYbmRvgCXDxjIm9u2IHuUlF8bjIqBLxu7urTn5fa63movQ5DEyxMt/Ka3so76TYa\nhMn3eoIrirtT6Pc4IuFVSWs4i1g+DXfQld3cuAIuhpbmM7ykgOuH9Gduzx7c11LD3e0HGFKQy3Pj\nR7HFTnLzN5u449SjKS4vZE1NMy3ROLtqahXgeSnlCCnlWVLK7b8S21VSyhlSygnAK++t326V5eU4\ngpxlm4xF8Htc7N20nkP7djN0QN9OtigKM6dNQdM0vty2D+ELMGJgJV0Lcvn8YBOugIeUKlFdKlf1\n6oWuwJxDOwgrNt+YcV7VW3k91cpKM05EWvRw+5hWVITqUtF8GmkNVI/2L9n2Lc1lWHE+k7uX8fiw\noaxMR7micTf1qskLY0dRWBrkr5t20bukgFMnVWF5Ajz3wQoyhploD0dekVKeK6UcK6U8LOsYfqEm\np1LKHdIyD7bt3vgT0Ti4eRWrXvo7qXgUM+snTOoWKd0injbpedQ0yoce1Zl23SHIQhF4i3vStPwR\n7FgDmi+A5vah+YKobl/nAh6AnfUv26aOZepI28I2dcJfP0WqejW2oWNlUmi5XUg37cXImKg55XSf\n/BsylmTghOOJhduws+JrWDZvL3icpW/9lGmkpYlkJGzzH+6nB2Blks/WffNB9Me/sy2T7W8/Tv13\nK5znmM6tf9KALhPPYOKNj1E5fTZV5/x/7Z13eFRl+v4/76nTMukEEkpoEQEpggIqirr23rGsbdW1\nrB3L2nsFsWBbsaCIZW1YULEXiguoIL1JDRAIpEw97f39cSaTROC7ul/afn+5r+tcM9eZyUzOfSX3\ned7nvZ/nuZp2g47YjN+qr0ZR98v7qEaAYPu9sFb/iFuzzPcYhwtR89pT8/UIaibeSd0Pz2NtWuXz\nbNvU/fw2tTNew02nfC94Ko6ddrGSDoFO/dnv3Osw84tJ2G5WlBtuGm+Ne4WXnn7Mj4zdjIPFlXz7\n7tiadCL21I7m1nLdV9+c/IvXtrjAH7zqeeA5jHr+ZR598mlwLYTj55bJdP3TDZOnHriL3bt05M0v\npqAEwpS3a8u+u3XgnfnLGDP/V2766RfMXJPepYW8MaA/d+3WjUFFBRSGTExTI6Z6rJc215d15E+t\nGgXjh/paLps5i4QqMcKNzgIj7IvHIR1LGdy2FaqhcGT7UsYPGsB7+w7k4r4VbApKbvvhFypaF3LW\nIXtDJJ8bRr/DkAF7epqmTdxOq7mtQkq5yPXkr+tr6lm2ppHbr7+bzI133M2m6vWbcYtQOO34Y7j5\nb3/h0XHjUQJhlECYiw8dwAvT51Fp21zw/XQWeSly80MM79OTl3r34Zg2rWkbCRI0NTwdVnhp9s3N\n59aOndEMX4DRFK75ZTYT1ldtkduOBVHO694JzVTpVBDlmX69+Wz/fXlgnz507VjI/T/N56OFy3nm\n4hPR8ooYNWESHdq2Yea8RQowfltwtk1GOAG46eRTiyeOu71D7wHZ3cV2/YZQ1KUXSqCx4mbBl++S\n2FBJ/6F/y8xo8wU83UQwFEVQMuA4ahdNxSwsx3XsbMGHoqj+Jp9tZQpBGqNy6bq+xc0IEul+BFpe\nu+x7hBFFaCbJ2hoCYZ1YyiGWcvhk+I3E1ldy19iPsIVEEXDJnY9gBkPZ0UWKgG/Hv55CiDeklM3y\nuTsEUo6tnPHlLX3PGoYa8IsAdF1n78uGo4ZysTMRfGzNcpZ9/Dy7nXIleUUlzXLlTQVZVRWK+h+H\np+biKQZGQRnRvc+jbtoYwn2GohXthmunMbsfjzBzcNfNwYlXo+W0QtEMQp32w7VSWZeL9FzsVJJU\nwiAQ1inu0o9fZvyLtoVRRr3yDNfdO4KC/Hw8KTntr1dQV1+f9XnbnmTNil9Zs2SBCny446mVS0Om\nMbs+kdpr5aaYwHMRnssD11+Gg4awU0g9gACuvfl29urbh6EnHAVCcN0l53PtnQ9xxp8GIYJhrjnx\nYP484hVeO/MwehblYYR1hCLQbY2eQYPubl7WcyxdmZ1A0bCMVnSVATlFaDkG+TkBNFNFyYy3aMj5\nuzgI1X/vgzPnsV9JEQeWlWBGDb5cuI7dSgoYc/mpqHkF3Pr6Z+REc5gya15NPJF8dkdzCxBPW0++\n8/1P9yxfsz7fsSyMoMtRQwbRv3dPCiMBpOcggJfGvcGixUu49+ZhIARnnXw8dz32D2YtX0PPkign\nHtCPu9/6kkrL5ooBPemZF0VYEs92aRvQKc2P/Ftu9aDGJXt0oWdRPlpQ+x+5fW/ZKjamLS7u3gUz\narDIsVlVH+eDYWfRql1bpq7YwMjXP+Lsk49JT/55zntSytjWOPgj2CYRcgYvVc2bZqQ2VWVPCCEw\nos0rCMOFrQkWtN4s1wx+1IdjoaoKuR12o/PQ+wjk5GTcEwEELrHpLyPj61F0I5uaSM8bj1e3CqGq\nfvSsGwTK9kBoATzHwrGSSDtF8RG3IrRwVmhVRVDeay9qqtY2c1MEcqJoup79nR3b4pNXRzuuYz+6\nDfn63ZBSrgQ+XznpQ1ttchMzowV+CkEI/x8/lEOgoA1CD/JbG6LrSZx0AiEEqiaIduhJsLC170Qx\nggRa74bRqhv2hkVIN40QAiWYj71iKp6dQG1IE6kqWm4blHAR9bPepm7aGOz4pkzFnovreFQvX8gH\nj99FMJpPUWk70HTfc+54eELBjESzPm9PSj4d+2zMdZ2nduRE5KZIWvbDX/40r27momVIx8ZLJwkZ\nKtGgjvBchGuBa9G+bSnt25aS8U7ypwMGE41GePOrf5GUKnv36s6+3cr5x7R57L97OUY06Fu1wgaf\nblzPzfPmYeaamFETPazzQ7KeG5csQAZV9LCBETHIzQ1xSOdSzIiJFjCIC8DQUQzfYaDqGnrQP9rl\nRWibHyGYH2BKTR1vzl3K2EtOIlyYz7OfT+ejqT9z1YVns3rt+iQ7eJp3E7wyee5io6Qgj7mLl+Kl\nkwjPpnVBtDm3ZW2acRsIhbn2oj9z1+g3kHoQRw/zwJmH8fePpzC4Wwci+ZEst3FDcvnMWSx0k1lu\n3YDK9YsXMD1Vn+VWDxsc0LENrQoiaAEDV9dIKmKL3LbNj9A2z+c2Yepc8fEUhg89lH69Kli8KcnQ\n2x5j9EO38dJbH1iWZT+yrcjaZoKcSWKPnv3+82ktIxjObzahVEXQtvcguh504hY/Y8740cwaex+a\n4Sfco+0qqJ0zAZmo8jfqIoWYpXug55aiGUE/rxyIohd1Rctr658zgiiajlDUbPScWvIV8dnvkV49\ni9jSyaiqQtBQURXBXseeievYbNpQlc1n/hbfvP9P6XnuTCnlz5u9uIPg2el75r7/go3TmFZtEOeG\nsUNmbgGdj70YLVO/D40bf5t+ncO/RlxCetMaFFVB01U0Q0UztOwNL9C2N3qkFfGpzyJTG/1Nv4KO\nKIogMWMMQtWz0UR69Szc2kq0kh7UT3sBJ16NUIT/uapAqCq5rdow9Iq/46lGtgF+g7e74Xl11Vqm\nfvyOKj3viR1OaiPeq9xYE9+wqZaZcxf4jYaszFLatRCOjfAcrrzoPPbZu5//ExnhuO+Gq7j1iRcZ\netujPP7hdzx22elMX7mO0TMXYeZF/CMaYK8OJRxQ3hozamBGfVHuWVrA4LJWRHIDmXMGZjSAHg6g\nhf3Hq7+Yxivzf0UPNZ5XAwZ62OSygT3oU17Catfl719OY/TZR9G2rJjKeot7Xn6PD198nIeeezWW\nTKXuybh3djiklPVS8lROKOC8MeHLrXJ70H4D+eu5Z2W5lYrKRX8eyqyFv3LhQ//gklGvcfQBAzhu\nr925aPw3eOFAltuiohwOLG9DlzZ5WW5z84MMLmtFj9b5W+X2qZ8XcPukmVvk9pBu7TmtTxdEOMB1\nX07jqF5dOGX/viiBMFc9OY6b/nY+VXVJLNuZK6Wc/j+z8PuxLSNkPMe+b/F3H3l161ZtJsYNaBrh\nNT2nKYKu+x9DxUEnowqBrqvopooeCrPm4/sRXhIjnEde72MxcovRMk4KI5RDuOIgAvll6OFcVDOA\nZgT9XKgZRAtEyKk4iEiPI4nN+wTd0DGDOobmX7qiKBx50TBsu7E1rCcbLXDpZJI3n3wolYrHrtuW\nXP1RSCmngZy25Ku33d++1lSURaZnyG9fj7btQpcjzvGjYk1B0QSqqqCbKprhu1NCHfoT6rQPOX1P\nJTnzTaxfv8HduBinaj7RPc9ACwSzuXshQFoxnJU/oOeWEiwq93kNaKjSRVW1bHFNQ0/pptWPDauU\nd54dmdZ0c8y2HtX0RyCldFKWc2MwYKaveOhZXCuNdGywrWwE1yAcomm+U9XYf5+BDOrXm2hulNOO\nOpi8wkLG3/wXxk2fx8NTfkGGTMy8CBXtWnF6n93QwwHMaIBgfpCOpXmc16+CUEEIMxrAyAmhhxsf\nhanzl4E9OXC3Dji6mhEL//WG91QDF3z4HTccNoh99+iMEgrx8jczGHrEgaxYW83Ps+clgRd2FrcA\nluM8uGTVWvu5dz5lwZJlv5vbYCjCyNuHMWnmPM474TCUYJj7zj2Gzm2KOOPNz1kvPcy8COG8CBfu\n3YPigmiW21BBkL/0r6B9af4WuVUDBif1reDUvhUkFFBMfTNu1XCA2777CaGp3Hnan1BCIRZU1TJ/\n2WrOPfUEbnlgZKI+Fhu2LbkS29p3r2r6La1373fdYTc9Ff1379V+I87pjBMjlnKIZ6aBpJM2Kz57\nmZp531F67J14ojEN4Tm2v/OvqqhGwLfHqXomleH5uWNFRSgKGyf9A7tmFb0ufozcwgjFUZPCiEFB\nxCQnoBHQVAKaP5BVEQIl05h63OP3Jz957cWJqUT8+G1K1H8AIUQ31QjMOObhd0N6TkGzdI/7m/RP\n0+hZVUSjH9x2cSw3M23FJZ2ysVMuVtrBtVI4VhLXSmFVryC9+mdQNCK7DUELF6Bqhh8ZSg/PSZNY\nOgU1mEu0Yj8CEYPcwhCtisJEZT2JZbM46JiTCOkKpqagq0q2zwD4lY+L5s3mznOOq7OtdEcp5cad\nQmoGQgglHDBmtS7M637T+aeJP59whD+12wwiVR2pGqBoSEUFRcnygOuwft1a9jzsJN4ZeTv92hfj\n1ddQtWoFFz/5FrNXreOiQb04rGs7WgWMTCMhzz8y+yJCUfAE/FK1iSmrqphZuZ75VRuprItjqCqG\nphJPW5QX5NKrtIhOhbkUh4PUJNM8/8Mc/rp/Hy4/fBBGTgg1r4BB1z7CIzddwUV3Plq3dMWqC6SU\n/9yZ3ALomnpDp9KS2zu1axN8f9Q9v5tb4dqcdtGVdGpTxD3nnYBXX4Nbu4GH//kFT0z8geP36MJJ\ne3Rm94IoqqJskVuhKqyOxZm0oooZq6uYs7aaZRvrcDyPoK6Rdlwipk7fslZUFOfTJhpCVxTe+WUJ\nuq7y8l9PpLA4DzWvgBEfTmJt3KKgVevUyOde+TIWjx+1LXnaZpt6DfBc5+F1C366YNk8HYn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3LWZdeSHw5hSptnbr8mPe6Jh1anU8k9/5vEGPxWqK6Vusyqq77r50cvSm6Y9yOpuEUiZpGK2/6R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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff39ca55610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from collections import OrderedDict as dict\n",
"from mne.viz import plot_topomap\n",
"\n",
"data = dict(left=X[y==1].mean(axis=0),\n",
" right=X[y==-1].mean(axis=0))\n",
"data['subtraction'] = data['left'] - data['right']\n",
"data['dot product'] = 2 * X.T.dot(y[:, None])[:, 0] / len(X)\n",
"\n",
"fig, axes = plt.subplots(1, 4)\n",
"for ax, (label, topography) in zip(axes, data.iteritems()):\n",
" plot_topomap(topography, epochs.info, axes=ax, show=False)\n",
" ax.set_title(label)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This subtraction is applied at the sensor level. Consequently, the signals are still mixed. To estimate whether there is a difference in source space, a first approximation consists in estimating the sensor covariance $\\Sigma \\in R^{c \\times c}$ across trials (with $X$ centered):\n",
"\n",
"$$\\Sigma=XX^T$$\n",
"\n",
"Estimating whether the two conditions differ thus consists in inverting $\\Sigma$ to retrieve a *spatial filter* $w \\in R^{c}$):\n",
"\n",
"$$w = (XX^T)^{-1} X y = \\Sigma^{-1} X y $$\n",
"\n",
"When there are more than one stimulus feature, $Y \\in R^{n \\times s}$ is a matrix of samples $n$ by stimulus features (i.e. modeled sources $s$), and $W \\in R^{s \\times c}$ is thus a matrix. The above model corresponds to a least-squared multivariate linear regression. For two-class problems, it is equivalent to linear discriminant analysis (LDA) and an ANOVA."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model interpretation\n",
"\n",
"$W$ is an inverse operator that linearly map the sensors to a source space. It is therefore not interpretable in sensor space:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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zz/LqKy8TBD75fJ5cLkfJdenu7KRcLtM5bx5vv/UmTc3NTJo0iX333pvNNt4A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F7j+Rde5PpLzjVBMhW5yqCFkyUkL7/0MpM22NBIQ0QxvbWI31/eDP52hk1a7g0jO8f0/4CQMTrO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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff39c9e3f50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Ensure X is centered\n",
"Xn = X - X.mean(axis=0)\n",
"cov = Xn.T.dot(Xn)\n",
"\n",
"# compute spatial filter\n",
"w = np.linalg.pinv(cov).dot(Xn.T.dot(y))\n",
"\n",
"# Plot W coefficients\n",
"plot_topomap(w, epochs.info);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To interpret the linear coefficients of an forward model (sensor => source), we need to construct its dual: i.e. ($A \\in R^{c, s}$) which linearly project sources onto the sensors. $W$ is commonly referred to as **filters** and its dual as **patterns** [ref Haufe]:\n",
" $$ A = \\Sigma_X W \\Sigma_Y^{-1}$$\n",
"\n",
"In the present example, $Y$ is a binary vector and our linear model is a simple multivariate linear regression. The resulting patterns therefore correspond to our original subtraction."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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SXErDVAtgi7zkMoMqu04JsKmklFueHsP7X//AAyPO45RjjspWJ0rAQSbFJWWs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99jwbwD+cMDT3DLlZdYLpjDREwTTNvn1UyEblhMw9QQhsbn5s/irtdXc+KUMUjD9K0Dz5XTdIHU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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff3a9101150>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Compute patterns manually\n",
"patterns = cov.dot(w)\n",
"\n",
"# MNE decoding module is built to use scikit-learn and compute \n",
"# patterns automatically\n",
"from sklearn.linear_model import LinearRegression\n",
"from mne.decoding import LinearModel\n",
"\n",
"# Define least-squared multivariate regression\n",
"model = LinearModel(LinearRegression())\n",
"\n",
"# Fit sensors -> condition mapping\n",
"model.fit(X, y)\n",
"\n",
"# Plot patterns\n",
"plot_topomap(model.patterns_, epochs.info, show=False)\n",
"plt.gca().set_title('automatic patterns');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model evaluation: scoring metrics and cross-validation\n",
"\n",
"Any model is likely to find non-zero linear coefficients. How can we evaluate the validity of these coefficient (i.e. how can we go from an descriptive statistical estimate to an inferential)? There exists two main approaches:\n",
"* Estimating the posterior probability based on prior assumptions of the data distribution. We will not discuss this parametric approach here, mainly because it rapidly becomes impractical with an increasing number of parameters.\n",
"* Testing the extent to which the model can predict independent an dataset.\n",
"\n",
"To evaluate a supervised model on an independent dataset, we need to adopt:\n",
"* a **coding direction**. Here we will start with a decoding approach.\n",
"* a **scoring metrics**. Here we will start with an $R^2$ correlation coefficient: $R^2 = \\sum |y - \\hat{y}|^2 $\n",
"* a **validation scheme**. Here we will split the data into two halves, for fitting and evaluating respectively."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Test set: R²=-3.73\n",
"Test set: R²=-3.73\n",
"Train set: R²=1.00\n"
]
}
],
"source": [
"# Extract data with X y notation\n",
"X = epochs.get_data()[:, :, 0] # shape (n_epochs, n_channels, 1 time sample)\n",
"y = epochs.events[:, 2] # shape (n_epochs)\n",
"\n",
"# Define validation scheme\n",
"trials = range(len(X))\n",
"train = trials[::2] # every even trial\n",
"test = trials[1::2] # every odd trial\n",
"\n",
"# Define model\n",
"decoder = LinearModel(LinearRegression())\n",
"\n",
"# Fit training set\n",
"decoder.fit(X[train], y[train])\n",
"\n",
"# Predict testing set\n",
"y_pred = decoder.predict(X[test])\n",
"\n",
"# Score predictions\n",
"R2 = lambda y_true, y_pred: 1 - np.sum((y_true - y_pred) ** 2) / np.sum((y_true - y_true.mean()) ** 2)\n",
" \n",
"print('Test set: R²=%.2f' % R2(y[test], y_pred))\n",
"\n",
"# We can use scikit-learn API directly:\n",
"print('Test set: R²=%.2f' % decoder.score(X[test], y[test]))\n",
"\n",
"# Compare to perfect predictions on training set (i.e. a classic results of double-dipping)\n",
"print('Train set: R²=%.2f' % decoder.score(X[train], y[train]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Encoding and decoding\n",
"\n",
"The above example validates the linear model in a decoding fashion: it tests the extent to which the stimulus category can be predicted from the neural recordings.\n",
"\n",
"A similar model can be used in an encoding fashion: i.e. to test the extent to which the neural recordings can be predicted from the stimulus category."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Test set: R²=-0.11\n"
]
}
],
"source": [
"X = epochs.events[:, [2]]\n",
"Y = epochs.get_data()[:, :, 0]\n",
"n = len(X)\n",
"train, test = range(0, n//2), range(n//2, n)\n",
"encoder = LinearModel(LinearRegression())\n",
"encoder.fit(X[train], Y[train])\n",
"print('Test set: R²=%.2f' % encoder.score(X[test], Y[test]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the present example, the encoding model is not terribly useful, because the stimulus features are all orthogonal to one another. However, it is important to note that with a least-squared linear regression the patterns of the encoder and of the decoder are dual (it is possible to analytically transform an encoding model into a decoding one). "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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quj43ms+Pmp5Nt5HjSEuvzqdzvuZQWGf2zOn8tOh7/D4f3Xr2oVmbdpW1nu/n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WtNkkpksG1FyxdPIWaI4mEHkk6FyaRsoimLaDJDynLI2IpzL7qUIp/G9M+mcs/dd1HeuYI99zuQ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\nlIamnWrq2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dKqgAI2YYjIONyJuJ02dls2NApxYQUUUMAmiQL5FVBAAZskCm5vAQUUsEmi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COP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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff398034450>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# The decoder models the covariance of neural recordings\n",
"# The encoder models the covariance of the stimulus features\n",
"# When a LSR, the patterns of the two models are identical.\n",
"\n",
"fig, axes2 = plt.subplots(2, 2)\n",
"for axes, model, name in zip(axes2, (encoder, decoder), ('encoder', 'decoder')):\n",
" for ax, coef in zip(axes, ('filters_', 'patterns_')): \n",
" plot_topomap(np.squeeze(getattr(model, coef)), epochs.info, axes=ax, show=False)\n",
" ax.set_title('%s : %s' % (name, coef[:-1]))\n",
"plt.show();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Scoring metrics\n",
"\n",
"The scoring metrics acts as a measure of effect size. Many different scoring metrics can be used to evaluate the model: R², R, accuracy, Area Under the ROC Curve (AUC), precision score etc. Most are available under `sklearn.metrics` and depend on the type of predictions (are they categorical, are they continuous) and the robustness we want to achieve (is our data balanced, do we expect outliers etc).\n",
"\n",
"As a rule of sum we recommend continuous non-parametric scoring metrics:\n",
"* Spearman R values for regression models\n",
"* AUC for categorical models\n",
"\n",
"Additionally, when dealing with many categories, it is common in neuroscience to report as a score the entire confusion matrix. Additional analysis can then be applied to:\n",
"* cluster different brain responses - an analysis referred to as representational similarity analysis (RSA) (Kriegeskorte et al XXX) [see example RSA].\n",
"* correlates the confusion matrices to other types of data (MRI, behavior, simulations, e.g. Cichy et al 2014)\n",
"\n",
"### Validation scheme\n",
"\n",
"Most of validation schemes are 'cross-validation', indicating that the model is fitted and evaluated multiple times on different partitions of the data. Half validation is the most reliable method, but in practice we recommend Stratified non-shuffled partitions ('K-Fold') with 5 to 10 splits. Unlike 'leave-one-out' these cross-validation schemes allow within-split error estimation, and ensure a larger indepedence between trials."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cross-validated AUC=0.69 (+/- 0.08)\n"
]
}
],
"source": [
"from sklearn.preprocessing import LabelEncoder\n",
"from sklearn.model_selection import StratifiedKFold, cross_val_score\n",
"\n",
"X = epochs.get_data()[:, :, 0] # decode first time sampel\n",
"y = LabelEncoder().fit_transform(epochs.events[:, 2]) # ensure y in [0, 1]\n",
"\n",
"scores = cross_val_score(\n",
" estimator=LinearRegression(), \n",
" X=X, y=y, \n",
" cv=StratifiedKFold(n_splits=5),\n",
" scoring='roc_auc')\n",
"\n",
"print('Cross-validated AUC=%.2f (+/- %.2f)' % (np.mean(scores), np.std(scores)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Inferential statistics\n",
"Note that you should apply inferential statistics directly on trial predictions or splits' scores, because the training sets are not independent with one another. To estimate whether a score is above chance, you need to adopt a shuffling approach."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[....................................... ] 99.50000 | p<=0.000\n"
]
}
],
"source": [
"from mne.utils import ProgressBar\n",
"true_auc = np.mean(scores)\n",
"\n",
"shuffled_aucs = list()\n",
"y_shuffle = y.copy()\n",
"n_permutations = 200\n",
"\n",
"progress = ProgressBar(n_permutations)\n",
"for repeat in xrange(n_permutations):\n",
" progress.update(repeat)\n",
" # shuffle target\n",
" np.random.shuffle(y_shuffle)\n",
" \n",
" # estimate score\n",
" scores = cross_val_score(estimator=LinearRegression(),\n",
" X=X, y=y_shuffle,\n",
" cv=StratifiedKFold(n_splits=5),\n",
" scoring='roc_auc',\n",
" n_jobs=-1)\n",
" # store scores\n",
" shuffled_aucs.append(np.mean(scores))\n",
"\n",
"# Check probability of getting the true score randomly\n",
"print('p<=%.3f' % np.mean(np.array(shuffled_aucs)>true_auc))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## From analytic solution to optimization: loss function, regularization\n",
"The least-square linear model is not well posed when the number of trials is smaller than the number of parameters.\n",
"\n",
"Consequently, it is common to use a regularized model:\n",
" $$ W = (X^T X + \\lambda I)^{-1} X y $$\n",
"\n",
"This additional $\\lambda$ bias term is a spherical prior (assume equal variance across dimensions). In an optimization context, it is equivalent to an $l2$ penalty, where $w$ is parameterized to minimize a square loss function: \n",
"$$ argmin_w = \\sum ((w X y) - y)^2 + \\lambda ||w||^2_2$$\n",
"\n",
"In optimization, the square loss is equivalent to normal distribution assumptions. The above models are therefore **generative**, they are based on the joint probability between $X$ and $y$: $P(X,y)$. In practice, the assumption of normal distribution is often relaxed by using **discriminative** models, i.e. model based on the conditional probability: $P(y|X)$. This is for example the case with linear support vector machine (SVM) which are based on a hinge loss and a penalty. There is no analytic solution for SVM, which are instead fitted with a gradient-descent optimization. In scikit-learn, the default loss and penalty are the hinge square and the $l2$ respectively:\n",
"$$argmin_w = \\sum hinge((w X y), y)^2 + \\lambda ||w||^2_2$$\n",
"\n",
"Optimization problems are solved by gradient descent and stop after a numerical tolerance. It is therefore important to normalize the data prior to this optimization."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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+n2Y5MBnlRXWkQBz6jC1aVt5zYgHpaaawRIyEIBEjZcIoSeLpxcuRisdw3clj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5dx+GDGk3Ss+JyN9jyMfNYN2g8oCs3L+fd5x7HTsT9hxMRtYt9tAARgyUfvs+i92aw35XsByMhg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\nun8NKAApAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff3a383d350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.svm import LinearSVC\n",
"\n",
"# Normalize with z-score\n",
"mean = X.mean(axis=0)\n",
"std = X.std(axis=0)\n",
"X_norm = (X - mean) / std\n",
"\n",
"# fit SVM\n",
"svm = LinearSVC(loss='squared_hinge', penalty='l2', C=1, random_state=0)\n",
"svm.fit(X_norm, y)\n",
"\n",
"# Manually compute patterns and re-scale\n",
"patterns = np.cov(X_norm.T).dot(svm.coef_[0]) * std + mean\n",
"\n",
"# Plot patterns\n",
"plot_topomap(patterns, epochs.info);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Pipelines and cross-validation\n",
"To avoid losing track of the manipulation of the data, and ensuring independence across training and testing sets, we can make use of a scikit-learn pipeline. The pipeline is chain of forward transforms ending with a final estimator (e.g. a classifier or a regressor).\n",
"\n",
"The function `mne.decoding.get_coef` allows inverting the parameters of the final estimator to facilitate interpretation. This approach only works if all of the transforms are invertible."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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+n2Y5MBnlRXWkQBz6jC1aVt5zYgHpaaawRIyEIBEjZcIoSeLpxcuRisdw3clj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5dx+GDGk3Ss+JyN9jyMfNYN2g8oCs3L+fd5x7HTsT9hxMRtYt9tAARgyUfvs+i92aw35XsByMhg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\nun8NKAApAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff39c5852d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.pipeline import make_pipeline\n",
"from sklearn.preprocessing import StandardScaler\n",
"from mne.decoding import get_coef\n",
"pipeline = make_pipeline(StandardScaler(), LinearModel(svm))\n",
"pipeline.fit(X, y)\n",
"patterns = get_coef(pipeline, 'patterns_', inverse_transform=True)\n",
"plot_topomap(patterns, epochs.info);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Only the *state-less* transforms (i.e. steps that do not store a parameter fitted from the data) can be performed outside the cross-validation. For example, a fourier decomposition is state-less (it does not learn any parameter), but a principal component is not (it learns the principal components from a dataset), even though it is unsupervised.\n",
"\n",
"Note that the cross-validation must be applied at the highest level. Using the same cross-validation separately across folds can lead to score inflation."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Correct CV: AUC = 0.540 +/- 0.158\n",
"Incorrect CV: AUC = 0.772 +/- 0.133\n"
]
}
],
"source": [
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.feature_selection import SelectKBest, f_regression\n",
"from sklearn.model_selection import KFold, cross_val_predict, cross_val_score\n",
"\n",
"cv = KFold(n_splits=25, random_state=0) # deterministic cross-validation\n",
"feature_selection = SelectKBest(f_regression, 5) # not state-less transform\n",
"clf = LogisticRegression() # classifier\n",
"\n",
"pipe = make_pipeline(feature_selection, clf)\n",
"\n",
"not_ok = list()\n",
"ok = list()\n",
"for repeat in range(10):\n",
" X = np.random.rand(50, 200)\n",
" y = np.arange(50) % 2\n",
"\n",
" # Incorrect cross-validation: in-and-out of CV\n",
" # first step: e.g. to extract some features\n",
" Xt = cross_val_predict(feature_selection, X, y, cv=cv, method='transform')\n",
" # second step: e.g. to finalize classification\n",
" not_ok.append(cross_val_score(clf, X=Xt, y=y, cv=cv, scoring='roc_auc'))\n",
"\n",
" # Correct cross-validation: pipeline\n",
" ok.append(cross_val_score(pipe, X=X, y=y, cv=cv, scoring='roc_auc'))\n",
"\n",
"# print\n",
"for name, score in (('Correct CV', ok), ('Incorrect CV', not_ok)):\n",
" print('%s: AUC = %.3f +/- %.3f' % (name, np.mean(score), np.std(score)/np.sqrt(len(score))))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model comparison\n",
"\n",
"In practice, most estimators tend to yield to similar results, although discriminative models tend to be more robust than generative ones. Here is a quick comparisons across classic approaches."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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YtC+J06E4Rm3G5pGZPzh3ffR1VsE3denshcBLG7MRbcyISF8rVjxRufZBg3ff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\nYc94hdEpGim5asXcV0TkwA1h7v8NXuQ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ffsXSr7/mp59+RlEUiouLqaquZvCgweTk5qCp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UAAAg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\nM5Nj7gsPYz5xJ9NmPkjP3Y6m2+4nYtmC1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hoaGzj/7LP4zcyr2WGncWFClLVcLvzTrWQs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\nY2NjY9Ps+H+/2+Y8r8Oo7QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff392bbe310>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.model_selection import StratifiedKFold\n",
"from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
"from sklearn.decomposition import PCA\n",
"from sklearn.naive_bayes import GaussianNB\n",
"from sklearn.linear_model import LogisticRegression, RidgeClassifier\n",
"from sklearn.preprocessing import LabelBinarizer\n",
"\n",
"class GaussianNBCoef(GaussianNB):\n",
" \"\"\"Add coef_ parameter to Gaussian Naive Bayesian for simpler plotting\"\"\"\n",
" @property\n",
" def coef_(self,):\n",
" return self.theta_[0] - self.theta_[1]\n",
"\n",
"\n",
"models = dict(\n",
" pca_naivebayes=make_pipeline(StandardScaler(),\n",
" PCA(n_components=20, random_state=0),\n",
" LinearModel(GaussianNBCoef())),\n",
" lda=make_pipeline(StandardScaler(),\n",
" LinearModel(LinearDiscriminantAnalysis())),\n",
" ridge=make_pipeline(StandardScaler(),\n",
" LinearModel(RidgeClassifier())),\n",
" svc=make_pipeline(StandardScaler(),\n",
" LinearModel(LinearSVC(random_state=0))),\n",
" logistic=make_pipeline(StandardScaler(),\n",
" LinearModel(LogisticRegression(random_state=0))),\n",
")\n",
"\n",
"# Extract data with X y notation\n",
"X = epochs.get_data()[:, :, 0] # shape (n_epochs, n_channels, 1 time sample)\n",
"y = LabelBinarizer().fit_transform(epochs.events[:, 2])[:, 0]\n",
"\n",
"# Cross validation\n",
"cv = StratifiedKFold(n_splits=10, random_state=0)\n",
"\n",
"fig, axes = plt.subplots(1, len(models), figsize=[12, 8])\n",
"\n",
"for (name, model), ax in zip(models.iteritems(), axes):\n",
" \n",
" # cross validate each model\n",
" accuracies = list()\n",
" patterns = list()\n",
" for train, test in cv.split(X, y):\n",
" # fit model\n",
" model.fit(X[train], y[train])\n",
" \n",
" # score\n",
" accuracies.append(model.score(X[test], y[test]))\n",
" patterns.append(get_coef(model, 'patterns_', inverse_transform=True))\n",
" \n",
" # plot\n",
" plot_topomap(np.mean(patterns, axis=0), epochs.info, show=False, axes=ax)\n",
" ax.set_title('%s (%.2f)' % (name, np.mean(accuracies)))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the above results, the scoring metrics is accuracy. We recommend not using accuracy as a scoring metric, because \n",
"\n",
"* 1) it induces a discretization of the classifier predictions, and thus a loss of information.\n",
"\n",
"* 2) it can be affected by variance / bias issues.\n",
"\n",
"You can simply specify the scoring metrics in the `cross_val_score`, this won't change the model, only its evaluation:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"pca_naivebayes: AUC=0.63\n",
"lda: AUC=0.74\n",
"ridge: AUC=0.80\n",
"svc: AUC=0.79\n",
"logistic: AUC=0.77\n"
]
}
],
"source": [
"for (name, model), ax in zip(models.iteritems(), axes):\n",
" \n",
" # cross validate each model\n",
" auc = cross_val_score(model, X, y, scoring='roc_auc', cv=cv)\n",
" \n",
" # mean score across CV splits\n",
" print('%s: AUC=%.2f' % (name, np.mean(auc)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is a quick illustration to show the potential issue with accuracy metrics. In here, two conditions only vary in the variance of the signal, but not in their mean amplitudes. The accuracy would indicate an effect, but not the AUC"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
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IwsYoomUErFvJcLjZhJ89e/bgrrvuChIrIEWRx4wZY+v5SLARxqjFU3LdYtHlTmQWL16M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\nBEsQDoIESxAOggRLEA6CBEsQDuL/AZ83kqMZx1jqAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff39c66f9d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.metrics import roc_auc_score, accuracy_score\n",
"import seaborn as sns\n",
"sns.set_style('white')\n",
"\n",
"# This illustrates that unlike AUC, accuracy can be biased by variance\n",
"X = np.random.randn(2000, 2)\n",
"y = np.random.randint(0, 2, 2000)\n",
"\n",
"# Increase the variance of one class. Note that \n",
"X[y==0] *= 10\n",
"\n",
"# Find a random, non centered coef\n",
"# For simplicity we'll take a vertical line\n",
"coef = -2\n",
"\n",
"# Generate predictions\n",
"y_pred = X[:, 0] - coef\n",
"\n",
"# Plot\n",
"fig, ax = plt.subplots(1, figsize=[4, 4])\n",
"ax.scatter(X[y==0, 0], X[y==0, 1], s=4, c='b', label='y 1')\n",
"ax.scatter(X[y==1, 0], X[y==1, 1], s=4, c='r', label='y 2')\n",
"ax.axvline(coef, color='k', label='w')\n",
"ax.spines['top'].set_visible(False)\n",
"ax.spines['right'].set_visible(False)\n",
"ax.set_aspect('equal')\n",
"plt.legend()\n",
"plt.xlabel('X 1')\n",
"plt.ylabel('X 2')\n",
"plt.xticks([])\n",
"plt.yticks([])\n",
"plt.title('Accuracy=%.2f\\n AUC=%.2f' % (accuracy_score(y, y_pred > 0.),\n",
" roc_auc_score(y, y_pred)));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Non linear estimator\n",
"\n",
"Until recently, most neuroscientific and neuroimaging studies have made use of linear models. Indeed, it can be critical to ensure that the fitted model is linear, because non-linear steps can create interaction effects.\n",
"\n",
"Example:\n",
"* A subject performs a two-alternative forced choice task on the position of a stimulus. \n",
"* The neuroscientist wants to know whether the subject is performing error monitoring during this task: i.e. whether there exists some neurons that integrate and compare sensory and motor activity such that they fire in case of a mismatch between sensory and motor responses.\n",
"* Some neurons appear to (linearly) respond to the location of the stimulus, whereas others correlate with the button press.\n",
"* Unlike linear classifiers, a non-linear classifier can in principle decode error trials even if no neuron responds specifically to error trials."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"linear SVC: AUC=0.47 (+/- 0.03)\n",
"rbf SVC: AUC=1.00 (+/- 0.00)\n"
]
},
{
"data": {
"image/png": 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EFStW4OLFi9DpdMjIyMA999xjdk5ERIRppTgAyMrKgk6n69TzCIIgLGFV+Pn6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\nIyHhRxCER0LCjyAIj+T/AZswSLq/idbdAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff3792694d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.svm import SVC\n",
"\n",
"# The risks of non linear estimator\n",
"n_trials = 1000\n",
"\n",
"# Defined 4-modal distribution\n",
"X = np.c_[np.random.randint(0, 2, n_trials),\n",
" np.random.randint(0, 2, n_trials)] * 2. - 1\n",
"\n",
"# Group modes by interaction\n",
"y = np.prod(X, axis=1)\n",
"\n",
"# Add noise\n",
"X += np.random.randn(*X.shape) / 5.\n",
"\n",
"# Plot\n",
"fig, ax = plt.subplots(1, figsize=[3, 3])\n",
"ax.scatter(X[y==1, 0], X[y==1, 1], c='b', s=5, label='Correct')\n",
"ax.scatter(X[y==-1, 0], X[y==-1, 1], c='r', s=5, label='Incorrect')\n",
"ax.set_xlabel('Sensory position')\n",
"ax.set_ylabel('Motor response')\n",
"plt.legend(bbox_to_anchor=(1.1, 1.05));\n",
"\n",
"\n",
"linear_scores = cross_val_score(SVC(kernel='linear'), X, y, scoring='roc_auc')\n",
"print('linear SVC: AUC=%.2f (+/- %.2f)' % (np.mean(linear_scores), np.std(linear_scores)))\n",
"rbf_scores = cross_val_score(SVC(kernel='rbf'), X, y, scoring='roc_auc')\n",
"print('rbf SVC: AUC=%.2f (+/- %.2f)' % (np.mean(rbf_scores), np.std(rbf_scores)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Summary of key ML notions\n",
"\n",
"Let us summarize the key notions of supervised machine learning.\n",
"\n",
"First, we can see that each ML analysis is characterized by five stages: \n",
"1. **Preprocess**: this step refers to the transformation of the data with stateless operators. This can for instance include time-frequency decomposition or subselection of a priori defined regions of interest.\n",
"2. **Fit**: where the parameters the model are tuned to map $X$ to $Y$. In the case of linear modeling, $W$ is simply a vector or a matrix. In many ML analyses, the fitting stages consists in the successive fitting and transformation of $X$.\n",
"3. **Predict**: the predicted targets $\\hat{Y}$ provided by the model, given the data.\n",
"4. **Score**: the extent to which the predicted targets $\\hat{Y}$ match the true target labels $Y$.\n",
"5. **Interpret**: inspect the model parameters, notably by inverting the fitted patterns.\n",
"\n",
"Second, linear models (at the exception of CCA, PLS and alike) can be either fitted in an encoding or in a decoding fashion:\n",
"\n",
"1. **Decoding** consists in predicting the experimental conditions from the neuronal activity. A typical decoding consists in fitting an SVM on brain responses to predict the stimulus category. Decoding is of primary interest when the experimental conditions are simple (e.g. highly controlled stimuli), and the neuronal activity is complex and noisy (e.g. MEG).\n",
"\n",
"2. **Encoding** consists in predicting the neuronal activity from the experimental conditions. A typical encoding consists in fitting a general linear model (GLM) on the stimulus variables to predict brain responses. Encoding is of primary interest when the experimental conditions are complex (e.g. natural stimuli) and the neuronal activity has a high signal-to-noise ratio (e.g. fMRI or spikes).\n",
"\n",
"Once fitted, all linear models intrinsically have a decoding and encoding counterpart. Consequently, although encoding and decoding can refer to the way the model was fitted, these terms primarily indicate how the model is used to make predictions.\n",
"\n",
"Third, model **predictions** ($\\hat{Y}$) and model **interpretation** ($\\hat{A}$) are distinct. Predictions can be interpretable at the single trial level, either in neural space or in stimulus space. Model interpretation refers to understanding how the stimulus space maps onto brain activity and vice versa. \n",
"\n",
"Fourth, **generative** models (which fit the joint probability $P(X,Y)$) are easier to interpret than **discriminative** models (which fit the conditional probability $P(X|Y)$), because the mapping between brain activity and stimulus category is independent of the other categories."
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"# Frequent questions\n",
"## How to deal with imbalanced datasets?\n",
"\n",
"It is common to have imbalanced datasets: i.e. datasets where one category is much more common than another. This is for instance the case in odd-ball paradigms. While it is possible to reject trials to enforce balance, we recommend using\n",
"* a stratified cross-validation scheme to ensure that the trials distributions are similar across splits.\n",
"* sample weighting (i.e. use `sample_weight` in sklearn estimators) to minimize the fitting biases.\n",
"* a metrics that is independent of dataset imablance (e.g. AUC) or use `sample_weight` at the scoring stage.\n",
"\n",
"## Can we use non-linear models?\n",
"\n",
"It depends on the questions.\n",
"* If the question is assessing the amount of information that can be extracted from the data, it is not a problem. Note that MNE functions and classes are compatible with scikit-learn API, and therefore can make use of models with non-linear kernels (e.g. `sklearn.svm.SVC(kernel=\"rbf\")`, decision trees `sklearn.ensemble.AdaBoostClassifier()`) and feedforward neural networks (e.g. `sklearn.neural_network.MLPClassifier()`).\n",
"* If it is a interpretation question, such as 'Is there a neural sources responding to $y_i$ but not $y_j$, then linear models should be favoured, because non-linear models make use of interaction in the feature space. \n",
"* However, there is fast progress in interpreting non-linear models, and making generative non-linear models, which overcome these limitations. However, these approaches are currently not well established in neuroimaging and go beyond the scope of this tutorial.\n",
"\n",
"## Can I decode multiple stimulus features at once?\n",
"In some cases, we can attempt to decode multiple stimulus features at once. For example, we can decode the orientation, the spatial frequency, the phase and the contrast of a Gabor patch. \n",
"\n",
"If the stimulus features are orthogonal to one another (i.e. $\\Sigma_Y$ is diagonal), then a separate estimator for each stimulus features will be equivalent to a single multi-target estimators. \n",
"\n",
"However, if the stimulus features are not orthogonal, then the covariance and the precision of the stimulus needs to be estimated. If the stimulus features are simple, you can adopt of canonical correlation or partial least square regression analysis. If the stimulus features are complex and numerous, it is preferable to consider an encoding model.\n",
"\n",
"## Can meta-trials be used to improve decoding performance?\n",
"It is common in neuroimaging to create **meta-trials**, i.e. averages of a substets of the data to presumably increase the signal to noise ratio.\n",
"\n",
"In most cases, we recommend not to do this, and to favour ensembling methods instead (e.g. bagging), because the average of multivariate data can create spurious patterns [ref needed]. Note that in any case:\n",
"* meta-trials must be made within the cross-validation to ensure the independence between the training and testing sets\n",
"* the scores should be estimated on the original single trials. Indeed, scores are measures of effect sizes. However, the signal-to-noise ratio of meta-trials is aribtrary as it correlates with a free parameter: the number of trials used for each meta-trials.\n",
"\n",
"The main case where meta-trials are useful is for multi-unit recordings. In this setup, it is common to only be able to record a small number of neurons at a given time. To summarize the data, decoding analyses over all neurons can be used. In this case, one need to generate **pseudo-trials**: i.e. stack different recordings sessions with identical stimulation parameters with one another, as if they were all neurons were recorded simultaneously.\n",
"\n",
"\n",
"## How can I compute stats?\n",
"\n",
"## Is it useful to do feature selection?\n",
"\n",
"## Can I do source space decoding?\n",
"\n",
"## Denoising\n",
"An alternative to this forward pipeline is, many ML models can be used to **denoise** the data. This is for example the case for the `CSP` and `Xdawn` objects. In the current framework, denoising can be thought at a forward-backward operation (i.e. `fit` -> `transform` -> `inverse transform`) which will project the signal it is information bases, and project it back to its original space.\n",
"\n",
"\n",
"## Can I decode across subjects"
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