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izmailovpavel/sghmc_bad_cond_num.ipynb

Last active October 13, 2017 21:45
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sghmc_bad_cond_num.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import torch\n",
"from torch.autograd import Variable\n",
"import torch.optim as optim\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [],
"source": [
"class NomalDist:\n",
" def __init__(self, mu, sigma):\n",
" self.d = mu.size\n",
" sigma_cho = np.linalg.cholesky(sigma)\n",
" self.mu = Variable(torch.from_numpy(mu).float())\n",
" self.sigma = Variable(torch.from_numpy(sigma).float())\n",
" self.sigma_inv = torch.inverse(self.sigma)\n",
" self.sigma_cho = Variable(torch.from_numpy(sigma_cho).float())\n",
" \n",
" def loss(self, x):\n",
" return torch.matmul(torch.transpose(x - self.mu[:, None], 0, 1), \n",
" torch.matmul(self.sigma_inv, (x - self.mu[:, None])))\n",
" \n",
" def sample(self, n_samples):\n",
" z = Variable(torch.randn((n_samples, self.d)).float())\n",
" samples = torch.transpose(torch.matmul(self.sigma_cho, torch.transpose(z, 0, 1)), 0, 1)\n",
" samples += self.mu[None, :] \n",
" return samples.data.numpy()"
]
},
{
"cell_type": "markdown",
"metadata": {
"scrolled": true
},
"source": [
"Example samples"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10bc03668>]"
]
},
"execution_count": 123,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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zn8237DKu0ZCOH6cSBygYrRXGUVSVc/16eLyyIh09WsxYpqdpkQCUBDP8qovP5GdmwuPH\nH18L9lmbmAh1/dPT0m1t8wfSOECpEPCrLOpwubISyh1XVsLM/u238xvDrVvh3+XL0nPPrd89SxoH\nKBXq8KusV319HuhqCRSu8Dp8M3vazC6a2U9b//Zkda/aKvpUKrpaApWSdUrnK+5+b+vf6YzvVQ9F\nnkq1eTPnyQIVRpVOlRRxKtXERMjRc/IUUHlZTxGfNLOfmdlxM3tXxvcaf3mfShWdJUtHS2AsDBXw\nzexlMzub8O9BSUcl/bWkeyW9LunLKT9j3syWzGzp0qVLwwxn/OWVsydlA4ylXKp0zGxG0nfc/e+7\nvY4qnZhmM8zoV1bWulmaZd9tkqoboHL6rdLJLIdvZne5++uthw9JOpvVvcZOWq4+62BP1Q0w1rJc\ntP2Smd0rySUtS3o8w3uNh/isPm+NBouywJjLLOC7+76sfvZYap/V54lgD9QCrRXKIu8KnLiVlfBh\nEz/jFsDYIeCXRdG7Zq9eDR86AMYWAT9rSd0sk2R1KpVZ/68t+kMHQKYI+FlK6maZljrJqjrmwx8O\n1TdxaR8CZTkKEUAmCPhZSsrLp6VO5uakqanRj+H8+bCBKt62+MCBzg8BSjKBsUfAz1JaimRlJTm9\nk0Uf+wsXwofJ8vJai4QjRzo/BNhVC4w9mqdladeu9Jr6KL0TOXRoY/eYmAg/5/Tp5HulpWnm5gjw\nQM0ww8/S4mJn6iTu6tUQ6OfnpdXV/n/u5KR06lRYF7hxI8zYk+5FmgZADAE/S3NzIVUyMZH+mtXV\n3vX3U1O9+9BH9yJNAyAFAX9U0sov5+ZC7nwYb78t/eEP0smT3dsUt+fqCfYAYgj4o9Cr/HL79vT/\n9vbb+7sHG6MADImAPwqDlF+227q1e54/jo1RAIZAwB9EWtomLRBfuBBe021B9sqVztz79HTya9kY\nBWAIBPx+dUvbpAXi7dvXl14m2bWrM/d++DAVNwBGjoDfr0OH0tM2aSWR0WvSbNmSHMSpuAGQAQJ+\nP7qlZaLNTkkB+sqV7j/3sceouAGQGwJ+P3otvu7bJ+3dG76Pl072yrmfPj2S4QFAPwj4/ehVHROd\nNdtejtkr507VDYAcEfD7MUh1TLwcc24uveJm0J8LAEMi4MellV326onTLj5zP3w4LM6227yZqhsA\nuaJbZqT9EPF4N8towXRhIVw3W0vjJInP3KP/9tChtYXf6enwQcBCLIAcmXcLXDmbnZ31paWlYm4+\nM5PcXrjRCIuwcc1mevCfnKSEEkCuzOyMu8/2eh0pnUi33bLtopJJ91CVQ708gAog4EfSFlDN0g8e\nl6iXB1AZBPzI4mLy4uqtW9Kjj3YP+gBQAQT8yNyctG1b8nPXrtGaGEDlEfDjurVCYJMUgIoj4Md1\n2wjFJikAFUfAj1tcDBui2qV1tQSACqlnwE/aURvV1l+/HipzIps2reXwWbgFUGH122mbtKN2//4Q\n5K9dC9fcw0w/fi1p5y0AVEj9ZvhJ589ev74W2Ltd4yBxABVWv4A/bLUN1ToAKqp+AX/YahuqdQBU\nVP0CflKr482bO3fZJl3jIHEAFVa/gJ90QPizz0rHj/e+RmM0ABU2VHtkM/ukpKcl/Z2k+9x9Kfbc\n5yU9JummpH9395d6/bxC2yMDQEX12x552LLMs5I+IelrbTffLelhSe+X9JeSXjazv3H3m0PeDwCw\nQUOldNz9F+7+asJTD0p63t3/5O6/lnRe0n3D3AsAMJyscvjvkfSb2OPXWtcAAAXpmdIxs5clvTvh\nqQV3//awAzCzeUnzkrSLkkcAyEzPgO/uH9nAz70o6X2xx+9tXUv6+cckHZPCou0G7gUA6ENWKZ0X\nJT1sZlvN7G5J90j6cUb3AgD0YaiAb2YPmdlrkj4g6btm9pIkufs5Sd+S9HNJ35P0OSp0AKBYQ5Vl\nuvsLkl5IeW5REttSAaAkqr/TNqm3PQCgQ7X74Sf1tqdnPQAkqvYMP6m3PT3rASBRtQN+Wm96etYD\nQIdqB/y0jVps4AKADtUO+Em97elZDwCJqh3wk3rb07MeABJVu0pHCsGdAA8APVV7hg8A6BsBHwBq\ngoAPADVBwAeAmiDgA0BNmHt5zhwxs0uSVgb8z3ZIupzBcMYB70063pt0vDfpyvreNNx9Z68XlSrg\nb4SZLbn7bNHjKCPem3S8N+l4b9JV/b0hpQMANUHAB4CaGIeAf6zoAZQY70063pt0vDfpKv3eVD6H\nDwDozzjM8AEAfahswDezT5rZOTO7ZWazbc993szOm9mrZvaxosZYBmb2tJldNLOftv7tKXpMRTOz\nB1q/G+fN7Kmix1MmZrZsZv/b+l1ZKno8RTKz42b2hpmdjV3bbmY/MLNftr6+q8gxDqqyAV/SWUmf\nkPTD+EUz2y3pYUnvl/SApCNmNpH/8ErlK+5+b+vf6aIHU6TW78JXJX1c0m5Jn279zmDNv7R+Vypb\nfjgizynEkLinJL3i7vdIeqX1uDIqG/Dd/Rfu/mrCUw9Ket7d/+Tuv5Z0XtJ9+Y4OJXafpPPu/it3\nvybpeYXfGWAdd/+hpCttlx+UdKL1/QlJ/5broIZU2YDfxXsk/Sb2+LXWtTp70sx+1voTtVJ/gmaA\n34/uXNL3zeyMmc0XPZgSutPdX299/1tJdxY5mEGV+gAUM3tZ0rsTnlpw92/nPZ6y6vY+SToq6QsK\n/yN/QdKXJT2a3+hQMR9y94tm9heSfmBm/9ea6aKNu7uZVarMsdQB390/soH/7KKk98Uev7d1bWz1\n+z6Z2X9L+k7Gwym72v1+DMLdL7a+vmFmLyikwAj4a35nZne5++tmdpekN4oe0CDGMaXzoqSHzWyr\nmd0t6R5JPy54TIVp/VJGHlJY7K6zn0i6x8zuNrMtCgv8LxY8plIwsykz2xZ9L+mj4vel3YuSHml9\n/4ikSmUaSj3D78bMHpL0X5J2Svqumf3U3T/m7ufM7FuSfi7phqTPufvNIsdasC+Z2b0KKZ1lSY8X\nO5xiufsNM3tS0kuSJiQdd/dzBQ+rLO6U9IKZSSE2fMPdv1fskIpjZt+U9M+SdpjZa5L+Q9IXJX3L\nzB5T6Oz7qeJGODh22gJATYxjSgcAkICADwA1QcAHgJog4ANATRDwAaAmCPgAUBMEfACoCQI+ANTE\n/wOMKWenOWH35QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10efc3550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu = np.zeros([2], dtype=float)\n",
"sigma = np.array([[10, 9.9], [9.9, 10]])\n",
"dist = NomalDist(mu, sigma)\n",
"samples = dist.sample(1000)\n",
"plt.plot(samples[:, 0], samples[:, 1], 'ro')"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class SGHMC:\n",
" \n",
" def __init__(self, var, alpha, eta, log_density):\n",
" \"\"\"\n",
" Stochastic Gradient Monte Carlo sampler.\n",
" \n",
" Args:\n",
" var: `Variable` corresponding to the variable that is sampled\n",
" alpha: momentum parameter\n",
" eta: learning rate parameter\n",
" log_density: function computing log_density for a given sample\n",
" and batch of data\n",
" \"\"\"\n",
" self.var = var\n",
" self.alpha = alpha\n",
" self.eta = eta\n",
" self.log_density = log_density\n",
" self.optimizer = optim.SGD([self.var], lr=1, momentum=(1 - self.alpha))\n",
" \n",
" def _noise(self):\n",
" std = np.sqrt(2 * self.alpha * self.eta)\n",
" n = Variable(torch.normal(0, std= std * torch.ones(self.var.size())))\n",
" return torch.sum(n * self.var)\n",
" \n",
" def sample(self):\n",
" loss = self.log_density(self.var) * self.eta\n",
" loss += self._noise()\n",
" loss.backward()\n",
" self.optimizer.step()\n",
" self.var.grad.data.zero_()\n",
" return self.var"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x = torch.from_numpy(np.array([[-10], [0]])).float()\n",
"x_v = Variable(x, requires_grad=True)\n",
"mu = np.zeros([2], dtype=float)\n",
"sigma = np.array([[10, 9.9], [9.9, 10]])\n",
"dist = NomalDist(mu, sigma)\n",
"sghmc = SGHMC(x_v, .01, 5e-3, dist.loss)"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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"9900\n"
]
}
],
"source": [
"samples = []\n",
"for epoch in range(10000):\n",
" w_sample = sghmc.sample()\n",
" samples.append(np.copy(w_sample.data.numpy()).T)\n",
" if not(epoch % 100):\n",
" print(epoch)"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10000, 2)"
]
},
"execution_count": 128,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"samples = np.vstack(samples)\n",
"samples.shape"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10c2a2be0>]"
]
},
"execution_count": 129,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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6vb6r/O4ISYLCMKJUtbBuMDD3vNtI2MCa7Pjj4+b/DecnXNPFRZHEL7jAjZRi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\nIIQQMsT/BzZ2uK9hLfzzAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10bf69b38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"start_from=0\n",
"plus = 10000\n",
"plt.plot(samples[start_from:start_from+plus, 0], samples[start_from:start_from+plus, 1], 'bo')"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10bed2a58>]"
]
},
"execution_count": 130,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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lhiMArkCbXbQd3R1RWLqpaGYmqUVfWEj+vLy8NVOvq8dL/7cDatIxDZixo5D+2XhvLfr6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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c28f898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"freq = 10\n",
"new_samples = []\n",
"for i in range(int(samples.shape[0] / freq))[100:]:#[400:]:\n",
" new_samples.append(samples[i * freq][None, :])\n",
"new_samples = np.vstack(new_samples)\n",
"plt.plot(new_samples[:, 0], new_samples[:, 1], 'bo')\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Display the source blob
Display the rendered blob
Raw
sghmc_bad_condition_number.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import torch\n",
"from torch.autograd import Variable\n",
"import torch.optim as optim\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [],
"source": [
"class NomalDist:\n",
" def __init__(self, mu, sigma):\n",
" self.d = mu.size\n",
" sigma_cho = np.linalg.cholesky(sigma)\n",
" self.mu = Variable(torch.from_numpy(mu).float())\n",
" self.sigma = Variable(torch.from_numpy(sigma).float())\n",
" self.sigma_inv = torch.inverse(self.sigma)\n",
" self.sigma_cho = Variable(torch.from_numpy(sigma_cho).float())\n",
" \n",
" def loss(self, x):\n",
" return torch.matmul(torch.transpose(x - self.mu[:, None], 0, 1), \n",
" torch.matmul(self.sigma_inv, (x - self.mu[:, None])))\n",
" \n",
" def sample(self, n_samples):\n",
" z = Variable(torch.randn((n_samples, self.d)).float())\n",
" samples = torch.transpose(torch.matmul(self.sigma_cho, torch.transpose(z, 0, 1)), 0, 1)\n",
" samples += self.mu[None, :] \n",
" return samples.data.numpy()"
]
},
{
"cell_type": "markdown",
"metadata": {
"scrolled": true
},
"source": [
"Example samples"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10bc03668>]"
]
},
"execution_count": 123,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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zn8237DKu0ZCOH6cSBygYrRXGUVSVc/16eLyyIh09WsxYpqdpkQCUBDP8qovP5GdmwuPH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\n/wOMKWenOWH35QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10efc3550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mu = np.zeros([2], dtype=float)\n",
"sigma = np.array([[10, 9.9], [9.9, 10]])\n",
"dist = NomalDist(mu, sigma)\n",
"samples = dist.sample(1000)\n",
"plt.plot(samples[:, 0], samples[:, 1], 'ro')"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class SGHMC:\n",
" \n",
" def __init__(self, var, alpha, eta, log_density):\n",
" \"\"\"\n",
" Stochastic Gradient Monte Carlo sampler.\n",
" \n",
" Args:\n",
" var: `Variable` corresponding to the variable that is sampled\n",
" alpha: momentum parameter\n",
" eta: learning rate parameter\n",
" log_density: function computing log_density for a given sample\n",
" and batch of data\n",
" \"\"\"\n",
" self.var = var\n",
" self.alpha = alpha\n",
" self.eta = eta\n",
" self.log_density = log_density\n",
" self.optimizer = optim.SGD([self.var], lr=1, momentum=(1 - self.alpha))\n",
" \n",
" def _noise(self):\n",
" std = np.sqrt(2 * self.alpha * self.eta)\n",
" n = Variable(torch.normal(0, std= std * torch.ones(self.var.size())))\n",
" return torch.sum(n * self.var)\n",
" \n",
" def sample(self):\n",
" loss = self.log_density(self.var) * self.eta\n",
" loss += self._noise()\n",
" loss.backward()\n",
" self.optimizer.step()\n",
" self.var.grad.data.zero_()\n",
" return self.var"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x = torch.from_numpy(np.array([[-10], [0]])).float()\n",
"x_v = Variable(x, requires_grad=True)\n",
"mu = np.zeros([2], dtype=float)\n",
"sigma = np.array([[10, 9.9], [9.9, 10]])\n",
"dist = NomalDist(mu, sigma)\n",
"sghmc = SGHMC(x_v, .01, 5e-3, dist.loss)"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0\n",
"100\n",
"200\n",
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"9900\n"
]
}
],
"source": [
"samples = []\n",
"for epoch in range(10000):\n",
" w_sample = sghmc.sample()\n",
" samples.append(np.copy(w_sample.data.numpy()).T)\n",
" if not(epoch % 100):\n",
" print(epoch)"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(10000, 2)"
]
},
"execution_count": 128,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"samples = np.vstack(samples)\n",
"samples.shape"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10c2a2be0>]"
]
},
"execution_count": 129,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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6vb6r/O4ISYLCMKJUtbBuMDD3vNtI2MCa7Pjj4+b/DecnXNPFRZHEL7jAjZRi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\nIIQQMsT/BzZ2uK9hLfzzAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10bf69b38>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"start_from=0\n",
"plus = 10000\n",
"plt.plot(samples[start_from:start_from+plus, 0], samples[start_from:start_from+plus, 1], 'bo')"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10bed2a58>]"
]
},
"execution_count": 130,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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lhiMArkCbXbQd3R1RWLqpaGYmqUVfWEj+vLy8NVOvq8dL/7cDatIxDZixo5D+2XhvLfr6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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c28f898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"freq = 10\n",
"new_samples = []\n",
"for i in range(int(samples.shape[0] / freq))[100:]:#[400:]:\n",
" new_samples.append(samples[i * freq][None, :])\n",
"new_samples = np.vstack(new_samples)\n",
"plt.plot(new_samples[:, 0], new_samples[:, 1], 'bo')\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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