bootstrap_t_aug_2

effects_vs_delta.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 448,
   "id": "ab497cc2-d762-42ed-b90c-39d8eefb0bc4",
   "metadata": {},
   "outputs": [],
   "source": [
    "LAM = lambda **args: \\\n",
    "args['alpha'] * keyword_data[args['keyword']]['effect'] + args['beta'] * keyword_data[args['keyword']]['delta']\n",
    "\n",
    "Filter = lambda functional: \\\n",
    "np.argmax(functional)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "id": "ea37de13-38a0-404f-9d94-6869ad24d155",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'programming': {'effect': array([ 0.52727697,  0.62275902,  0.31992764, -1.47398622,  0.54000594,\n",
       "          0.69074962, -0.56053367, -0.26081456, -0.46688856, -0.47580749]),\n",
       "  'delta': array([ 0.0670864 ,  0.08354775,  0.04003509, -0.10704586,  0.0629095 ,\n",
       "          0.05717983, -0.03446123, -0.01716745, -0.03431878, -0.03526842])},\n",
       " 'iphone': {'effect': array([ 0.39874329, -0.22812587, -1.5355249 ,  0.57258721,  0.04357991,\n",
       "          0.61691486,  0.41334765,  0.23663399, -1.00647934,  0.33687891]),\n",
       "  'delta': array([ 0.04906107, -0.02348979, -0.11533874,  0.07157464,  0.00465422,\n",
       "          0.05769759,  0.03820275,  0.01912015, -0.06106605,  0.03389128])},\n",
       " 'lessons': {'effect': array([ 0.92381862, -0.1606284 ,  0.3732374 ,  0.08254097, -0.810276  ,\n",
       "          0.46417035, -0.63788485, -1.25698357,  0.57690274,  0.59065989]),\n",
       "  'delta': array([ 0.17997197, -0.01967962,  0.06275833,  0.00991244, -0.06583493,\n",
       "          0.04353218, -0.03588914, -0.06327196,  0.05551289,  0.09985146])},\n",
       " 'law': {'effect': array([ 0.85737955,  0.14047853,  0.07776645, -0.24235926, -0.29275087,\n",
       "         -0.04523782,  0.14086686, -0.29405953, -0.13099893,  0.13346111]),\n",
       "  'delta': array([ 0.1179123 ,  0.01402793,  0.00810001, -0.02359755, -0.02626759,\n",
       "         -0.00352435,  0.00948065, -0.01827477, -0.00961103,  0.01083245])}}"
      ]
     },
     "execution_count": 449,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keyword_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "id": "d7388fa2-1860-4a3e-a1ba-aedd6e52cabc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# what does a randomly sampled vector of comment likelihoods look like?\n",
    "N = 3 # as N->inf, we're more certain of our observed likelihoods and the filter will approximate it exactly\n",
    "# each step, we feed the filter some average of observed likelihoods and prior likelihoods\n",
    "\n",
    "_M = len(words)\n",
    "def get_y_sample(t=1,s=2.5,N=3,shift=0):\n",
    "    M = 500;\n",
    "    train_y = np.zeros((_M,  M   ,10))\n",
    "    for j in range(_M):\n",
    "        comparisonvect = word_stats[j]\n",
    "        # For simulating we'll assume that a keyword's commented distribution falls between 1) what we observed (and evaluated t scores for)\n",
    "        # and 2) a normal centered at 25% which is the average over the entire Hacker News dataset for all time slots\n",
    "        UNIFORM_PRIOR = .25\n",
    "        train_y[j,:,:] = \\\n",
    "        OHEnc.transform( \\\n",
    "        np.array(\n",
    "            [np.argmax(\n",
    "                np.array(\n",
    "                [1/(t+s)*(t*stats.t.rvs(loc=u[0],scale=u[1]**.5,df=30,size=N) + (.25+shift) * s*np.ones(N)) \\\n",
    "                 # DRAW NEW SAMPLES \\\n",
    "             for u in comparisonvect]\n",
    "        ).mean(axis=1)) for _ in range(M)]).reshape(-1,1))\n",
    "    return train_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "id": "c05b4c20-4b9b-4e43-a61a-b9ac04bea497",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_step(alpha,beta,Y,verbose=False,ret_matrix=False):\n",
    "    train_x = np.zeros((_M ,500, 10))\n",
    "    i = 0;\n",
    "    for i in range(_M ):\n",
    "        # get the \"most likely\" time point from the Filter\n",
    "        predicted = Filter(LAM(alpha=alpha,beta=beta,keyword=words[i]))\n",
    "        # Mark our predictions, and take a difference from \"actual\"/sampled best times to get an error\n",
    "        train_x[i,:,predicted] = 1\n",
    "    delt = np.abs(train_x - Y)\n",
    "    return (np.mean(delt,axis=1) ** 2).mean(axis=1).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "id": "ab3613b0-2c59-405e-bade-86b33eab661e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'alpha parameter')"
      ]
     },
     "execution_count": 528,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ve4MfIVjhK2PNzEqyvsGPEKxwojczK8nztz9wjd7MrCm1d3YhNfaqWHCiNzMrTXtnF/uPH8OolsamYid6M7OSZA8caWxtHpzozcxK017AxVLgRG9mVhrX6M3MmtjOXbt5esv2hp9DD070ZmaleOrZ7UQ0/tRKcKI3MytFEY8QrHCiNzMrQRGPEKxwojczK0HlEYKNvhc9ONGbmZWivXM7LSPE/uOd6M3MmlJ7ZxetE8bQMkIN35YTvZlZCdoLeOBIhRO9mVkJ1nd2cUABHbHgRG9mVor2zi4OdKI3M2tOXTt3sXHrTjfdmJk1qw2bs4ul3HRjZtakirxYCpzozcwKV+TtD8CJ3syscM/V6Au4cyXUmeglnSZpuaQVki6tMf/jkh6S9ICkn0mamZu3S9J96TV/MIM3MxuO2jd3MbplBPuOG1XI9kb2VUBSC3AFcCqwGlgkaX5EPJQrthSYFxFbJX0I+Bpwbpq3LSKOGdywzcyGr/Wd2zlg0hikxl8VC/XV6I8HVkTEyojYAdwAnJkvEBG3R8TWNHoXMGNwwzQzax5FPUKwop5EfzCwKje+Ok3ryYXALbnxsZIWS7pL0lm1FpB0USqzeMOGDXWEZGY2fGWJvpiOWBjkzlhJ7wXmAX+TmzwzIuYB7wa+Ieml1ctFxNURMS8i5rW2tg5mSGZmQ876zmIeIVhRT6JfAxySG5+Rpu1B0inAZ4AzImJ7ZXpErEl/VwILgWMHEK+Z2bC2ZXs3m7d3D7mmm0XAHEmzJY0GzgP2OHtG0rHAVWRJfn1u+hRJY9LwVOBEIN+Ja2a2V1m/udhz6KGOs24iolvSJcCtQAtwTUQsk3Q5sDgi5pM11UwAvpt6kZ+MiDOAlwNXSdpN9qPylaqzdczM9ipFXxULdSR6gIhYACyomnZZbviUHpb7FXDUQAI0M2smZSR6XxlrZlag9QXf/gCc6M3MCrWus4txo1uYMKauBpVB4URvZlagysVSRV0VC070ZmaFys6hL67ZBpzozcwK1b652NsfgBO9mVlhIqLw2x+AE72ZWWE6u7rp2rnbNXozs2a1Pp1DX9SzYiuc6M3MCvLcIwTdGWtm1pzKuCoWnOjNzArTvrnSdOMavZlZU1rfuZ2JY0cybnRxV8WCE72ZWWGKfoRghRO9mVlB2ju7ONCJ3sysebV3bi+8fR6c6M3MChERrC/h9gfgRG9mVohntuxg564o/Bx6cKI3MyvEcxdL9VSjv/squPMbDdm2E72ZWQGeP4e+h0S/9DuwcmFDtu1Eb2ZWgPXPXRVbo+lm5zZY/zAc/KqGbNuJ3sysAJWmm9ZabfTrfgO7u+GgYxuy7boSvaTTJC2XtELSpTXmf1zSQ5IekPQzSTNz886X9Gh6nT+YwZuZDRftnV3sN340Y0a2vHDm2iXZ34NKqtFLagGuAE4H5gLvkjS3qthSYF5EHA3cDHwtLbsf8DngBOB44HOSpgxe+GZmw0N7b48QXLMEJkyDSQc1ZNv11OiPB1ZExMqI2AHcAJyZLxARt0fE1jR6FzAjDb8JuC0inomIjcBtwGmDE7qZ2fDR6zn0a5dmtfkGPTC8nkR/MLAqN746TevJhcAt/VlW0kWSFktavGHDhjpCMjMbXnp8hOD2zfDUbxvWEQuD3Bkr6b3APOBv+rNcRFwdEfMiYl5ra+tghmRmVrpdu4MNm7fXrtGvvQ+IhnXEQn2Jfg1wSG58Rpq2B0mnAJ8BzoiI7f1Z1sysmT397HZ2Rw/n0De4IxbqS/SLgDmSZksaDZwHzM8XkHQscBVZkl+fm3Ur8EZJU1In7BvTNDOzvUbl1Mqad65cuxT2PRTG79+w7fd59/uI6JZ0CVmCbgGuiYhlki4HFkfEfLKmmgnAd5V1JjwZEWdExDOSvkD2YwFweUQ805B3YmY2RLX3drHUmiUNrc1DHYkeICIWAAuqpl2WGz6ll2WvAa55sQGamQ13ldsfvKCNfsvTsOkJmPcnDd2+r4w1M2uw9o4uRgj2Hz96zxlrl2Z/G3jGDTjRm5k1XHvndqZOGMPIlqqUu3YpIJh+TEO370RvZtZg7T1dLLV2CUydA2MnNXT7TvRmZg3W3rm9l47Yxp0/X+FEb2bWYOs7u154Dn3nWnh2XcPPuAEnejOzhtrRvZunt+xg2sSqRF9QRyw40ZuZNdSGZyuPEKxqulmzBNQCBx7V8Bic6M3MGuj5i6Wqa/RL4IC5MGqfhsfgRG9m1kCVRwgekK/RR2RNNwc3viMWnOjNzBqqcp+bPWr0Gx+HbRsL6YgFJ3ozs4Zq7+xiVIvYb1zuqtjKHSsL6IgFJ3ozs4bKHiE4lhEjck+PWrMEWsZkbfQFcKI3M2ug9Zu79myfh6x9/sCjoGVUITE40ZuZNVB7Z9ee59Dv3gVt9xfWbANO9GZmDfWC2x889SjseLawjlhwojcza5iunbvo2LZzz9sfPPfowGJOrYQ6HzxiZlaEFeuf5c5HN5QdxqDp2NYNVJ1auWYJjJ6Q3bWyIE70ZjZk/PWCh/n5I+v7LjiMjBAcPm3i8xPWLs3uPz+ipbAYnOjNbMhYs3Ebf3DEAXz9nFeWHcqgGTVyBBPGpFTbvQPWPQgnXFRoDE70ZjZkrO3Yxmteuj9Tqh+51yzWPwS7thfaEQvujDWzIeLZ7d1s7urmwMk1nsTULEroiIU6E72k0yQtl7RC0qU15p8kaYmkbklnV83bJem+9Jo/WIGbWXNZ17ENgOlNneiXwj77wZRZhW62z6YbSS3AFcCpwGpgkaT5EfFQrtiTwAXAJ2qsYltEHDPwUM2smbV1ZHd5nD658bftLc2apVltXuq77CCqp0Z/PLAiIlZGxA7gBuDMfIGIeDwiHgB2NyBGM9sLPJ/om7RGv2Nr1kZf4BWxFfUk+oOBVbnx1WlavcZKWizpLkln1Sog6aJUZvGGDc1zDq2Z1a9tUw8P6GgW6x6E2FV4+zwU0xk7MyLmAe8GviHppdUFIuLqiJgXEfNaW1sLCMnMhpp1nduYOmEMo0c26Tkiz3XEDs0a/RrgkNz4jDStLhGxJv1dCSwEiv85M7Mhb+2mLg7at0lr85B1xE6cDpOmF77pehL9ImCOpNmSRgPnAXWdPSNpiqQxaXgqcCLwUO9LmdneaF1HFwc2a7MNZLc+KKE2D3Uk+ojoBi4BbgUeBm6KiGWSLpd0BoCk4yStBs4BrpK0LC3+cmCxpPuB24GvVJ2tY2YGQFvHtubtiO3qgKcfLaV9Huq8MjYiFgALqqZdlhteRNakU73cr4CjBhijmTW5Ldu76ezqZvq+TXpq5dr7sr8FPQy8WpP2epjZcNL0p1auXZr9HapNN2Zmjdb23FWxzVqjX5JdDTtuv1I270RvZqVr+hp95YrYkjjRm1npKhdLveAh2s1gy1PQ8WRpzTbgRG9mQ0DlYqkxI4t7GEdhKu3zJdz6oMKJ3sxK19bR1cTNNksAwfTyHqbiRG9mpWvb1MSJfu0SmHoYjJnYd9kGcaI3s9I17cVSEVmNvsRmG/CjBM2sZJWLpQ6cvA88/CP4zc1lhzR4dnfDlvWldsSCE72ZlaxyauVBk8fAbX8JW56GidNKjmoQHXg0zDm11BCc6M2sVOtSop8Va+CZlfCWr8Nx7y85qubiNnozK9XadFXszKfuyCYcdnqJ0TQnJ3ozK1WlRj/pyf+B6cfA5P48wM7q4URvZqVq69jGYeO3MWL1YjjiLWWH05Sc6M2sVG0dXbx17P1AwOFutmkEJ3ozK9W6ji5OikUw+VCY9oqyw2lKTvRmVqpnNm3iyG33ZrV5qexwmpITvZmVZsv2bl65YymjYgcc8eayw2laTvRmVpq2ji5OGbGEnSMnwswTyw6naTnRm1lp1m3cwhtaltAx42RoGVV2OE3Lid7MSrPjibuZqk443KdVNpITvZmVZtKTt7EjWph41Gllh9LU6kr0kk6TtFzSCkmX1ph/kqQlkrolnV0173xJj6bX+YMVuJkNf4duuIMlI45kzIQpZYfS1PpM9JJagCuA04G5wLskza0q9iRwAXBd1bL7AZ8DTgCOBz4nyZ+omcFTKzhg+xPct8/vlx1J06unRn88sCIiVkbEDuAG4Mx8gYh4PCIeAHZXLfsm4LaIeCYiNgK3Af4fzcxg+Y8B+N3Uk0oOpPnVk+gPBlblxlenafWoa1lJF0laLGnxhg0b6ly1mQ1ry2/hEWYxZv+ZZUfS9IZEZ2xEXB0R8yJiXmtra9nhmFmjbXmKWHU3P+l+FdMn71N2NE2vnkS/BjgkNz4jTavHQJY1s2b121tR7Oa2Xa9uzmfFDjH1JPpFwBxJsyWNBs4D5te5/luBN0qakjph35immdnebPkCusZNZ1nMcqIvQJ+JPiK6gUvIEvTDwE0RsUzS5ZLOAJB0nKTVwDnAVZKWpWWfAb5A9mOxCLg8TTOzvdXObfDYz1ndejIgN90UoK5nxkbEAmBB1bTLcsOLyJplai17DXDNAGI0s2ay8g7YuZXfTMzubTNt8piSA2p+Q6Iz1sz2Ist/DKMnspgjmTphNGNGtpQdUdNzojez4uzeDct/AnNOYc3mbg50+3whnOjNrDhr7oUt6+Hwt9DW0eX2+YI40ZtZcZYvALXAnFNSoneNvghO9GZWnOULYNaJbG2ZSMe2nW66KYgTvZkV4+nHYMMjcPibaevoAuAgN90UwonezIqx/Jbs7+FvZl1K9K7RF8OJ3syKsfwWmPYKmDKTtZu2Aa7RF8WJ3swab+sz8OSv4PDTAZ6r0R8wyRdLFcGJ3swa77e3QuyGw98MwNqOLvYfP5qxo3yxVBGc6M2s8ZYvgInTYfoxAKzr2Mb0fd0+X5S67nUzLOzYCvdcXXYUZlbLip/BK8+FEVndsq2jixlTxpUc1N6jeRL9zq3w08+VHYWZ1aIWeMXZz422dXRx/Oz9Sgxo79I8iX7c/vAXbWVHYWa1jGiBkVnH69Yd3b5YqmDNk+glGO1/Bc2GusrFUr79QXHcGWtmhVr3XKL3OfRFcaI3s0K5Rl88J3ozK1Rbuip22iQn+qI40ZtZodo6fbFU0ZzozaxQbZt8sVTRnOjNrFBtHV0cOMkdsUWqK9FLOk3SckkrJF1aY/4YSTem+XdLmpWmz5K0TdJ96XXlIMdvZsPMuk4/WapofZ5HL6kFuAI4FVgNLJI0PyIeyhW7ENgYES+TdB7wVeDcNO+xiDhmcMM2s+Fo245dbNq60003BaunRn88sCIiVkbEDuAG4MyqMmcC30rDNwNvkKTBC9PMmkFbR3bGjWv0xaon0R8MrMqNr07TapaJiG6gA9g/zZstaamkOyS9rtYGJF0kabGkxRs2bOjXGzCz4aPNF0uVotGdsW3AoRFxLPBx4DpJk6oLRcTVETEvIua1trY2OCQzK4svlipHPYl+DXBIbnxGmlazjKSRwGTg6YjYHhFPA0TEvcBjwGEDDdrMhqd1Hb5Yqgz1JPpFwBxJsyWNBs4D5leVmQ+cn4bPBn4eESGpNXXmIuklwBxg5eCEbmbDjZ8sVY4+z7qJiG5JlwC3Ai3ANRGxTNLlwOKImA/8G/AdSSuAZ8h+DABOAi6XtBPYDVwcEc804o2Y2dC3rqPLtycuQV23KY6IBcCCqmmX5Ya7gHNqLPc94HsDjNHMmsTaTdv8ZKkS+MpYMyuML5YqhxO9mRWicrGUm26K50RvZoWoXCx1kK+KLZwTvZkVovJkKd/QrHhO9GZWiLUp0btGXzwnejMrhC+WKo8TvZkVoq2ji/18sVQpnOjNrBBtHT61sixO9GZWCCf68jjRm1kh2jq2+fbEJXGiN7OG88VS5XKiN7OGW9fp+9CXyYnezBqubVPlEYJuuimDE72ZNZyfLFUuJ3oza7jKfW7cRl8OJ3ozazhfLFUuJ3oza7i2ji4O9K0PSuNEb2YN19bR5ZuZlciJ3swabl3HNrfPl8iJ3swaatuOXWzcutOnVpaoroeDDwebtu7gnCt/XXYYZlale3cAPrWyTHUlekmnAf8AtAD/GhFfqZo/Bvg28GrgaeDciHg8zfs0cCGwC/hoRNw6aNHnjBgh5kyb0IhVm9kAHXvIvrx2ztSyw9hr9ZnoJbUAVwCnAquBRZLmR8RDuWIXAhsj4mWSzgO+CpwraS5wHnAkcBDwU0mHRcSuwX4jk8aO4pvvefVgr9bMbNirp43+eGBFRKyMiB3ADcCZVWXOBL6Vhm8G3iBJafoNEbE9In4HrEjrMzOzgtST6A8GVuXGV6dpNctERDfQAexf57JIukjSYkmLN2zYUH/0ZmbWpyFx1k1EXB0R8yJiXmtra9nhmJk1lXoS/RrgkNz4jDStZhlJI4HJZJ2y9SxrZmYNVE+iXwTMkTRb0miyztX5VWXmA+en4bOBn0dEpOnnSRojaTYwB7hncEI3M7N69HnWTUR0S7oEuJXs9MprImKZpMuBxRExH/g34DuSVgDPkP0YkMrdBDwEdAMfbsQZN2Zm1jNlFe+hY968ebF48eKywzAzG1Yk3RsR82rNGxKdsWZm1jhDrkYvaQPwxABWMRV4apDCGUyOq38cV/84rv5pxrhmRkTN0xaHXKIfKEmLe/r3pUyOq38cV/84rv7Z2+Jy042ZWZNzojcza3LNmOivLjuAHjiu/nFc/eO4+meviqvp2ujNzGxPzVijNzOzHCd6M7MmN2wSvaTTJC2XtELSpTXmj5F0Y5p/t6RZuXmfTtOXS3rTUIhL0ixJ2yTdl15XFhzXSZKWSOqWdHbVvPMlPZpe51cvW2Jcu3L7q/p+S42O6+OSHpL0gKSfSZqZm1fm/uotrobtrzpju1jSg2n7d6YHEVXmlXlM1oyr7GMyV+4dkkLSvNy0ge2viBjyL7J77DwGvAQYDdwPzK0q86fAlWn4PODGNDw3lR8DzE7raRkCcc0CflPi/poFHE32CMizc9P3A1amv1PS8JSy40rzni1xf/0fYFwa/lDucyx7f9WMq5H7qx+xTcoNnwH8JA2XfUz2FFepx2QqNxH4BXAXMG+w9tdwqdEP1adcDSSuRuozroh4PCIeAHZXLfsm4LaIeCYiNgK3AacNgbgaqZ64bo+IrWn0LrJbbkP5+6unuBqtntg6c6PjgcqZH6Uek73E1Uj15AqAL5A9irUrN23A+2u4JPqGP+WqhLgAZktaKukOSa8bpJjqjasRyzZ63WOVPYnsLklnDVJMLyauC4FbXuSyRcUFjdtfdccm6cOSHgO+Bny0P8uWEBeUeExKehVwSET8uL/L9qXP2xRbw7QBh0bE05JeDfxA0pFVtQ3b08yIWCPpJcDPJT0YEY8VGYCk9wLzgNcXud2+9BBX6fsrIq4ArpD0buCzPP/cilL1EFdpx6SkEcDfARc0Yv3DpUY/VJ9y9aLjSv+GPQ0QEfeStbsdVmBcjVi2oeuOiDXp70pgIXBskXFJOgX4DHBGRGzvz7IlxNXI/VV3bDk3AGe9yGULiavkY3Ii8ApgoaTHgd8D5qcO2YHvr0Z0PDSgI2MkWSfXbJ7vyDiyqsyH2bPT86Y0fCR7dmSsZPA6fgYSV2slDrIOmjXAfkXFlSt7LS/sjP0dWcfilDQ8FOKaAoxJw1OBR6nRmdXAz/FYsgN/TtX0UvdXL3E1bH/1I7Y5ueG3kT2oaCgckz3FNSSOyVR+Ic93xg54fw3Kh17EC3gz8Nv0pf5MmnY5WS0GYCzwXbKOinuAl+SW/Uxabjlw+lCIC3gHsAy4D1gCvK3guI4ja+vbQvafz7Lcsn+S4l0B/PFQiAv4feDB9IV/ELiw4Lh+CrSnz+s+YP4Q2V8142r0/qoztn/IfcdvJ5fYSj4ma8ZV9jFZVXYhKdEPxv7yLRDMzJrccGmjNzOzF8mJ3sysyTnRm5k1OSd6M7Mm50RvZtbknOhtyJP0uKSpAy0zHEn6M0njyo7DhjcnerMBktTSwNX/GdCvRN/geGwYcqK3IUPSDyTdK2mZpItqzJ8l6RFJ/ynpYUk3V9V2P6LsXvYPSjoiLXO8pF+nG1X9StLhNdZ7sqRfSPpxut/3leneI0j653RjsGWS/iq3zOOSvippCXCOpA9IWiTpfknfq8Ql6dq0jrskrUzbuibFf21ufW9McS6R9F1JEyR9FDgIuF3S7T2VqxXPwD8NayqDfbWcX3692BfpcnNgH+A3wP5p/HGyy/hnkd1S9sQ0/RrgE7kyH0nDfwr8axqeBIxMw6cA36ux3ZPJbgv7ErL7ht9Guv1CLqYWsqsVj85t75O5deyfG/5iLpZrye6nUrlldidwFFkl617gmPTefgGMT8t8Crgs/97TcF/lPtnXPvZr73z57pU2lHxU0tvT8CHAHLLbIOStiohfpuH/ILvF7N+m8f9Kf+8F/jANTwa+JWkO2Y/EqB62fU9kN/9C0vXAa8meH/DO9N/FSGA62UMgHkjL3Jhb/hWSvgjsC0wAbs3N+2FEhKQHgfaIeDBtZxnZj9eMtN5fpkcVjAZ+XSPG3+uj3I01ljFzorehQdLJZDXu10TEVkkLye4TVK36nh358cqdG3fx/Hf7C8DtEfF2ZY9xXNhDCC9Yr6TZwCeA4yJiY2pqyce0JTd8LXBWRNwv6QKy/xKq49qdG66Mj0zx3hYR7+ohtgr1UW5LD9NtL+c2ehsqJgMbU5I/gqz2Wsuhkl6Tht8N3FnHeiu3dL2gl3LHS5qd2ubPTeudRJY8OyRNA07vZfmJQJukUcB7+oip2l3AiZJeBiBpvKTK7XE3p3X3Vc6sR070NlT8BBgp6WHgK2RJrZblwIdTuSnAP/ex3q8BX5a0lN7/g10E/BPwMNmthr8fEfcDS4FHgOuAX/a8OH8J3J3KPNJHTHuIiA1kP0LXS3qArDnmiDT7auAnkm7vo5xZj3z3Shs2UtPLjyLiFYO83pPJOnXfOpjrNRsqXKM3M2tyrtGbmTU51+jNzJqcE72ZWZNzojcza3JO9GZmTc6J3sysyf1/O0N0JdWM6wAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if our train data were 100% accurate, we would want to filter based solely highest recorded comment rate\n",
    "# and we would always seek to minimize Training set error\n",
    "y_train = get_y_sample(t=1,s=0,N=200,shift=-.2)\n",
    "I = np.linspace(0,.4,30)\n",
    "plt.plot(I, [train_step(v,1.,     y_train) for v in I])\n",
    "plt.plot(I, [train_step(v,1., y_validate    ) for v in I])\n",
    "plt.title(\"Error: Training set (blue) vs Augmented set (orange)\")\n",
    "plt.xlabel(\"alpha parameter\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 511,
   "id": "9868d645-60ba-4031-99ba-aaa349af44c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import plotly.express as px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 525,
   "id": "0ed8b368-5a16-46bc-bf56-056cf00f7e4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5,));\n",
    "plt.pcolormesh(np.squeeze(q));\n",
    "plt.xticks(np.arange(0,30,30/4), np.round(I[::8],1))\n",
    "plt.yticks(np.arange(0,30,30/4), np.round(I[::8],1)); plt.colorbar();\n",
    "plt.xlabel(\"Effect weight\"); plt.ylabel(\"raw delta weight\");\n",
    "plt.title(\"Time/Comment rate Mode Identification Error\");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}