pca_ppca_compare.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reconciling PCA and PPCA\n",
    "\n",
    "PPCA is demeaned and standardized by default\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import StandardScaler \n",
    "from ppca import PPCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_returns = np.random.normal(0.005, 0.01, (120,20)) + 1.1*np.random.normal(0.01, 0.005, (120,1)) + 1.2*np.random.normal(0.01, 0.005, (120,1)) + np.random.normal(0.005, 0.01, (120,1)) + np.random.normal(0.005, 0.002, (120,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f36cd184b00>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(raw_returns[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 20)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "scaler.fit(raw_returns)\n",
    "returns = scaler.transform(raw_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit Both Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_comp = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod = PCA(n_components=n_comp)\n",
    "modp = PPCA()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "mod.fit(returns)\n",
    "modp.fit(returns, d=n_comp, tol=1e-5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare Betas\n",
    "\n",
    "It's ok if signs don't match; that's a feature of PCA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betas = mod.components_.T\n",
    "betas.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betasp = modp.C\n",
    "betasp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(betas[:,0], betasp[:,0]);\n",
    "plt.scatter(betas[:,1], betasp[:,1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare recovered factor returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 594,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 3)"
      ]
     },
     "execution_count": 594,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for each factor, what is the return per date\n",
    "factor_returns = mod.transform(returns)\n",
    "factor_returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 595,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 3)"
      ]
     },
     "execution_count": 595,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_returnsp = modp.transform()\n",
    "factor_returnsp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 596,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(factor_returns[:,0], factor_returnsp[:,0]);\n",
    "plt.scatter(factor_returns[:,1], factor_returnsp[:,1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare factor volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 597,
   "metadata": {},
   "outputs": [],
   "source": [
    "common_factor_volatility = np.std(factor_returns, axis=0)\n",
    "common_factor_volatilityp = np.std(factor_returnsp, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 598,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.74803076 0.74580423 0.7400688 ]\n",
      "[3.74803076 0.74580176 0.7400645 ]\n"
     ]
    }
   ],
   "source": [
    "print(common_factor_volatility)\n",
    "print(common_factor_volatilityp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare explained variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 599,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.70238673, 0.0278112 , 0.02738509])"
      ]
     },
     "execution_count": 599,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mod.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 600,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.70828914, 0.02804472, 0.0276149 ])"
      ]
     },
     "execution_count": 600,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diff(np.append(0, modp.var_exp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recover Common Returns (predicted returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for each stock, what is the return attributable to all common factors for each date\n",
    "common_returns = np.dot(factor_returns, betas.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 534,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 20)"
      ]
     },
     "execution_count": 534,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "common_returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 535,
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = returns - common_returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "metadata": {},
   "outputs": [],
   "source": [
    "resid_volatility = np.std(residuals, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inverse Transform to go from scaled space to original space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "metadata": {},
   "outputs": [],
   "source": [
    "recons = scaler.inverse_transform(common_returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 20)"
      ]
     },
     "execution_count": 538,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recons.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 539,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(recons, axis=0), np.mean(raw_returns, axis=0));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 540,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f680befba90>]"
      ]
     },
     "execution_count": 540,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((np.std(raw_returns, axis=0)-np.std(recons, axis=0))/np.std(raw_returns, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 541,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f680be64898>"
      ]
     },
     "execution_count": 541,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KTWhO+mB0bMIYBkg2All5AqmGRj5LW6h1uovz7v5p5MW/cMe/7ocvMnai/P8hAw6sv2LC9nKjii8+Zz4/eO7N2JlSi8tqBLIkpZHPIkVqvWO+68pzY582Spto4nIKcU1W5XIJz7x6qGJQKHcMkXooMIiUUal9vjjgxM23FNdkVW5xnqQX/DldnVWdj0gSCgzSlkqbli4+Zz7PvHqo4sW/nGqTvOVyH+V6UxWLGXsnUhflGKTtJFnYJmoW08lI3sblPpIuvhOXvxCJohyDSIwkC9tEzWIK6a1BUBoQHrr2vAmL9hTqWkv+QqQeCgzSUtJYTayWhG1hpHQagSHpFNj15C9E6tHsKTFEEouaSvu2zbtZ2L81cmK8OLXeZafVA6jamV9Bk9lJY+mJQVpG1AW10LhSTXNPVNI3idKAUk0Cu1iti99okJo0igKDtIxKF86kzT1xM6kWLupzujr56NjxCbOYFpptBoZy3P2TvaG5knIjozz63Juh93GBqlw31WZLo6lOWp+akqRlJLlwJuniCfmLdWFeosKAsnUrzubA+ivY/V+XR85iWtxbKMmU2nHNQ1ld/KbaVe9k6tITg7SMJE1ARv4CV+kut1ICOK7ZJkmPpmJRTzlZndSuXO6j2XWTxlJgkJaRZCptD/ZXupDVehGsNgEd95STxXxBrbkPmXrUlCQtpbCYzhtlBnVVupANDOVqXqOh2jxAuTWds6bcutfSXhQYpGX1xFywHGK7rxaakOJUugiuW3F2opXZCuLWdM6irOY+pPEUGKRllVu+Mzcyyq2bd3PD/3o2tL1cjiDJRXD10h5uWNabODi0UjOMxkpIgXIM0rKS5Bx2vH6YOwb2nFz2styFOulF8N7VS+g7c14oefzRJ8cj121otWaYLOY+pPE0iZ5MCYv6t5Zdv8Cg7AW83gVv4qas0B23ZIkm0ZOWVOsAq3LrMwMn++V3dhid0yy06loa7ehZ7YIqUgs9MUjqar2413PXPTCUi12fudTc2Z3MnjFdF3BpO3pikKZIOnNolFrGFhQHoc5pMHaich1Hjo4xdOfyBGcj0p7UK0lSVcvMoQVxieHcyCiLImZQLZ3CIUlQgNZLCIs0mgKDpKqe0bPlLthRc/dUmp6ikE8opn75IpWlEhjMbKWZ7TOzYTPrj9g/08w2B/ufN7OFwfbLzGyXme0J/q29W4hkQtzFvXt2Jxet3x55519QblxCQfHTR6VgMzbunDpreqhf/pd75/DHj7/Iwv6t/NrtT3LHQPxgN5F2VXdgMLMO4BHgcmAxcJ2ZLS4pdhNwxN0/DzwE3B9sfw/4mrsvAdYC36+3PtJcURf3zg7jw4+PV5y1s3SAVZxC76MkTUIjR8fY0X8JB9ZfwcXnzGfH64dPLpE57s6jz72p4CBSIo0nhguAYXff7+7HgE3AqpIyq4CNwesngEvNzNx9yN3fDrbvBbrMbGYKdZImKVzcu7s6T247fsJD3UMhPu9QmAvpwPor6LDo8FDYnqRJqDh4PPb8W5Fl4ranYWAoV/FJSSRr0uiV1AMU/886CFwYV8bdj5vZB8Bp5J8YCq4GXnD3T1KokzTZJ8c/zQTH9Yiu1BQ0HvPBcXcW9m+lu6uTU2Z08NGxZFNclDveZKinh5ZIM2Ui+Wxm55JvXvqDMmVuNrNBMxs8dKh1JiZrR0nXLJhT9FQRJW6SvIKR0TFGj43T2THxyWLu7M4J4x8qPYGkrZ4eWiLNlEZgyAFnFL1fEGyLLGNm04E5wPvB+wXAXwO/5+6vx32Ju29w9z5375s/v3WmMm5HSSeOGxkdK9u+nyQZfQI4Zcb0k0GkcJGfPWPiw/B1F54xYVu57fXS+gbSqtIIDDuBs8xskZnNANYAW0rKbCGfXAa4Btju7m5m3cBWoN/dd6RQF8mAasYJ/OC5N2Pb3YuT0eV8MDp2MogUmoWiEtz3rl7Cjct6TwaPDjNuXNZ7coK9tGl9A2lVqUyJYWa/DTwMdADfc/f/Zmb3AIPuvsXMZpHvcbQUOAyscff9ZnYHcDvwWtHhlrv7u+W+T1NiZFvU1BbldHd1csrM6CkqCiOby82DVAgcUWXqnRyvHppYT7Im6ZQYmitJJkXpfElxs5pGKVw8gUQB5uFrz+O2zbsjZ1c14ECZ1d4mW63zRolMBs2VJE1VOq//wFAu9uJdqjhBWyko3Lisl9VLe2KfKprdbKP1DaQVKTBIQ6xe2sPgLw/zg+feTBQcKiVoe4K7b8gv45kbGcUgdGxNfyFSGwUGSUVpk8nF58znmVcPTXjv5JO+4+70dHdx9NhxjhyNX/msXN7gjoE9oUDjcDI4lAYONeWIJKccg9St2mQzlM8jJN0X1zTVYcZf/O6Xyn5ewUHakXIM0jBJB7QVK+QRCj2GyiVoo/ZdtH57bJPUuDu3/3gPszqnVb2+g4goMEgKah2wlRsZDTXzPHTteRMu2HHJ20rfOTo2HhusynV9FZGMTIkhra3Wnj8GFWdcTfs7C9+ryexE4ikwSGJxM4UmmbqiVGkPIqhuHqEk39nd1Rk5fbeD5isSKUOBQRIpXUYzNzLKbZt3c8fAngnrKPR0d3Hjst6y7+PyA0mbpUqnyygNAF2dHdx15bl1f49IO1KOQRKJSjA7+bmO+s6cV/VArsLYg1LVNBEVf2fcCOOsDnwTyTIFBkkk7g670CxTbS+fdSvOjuxKWuuAtLjAlPb3iLQDBQZJ5PTurtjePLU0yxQu4pM9j1CjvkdkKtEAN0mk3FxHzZzBVESSSzrATclnSWT10h5uWNYbmeRVs4zI1KKmJEns3tVL6DtzXmyzjKaYFpkaFBikKnFJXi18LzJ1KDBIKsotfF+6LoOeKkSyTYFBUpFk4fu0nyoUZEQmh5LPkookC9+Xe6qoVtRI7GrmWhKReAoMkoqouYtKeywleapIKs0gIyJhakpqU2k3wyQZSBY3SK6W6SnSDDIiEqbA0IYmqwdRpfmS0pyeIs0gIyJhakpqQ3HNMH/8+IuT2kYfNQtrrctsJmm6EpHapPLEYGYrgf8OdADfcff1JftnAv8HOB94H7jW3d8I9t0O3ASMA//Z3belUSeJF9fcUlgSE/IX8cno9VPtLKzljgOaA0lkMtQ9V5KZdQC/AC4DDgI7gevc/eWiMn8EfNHd/9DM1gC/4+7Xmtli4DHgAuB04GngC+5edgFhzZVUn6X3/JQjR8fKlpk7u5MPPz7O2IlP/z66OjtqvsMXkeZr5FxJFwDD7r7f3Y8Bm4BVJWVWARuD108Al5qZBds3ufsn7n4AGA6OJ5NkYCjHhx8fr1juyNGxUFAA9foRaRdpNCX1AG8VvT8IXBhXxt2Pm9kHwGnB9udKPqvb0QhpNes8uG3fhAt+NdTrR2Tqa5leSWZ2M3AzQG9vb5NrU7taLvBp9iKq98KuXj8iU18aTUk54Iyi9wuCbZFlzGw6MId8EjrJZwFw9w3u3ufuffPnz0+h2o0XNVr31s27Oe/un5btDZTmYK56Luzq9SPSHtIIDDuBs8xskZnNANYAW0rKbAHWBq+vAbZ7Puu9BVhjZjPNbBFwFvCPKdQpk6Iu8AAjo2Nlp3NIczBXXDfPG5f1Ttje2WF0d3XW3bVURFpL3U1JQc7gFmAb+e6q33P3vWZ2DzDo7luA7wLfN7Nh4DD54EFQ7nHgZeA48J8q9UhqZeUu5FEzkRakOZirXDfPcmstiEj70NKeDXTR+u2x6yYDGHBg/RUTtpfmGEBdR0WkelraM4OimnGKxT0BpDliWESkkpbplTQVFC7kd/9k74QBZpUSu2mNGBYRqUSBYZJFdU8dunO5FpkRkcxSYJhElcYfKBCISBYpxzCJtJiMiLQiBYZJpMVkRKQVKTBMoiTrIIuIZI0CwyTSYjIi0oqUfJ5EWkxGRFqRAsMkU+8jEWk1akoSEZEQBQYREQlRYBARkRAFBhERCVFgEBGREAUGEREJUXfVlGi2VBGZKhQYUlBpFtVmUsASkWqpKSkFWZ1FtRCwciOjOJ8GrIGhXFPrJSLZpsCQgqzOoprVgCUi2abAkIKszqKa1YAlItmmwJCCrM6imtWAJSLZpsCQgtVLe7jvqiX0dHdhQE93F/ddtaTpSd6sBiwRyba6eiWZ2TxgM7AQeAP4XXc/ElFuLXBH8PZed99oZrOBHwK/BowDP3H3/nrq00xZnEVV036LSC3M3Wv/sNkDwGF3X29m/cBcd/9mSZl5wCDQBziwCzgf+AS40N2fMbMZwM+AP3P3v630vX19fT44OFhzvUVE2pGZ7XL3vkrl6m1KWgVsDF5vBFZHlFkBPOXuh4OniaeAle5+1N2fAXD3Y8ALwII66yMiInWqNzB81t3fCV7/E/DZiDI9wFtF7w8G204ys27ga+SfGiKZ2c1mNmhmg4cOHaqv1iIiEqtijsHMngZ+JWLXt4rfuLubWdXtUmY2HXgM+Ct33x9Xzt03ABsg35RU7feIiEgyFQODu381bp+Z/bOZfc7d3zGzzwHvRhTLAV8per8A+Pui9xuA19z94UQ1FhGRSVVvU9IWYG3wei3wNxFltgHLzWyumc0FlgfbMLN7gTnArXXWQ0REUlJvYFgPXGZmrwFfDd5jZn1m9h0Adz8M/CmwM/i5x90Pm9kC8s1Ri4EXzGy3mf1+nfUREZE61dVdtVnUXVVEpHqN6q4qIiJTjAKDiIiEKDCIiEiIAoOIiIQoMIiISIgCg4iIhCgwiIhIiAKDiIiEKDCIiEiIAoOIiIQoMIiISIgCg4iIhCgwiIhIiAKDiIiEKDCIiEiIAoOIiIQoMIiISIgCg4iIhCgwiIhIiAKDiIiEmLs3uw5VM7NDwC9TOtxngPdSOlaW6Lxai86rtbTqeZ3p7vMrFWrJwJAmMxt0975m1yNtOq/WovNqLVP1vArUlCQiIiEKDCIiEqLAABuaXYFJovNqLTqv1jJVzwtQjkFEREroiUFEREKmfGAws3lm9pSZvRb8Ozem3NqgzGtmtjbYNtvMtprZq2a218zWN7b2kfVcaWb7zGzYzPoj9s80s83B/ufNbGHRvtuD7fvMbEUj611JredlZpeZ2S4z2xP8e0mj615OPb+vYH+vmX1oZt9oVJ2TqPPv8Itm9mzwf2qPmc1qZN3LqePvsNPMNgbn84qZ3d7ouqfK3af0D/AA0B+87gfujygzD9gf/Ds3eD0XmA1cHJSZAfwcuLyJ59IBvA78alCfF4HFJWX+CPgfwes1wObg9eKg/ExgUXCcjmb/flI4r6XA6cHrfwPkmn0+aZxX0f4ngB8C32j2+aT0+5oOvAR8KXh/2hT5O7we2BS8ng28ASxs9jnV+jPlnxiAVcDG4PVGYHVEmRXAU+5+2N2PAE8BK939qLs/A+Dux4AXgAUNqHOcC4Bhd98f1GcT+fMrVny+TwCXmpkF2ze5+yfufgAYDo6XBTWfl7sPufvbwfa9QJeZzWxIrSur5/eFma0GDpA/ryyp57yWAy+5+4sA7v6+u483qN6V1HNeDpxiZtOBLuAY8C+NqXb62iEwfNbd3wle/xPw2YgyPcBbRe8PBttOMrNu4GvAzyajkglVrGdxGXc/DnxA/q4syWebpZ7zKnY18IK7fzJJ9axWzedlZqcC3wTubkA9q1XP7+sLgJvZNjN7wcz+pAH1Taqe83oC+Ah4B3gT+HN3PzzZFZ4s05tdgTSY2dPAr0Ts+lbxG3d3M6u6G1ZwF/AY8Ffuvr+2WspkMrNzgfvJ35FOBXcBD7n7h8EDxFQxHfgN4NeBo8DPzGyXuzfzhisNFwDjwOnkm6F/bmZPt+r1YkoEBnf/atw+M/tnM/ucu79jZp8D3o0olgO+UvR+AfD3Re83AK+5+8MpVLceOeCMovcLgm1RZQ4GAW0O8H7CzzZLPeeFmS0A/hr4PXd/ffKrm1g953UhcI2ZPQB0AyfM7GN3//bkV7uies7rIPAP7v4egJk9CXyZ5j6JF9RzXtcDf+fuY8C7ZrYD6COfr2w57dCUtAVYG7xeC/xNRJltwHIzmxv0WloebMPM7iX/y7+1AXWtZCdwlpktMrMZ5JNfW0rKFJ/vNcB2z2fEtgBrgl4Vi4CzgH9sUL0rqfm8gia+reQ7GOxoWI2Tqfm83P033X0+qcwaAAAA9UlEQVShuy8EHgb+LCNBAer7O9wGLLF8j7/pwG8BLzeo3pXUc15vApcAmNkpwDLg1YbUejI0O/s92T/k2/9+BrwGPA3MC7b3Ad8pKvcfyCdkh4F/H2xbQD6p9AqwO/j5/Safz28DvyDfe+JbwbZ7gCuD17PI92IZJn/h/9Wiz34r+Nw+mti7Ks3zAu4g37a7u+jnXzf7fNL4fRUd4y4y1Csphb/DG8kn1P8f8ECzzyWlv8NTg+17yQe6dc0+l3p+NPJZRERC2qEpSUREqqDAICIiIQoMIiISosAgIiIhCgwiIhKiwCAiIiEKDCIiEqLAICIiIf8f3Zx3aS7ALQ4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(recons[:,0], raw_returns[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 549,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f680bc88470>]"
      ]
     },
     "execution_count": 549,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(recons[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PPCA Step By Step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(120, 20)"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "scaler.fit(raw_returns)\n",
    "returns = scaler.transform(raw_returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw = returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "min_obs = 10   # we need this many samples for a column to be valid\n",
    "d = 3          # number of dimensions we want reduced to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set any infinite values to the maximum single value; np.isinf does not change np.nan items\n",
    "raw[np.isinf(raw)] = np.max(raw[np.isfinite(raw)])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [],
   "source": [
    "# find the columns that are valid\n",
    "\n",
    "valid_series = np.sum(~np.isnan(raw), axis=0) >= min_obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True])"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valid_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = raw[:, valid_series].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = data.shape[0]\n",
    "D = data.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "observed = ~np.isnan(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       ...,\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True],\n",
       "       [ True,  True,  True, ...,  True,  True,  True]])"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "missing = np.sum(~observed)  # count of missing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set all the nan's to zero\n",
    "data[~observed] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialize with random numbers\n",
    "C = np.random.randn(D, d)    # these are the betas I think"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [],
   "source": [
    "CC = np.dot(C.T, C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.dot(np.dot(data, C), np.linalg.inv(CC))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "reconst = np.dot(X, C.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [],
   "source": [
    "reconst[~observed] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_sq = np.sum((reconst - data)**2)/(N*D - missing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0 = np.inf\n",
    "counter = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.02150492  0.5079911   0.67628206]\n",
      " [-0.02082786  0.49199737  0.65498982]\n",
      " [-0.02072448  0.4895555   0.65173899]\n",
      " [-0.02054025  0.48520356  0.64594531]\n",
      " [-0.02048523  0.48390383  0.64421499]\n",
      " [-0.02070666  0.48913439  0.65117837]\n",
      " [-0.02163598  0.5110869   0.68040346]\n",
      " [-0.02083183  0.49209123  0.65511477]\n",
      " [-0.0209784   0.49555351  0.65972406]\n",
      " [-0.02125682  0.50213031  0.66847967]\n",
      " [-0.02008275  0.47439637  0.63155783]\n",
      " [-0.02066371  0.48811984  0.64982771]\n",
      " [-0.01980392  0.46780987  0.6227893 ]\n",
      " [-0.02038977  0.48164888  0.641213  ]\n",
      " [-0.02032137  0.48003317  0.63906202]\n",
      " [-0.01999656  0.47236046  0.62884745]\n",
      " [-0.01977814  0.46720091  0.62197861]\n",
      " [-0.02058571  0.48627746  0.64737498]\n",
      " [-0.02053916  0.48517784  0.64591106]\n",
      " [-0.02173866  0.51351252  0.68363266]]\n",
      "[[ 0.68409913  0.61336915 -0.85144902 ... -0.20547635  0.71162305\n",
      "   0.12548436]\n",
      " [ 0.17617702  0.86257838  0.27557288 ...  1.3912325  -0.07717596\n",
      "   0.29154601]\n",
      " [-0.11037744 -0.18899931 -0.89000641 ...  0.12665923 -0.22492831\n",
      "   0.68364549]\n",
      " ...\n",
      " [ 0.00516407  0.16615022 -0.65075397 ... -0.38426488 -0.14368956\n",
      "  -0.60691628]\n",
      " [-0.15998068  0.00976164  0.35117634 ...  0.31600742  0.76890072\n",
      "   1.02993319]\n",
      " [-1.15820397 -0.07112338  0.90661316 ... -0.5714833  -0.96568921\n",
      "  -1.17865735]]\n",
      "[[-0.23256325 -0.18487822 -0.23227229]\n",
      " [-0.22524116  0.18394518 -0.09664217]\n",
      " [-0.22412325  0.05724207 -0.13327922]\n",
      " [-0.22213089 -0.25077958  0.11518472]\n",
      " [-0.22153586  0.17624206  0.38148869]\n",
      " [-0.22393047  0.10314078  0.17788837]\n",
      " [-0.23398053  0.01051856 -0.08441828]\n",
      " [-0.22528413  0.28256429 -0.12287426]\n",
      " [-0.2268692  -0.22018249 -0.09481205]\n",
      " [-0.22988012 -0.20586662  0.01740553]\n",
      " [-0.21718326 -0.16730484 -0.46545239]\n",
      " [-0.22346599 -0.08317757  0.26421552]\n",
      " [-0.21416789 -0.26066196  0.09079655]\n",
      " [-0.22050352  0.48491131  0.00155507]\n",
      " [-0.21976384  0.3391507  -0.12862441]\n",
      " [-0.2162512  -0.1141393   0.43730852]\n",
      " [-0.21388911 -0.27962528 -0.31551097]\n",
      " [-0.22262254  0.2391127  -0.13714282]\n",
      " [-0.22211912 -0.21012798  0.26845716]\n",
      " [-0.23509101  0.08797891  0.06383225]]\n",
      "[[ 1.42118163e+01  4.34304351e-16 -5.65140838e-16]\n",
      " [ 4.34304351e-16  5.72119294e-01  1.11362555e-03]\n",
      " [-5.65140838e-16  1.11362555e-03  5.34416649e-01]]\n"
     ]
    }
   ],
   "source": [
    "from scipy.linalg import orth\n",
    "\n",
    "for i in np.arange(1,50):\n",
    "    Sx = np.linalg.inv(np.eye(d) + CC/sum_sq)\n",
    "    \n",
    "    # e-step\n",
    "    ss0 = sum_sq\n",
    "    if missing > 0:   # if we have any missing data, project it from our current known betas and factor returns\n",
    "        proj = np.dot(X, C.T)\n",
    "        data[~observed] = proj[~observed]\n",
    "    X = np.dot(np.dot(data, C), Sx)/ sum_sq\n",
    "\n",
    "    # m-step\n",
    "    XX = np.dot(X.T, X)\n",
    "    C = np.dot(np.dot(data.T, X), np.linalg.pinv(XX + N*Sx))\n",
    "    CC = np.dot(C.T, C)\n",
    "    reconst = np.dot(X, C.T)\n",
    "    reconst[~observed] = 0\n",
    "    ss = (np.sum((reconst-data)**2) + N*np.sum(CC*Sx) + missing*ss0)/(N*D)\n",
    "    \n",
    "    # calc diff\n",
    "    det = np.log(np.linalg.det(Sx))\n",
    "    if np.isinf(det):\n",
    "        det = abs(np.linalg.slogdet(Sx)[1])\n",
    "    \n",
    "    # trace is sum of diag\n",
    "    v1 = N*(D*np.log(ss) + np.trace(Sx) - det) + np.trace(XX) - missing*np.log(ss0)\n",
    "    diff = abs(v1/v0 - 1)\n",
    "    counter += 1\n",
    "    v0 = v1\n",
    "\n",
    "print(C)\n",
    "print(data)\n",
    "\n",
    "C = orth(C)   # make orthnormal basis\n",
    "print(C)\n",
    "\n",
    "covmat = np.cov(np.dot(data, C).T) \n",
    "\n",
    "print(covmat)\n",
    "\n",
    "vals, vecs = np.linalg.eig(covmat)\n",
    "order = np.flipud(np.argsort(vals))\n",
    "vecs = vecs[:, order]\n",
    "vals = vals[order]\n",
    "\n",
    "C = np.dot(C, vecs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00855054, -0.2019816 , -0.26889552],\n",
       "       [-0.2019816 ,  4.7712265 ,  6.35187292],\n",
       "       [-0.26889552,  6.35187292,  8.45616731]])"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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