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@arokem
Created January 24, 2017 05:29
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We consider the problem of fitting a PRF (population receptive field) to an EEG response. \n",
"\n",
"Let's assume that the response of an EEG component shows some preference towards some particular stimuli from a collection. We will estimate a regularized GLM for this component, to find the coefficients corresponding to these stimuli, and to a particular response characteristic of this component.\n",
"\n",
"We start with some generic imports:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll create a simulation with the following parameters:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"Fs = 1000 \n",
"duration = 10 * 60\n",
"ITI = 20 \n",
"n_trials = duration/ITI"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Time will be as following:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"t = np.linspace(0, duration, Fs * duration)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's assume that we have a set of ten different stimuli:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n_stimuli = 10"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This time-series will contain the number of each stimulus at the time point in which this stimulus was presented:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"stim_tseries = np.zeros(t.shape[0])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"stim = 1\n",
"for xx in range(int(n_trials)):\n",
" stim_tseries[xx * ITI * Fs] = stim\n",
" stim = np.mod(stim + 1, n_stimuli + 1)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x107322710>]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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fLBkzfr6IqxkHoF4v0I5gX9dQea5yEQD3AGhX1f+0VyQiCpX5tSuM6nrI00K/HMCnAFwh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\nEgx0IqJIMNCJiCLBQCciisT/A3DgmOhstMP3AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10698f1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(stim_tseries)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will use a Vandermonde function as the basis set to represent the responses of EEG components. This is a set of hermitian polynomials with a duration much smaller than the full time series (here 0.2 seconds)\n",
"\n",
"Each column of this matrix contains a polynomial function with different waveform, and the are all orthonormal."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/arokem/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:5: DeprecationWarning: object of type <class 'float'> cannot be safely interpreted as an integer.\n"
]
},
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x108c2f6a0>,\n",
" <matplotlib.lines.Line2D at 0x108c2f8d0>,\n",
" <matplotlib.lines.Line2D at 0x108c2fac8>,\n",
" <matplotlib.lines.Line2D at 0x108c2fcc0>,\n",
" <matplotlib.lines.Line2D at 0x108c2feb8>,\n",
" <matplotlib.lines.Line2D at 0x108c330f0>,\n",
" <matplotlib.lines.Line2D at 0x108c332e8>,\n",
" <matplotlib.lines.Line2D at 0x108c334e0>,\n",
" <matplotlib.lines.Line2D at 0x108c336d8>,\n",
" <matplotlib.lines.Line2D at 0x108c338d0>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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NRk79XsSp3UVoVXrc/e3pNdyf8P5e2F4kxa+q0nJ6bzFnD5RQaTbx7TgXqmwEXokMYK6f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\nhUKhaIUyDAqFQqFoxf8D/WmoqBn14hsAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1069c1c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from numpy.polynomial.hermite import hermvander\n",
"\n",
"vander_duration = 0.2\n",
"\n",
"vander_t = np.linspace(-1, 1, Fs * vander_duration)\n",
"\n",
"vander_i = 10\n",
"vander = hermvander(vander_t, vander_i)\n",
"vander = vander / np.sqrt(np.sum(vander**2, 0))\n",
"vander = vander[: , 1:]\n",
"\n",
"plt.plot(vander_t, vander)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Preallocate the design matrix:\n",
"X = np.zeros((stim_tseries.shape[0], n_stimuli * vander_i))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The design matrix contains the full Vandermonde matrix in the rows corresponding to the timing of each of the stimuli:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"for idx in np.where(stim_tseries > 0)[0]:\n",
" X[idx:idx+vander.shape[0], \n",
" int((stim_tseries[idx] -1) * vander_i):int((stim_tseries[idx]) * vander_i)] = vander"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider the case in which the EEG component in questions is sensitive to several stimuli, with a waveform made out of various Vandermonde components (and different components for each stimulus!)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"beta = np.zeros(X.shape[-1])\n",
"beta[8] = 1\n",
"beta[9] = 2\n",
"beta[28] = 0.5\n",
"beta[35] = 1"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Add noise to the output:\n",
"noise = 0.01"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"true_y = X @ beta \n",
"y = true_y + np.random.randn(true_y.shape[0]) * noise"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x108e31a90>]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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pADRzzm0A8H43jbxJ0VErWV9xqMnaNqoT6yaIxL0jngQ2s2nAMUFm3RntxpjZ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\nEZ/6f49k/w9CqxyCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x108278940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following is a regression, with Tikhonov (ridge) regularization, where `lambda_` is a regularization parameter that sets the magnitude of regularization"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import scipy.linalg as la"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"lambda_ = 1"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ols_matrix = la.pinv(X.T @ X + lambda_ * np.eye(X.shape[1])) @ X.T"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following operation estimates the coefficients on different wave-form/stimulus combinations:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"beta_hat = ols_matrix @ y"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1295a4a20>]"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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+wz1t/I+ffUP+trMgbGtexEQ6y2efOsvv/uVxTk3G89X/y5Mx5pbT3HpoYM3x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\nShbJm6wlAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1294a8a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(beta_hat)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x14f655828>]"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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NSrpT0psHHumYtUoSnebqAWf8/WgF+1pFDvxmY5BnsXV12NYtyl0O3BoR2b/f90TEMUkv\nBj4v6f6I+OaKXyIdAA4A7NmzJ8ewRmupxt/W1VN1xt+v1nu5bcuUV+AyG4M8Gf9R4NzM/d3AsS7H\nXk5bmScijqX/Pgr8Lcvr/9njboyImYiY2blzZ45hjVa3Us9iV49P7ubWei+3ba454zcbgzyB/27g\nfEnnSZomCe4runMk/QSwHfi7zLbtkjalt3cAlwAPtT+2CJZO7rrGv1atstm2LVPUG03CVz2bjVTP\nUk9ENCRdBdwGVIGDEfGgpOuA2YhofQlcAdwSy/8vfgnwQUlNki+Z92a7gYpkqcbfuaun4T7+3BZL\nPZunAJhbWHlhnJmtnzw1fiLiMHC4bdu72+7/QYfHfRn46TWMb8NYLPV0m6vHGX9ui6WeLbX0vgO/\n2Sj5yt2cupV6qi719G2x1JNm/L6Iy2y0HPhz6l7jb53cdeDPK9vVk9x3Z4/ZKDnw59RqO+xa43dX\nT27Zrp7kvt87s1Fy4M+pa8bvaZn71novz3Kpx2wsHPhz6jVXj2v8+bX+elo6uetSj9koOfDn1LOr\nx+2cubW3c7rUYzZaDvw5tcoR01V39azVilKPA7/ZSDnw51RvNJmuVqhUlk9d5K6e/tUbC9QqYut0\nUjbzfD1mo+XAn1On9XbBXT2DqM83ma5V2JyWzZzxm42WA39Oc43mivo++MrdQdTTJSxbJ8od+M1G\ny4E/p27TCrjG37/kr6fq4l9Q7uoxGy0H/pzqHRZaB/fxD6Ke/vW0mPG7j99spBz4c6rPLzC9ao3f\ngT+v+nxa6nGN32wsHPhzSrLUlaWexa6eBQevvFqlnlZrrEs9ZqPlwJ9T764eZ/x5tcpmlYqYrlac\n8ZuNmAN/Tl1r/O7q6Vs90yG1qVZxjd9sxHIFfkn7JD0i6Yikqzvs/zVJxyXdm/68I7PvSknfSH+u\nHObgRympS7urZxhapR5IpsBwqcdstHquwCWpClwPvI5k4fW7JR3qsITixyLiqrbHngNcC8wAAdyT\nPvYHQxn9CNUbC+7jH5LWyV1IJr1zqcdstPJk/BcDRyLi0YiYA24B9ud8/tcDt0fEiTTY3w7sG2yo\n49Wt1DMJGf+Tz9b5Yb0xtOfLvpebaq7xm41ansC/C3gsc/9ouq3dL0m6T9Ktks7t87FIOiBpVtLs\n8ePHcwxrtLpdwCWJakUslHjKhl/50F380W2PDO35sqWe6VrFc/WYjViewK8O29rT2/8J7I2IlwH/\nC/hIH49NNkbcGBEzETGzc+fOHMMarfp8564eSLL+Mmf8333qFN996tTQnm/Zyd0pl3rMRi1P4D8K\nnJu5vxs4lj0gIr4fEfX07n8H/mnexxZFvctcPZDU+ZslDfzNZvBsvcHJU/NDe87lNX6f3DUbtTyB\n/27gfEnnSZoGLgcOZQ+Q9ILM3TcBD6e3bwMuk7Rd0nbgsnRboURE11IPlDvjf6beIAJOnh5mjT/T\n1eMav9nI9ezqiYiGpKtIAnYVOBgRD0q6DpiNiEPAb0l6E9AATgC/lj72hKT3kHx5AFwXESfW4XWs\nq7mFzuvtttQqKm1XTyvTH1bG31ho0gyWdfWc+OHcUJ7bzPLpGfgBIuIwcLht27szt68Bruny2IPA\nwTWMcey6LbTeUq1USpvxnzw9v+zftVp8Lxdr/M74zUbNV+7m0LqytNNcPZBm/CVdc/fkqaTE82y9\nMZTzGO2L1rvGbzZ6Dvw5LC60PoFdPa1MPyKp969V+3u5qVb1lA1mI+bAn0OvUk+tWt4+/mxtfxh1\n/qW/nnwBl9m4OPDnsBisJjLjb2RuDyHwt5d6PFeP2cg58OewVJ5YpcZf1sC/LONfh1JPOi1zRDnf\nP7ONyIE/h16lnorKnPHPd7w9qJUZf5UImC/pyXGzjciBP4f2FsR2SY2/nIHrmdMNpKXba9Wpxg9e\nhctslBz4c2hNItb9yt0S9/Gfmuf52zYv3l6rlV09XnfXbNQc+HPo2dVT4tk5T56e54Vnb1m8vVYr\n+/iry7ab2fpz4M+hPVi1q1ZEo6Q16pOnGmzfOs2Zm2rrc3I3Lfl4amaz0XHgz2GuV42/zF09p+fZ\ntqXGts214WT8XWv8zvjNRsWBP4eJvnL31DzbNk+xbcvUkGr8LvWYjZsDfw69Sj1lzfibzeCZeoNt\nW6bYtnlqSDX+Lid3XeoxGxkH/hxa5YnpCZud89m5ZC7+bZtrbNsypBp/21XQizV+Z/xmI+PAn0O9\nscBUVYsLq7cra1dPq7Qz3Iy/SbUiatWlSdpa281sNBz4c1ht9S2AarWcNf5Whp9k/MOq8S9fu9gX\ncJmNXq7AL2mfpEckHZF0dYf9/0bSQ5Luk/Q5SS/K7FuQdG/6c6j9sUXQHqzalbXG38rwt22eYtvm\nGs8MYU7+5Es0G/jTjN9TM5uNTM8VuCRVgeuB15Esnn63pEMR8VDmsK8CMxHxI0m/Cfwn4JfTfaci\n4oIhj3uksouDd1LWPv5lpZ4tU0Qkdf9tm6cGfs7kvVz668k1frPRy5PxXwwciYhHI2IOuAXYnz0g\nIr4QET9K794J7B7uMMer3mh2XX0Lypzxt0o9U4vBfq3lnnpjYdn1EC71mI1ensC/C3gsc/9ouq2b\ntwOfztzfLGlW0p2S3tztQZIOpMfNHj9+PMewRqdXqaesXT1LGX+NszbX0m1r6+zpWupxxm82MnkW\nW+/UytIxykn6FWAGeHVm856IOCbpxcDnJd0fEd9c8YQRNwI3AszMzGyoKNoerNqVtaunNRvnmZuS\nk7vJtrVm/MtLPdOLffzle//MNqo8Gf9R4NzM/d3AsfaDJL0W+H3gTRFRb22PiGPpv48CfwtcuIbx\njkV7XbpdWa/cPXl6njM31ahVK0ulnjVOzdz+11O1IqaqcqnHbITyBP67gfMlnSdpGrgcWNadI+lC\n4IMkQf+JzPbtkjalt3cAlwDZk8KF0F6XblfaGv+pebalJZ5tW2qL29aiPt9c8V5uqlVd6jEboZ6l\nnohoSLoKuA2oAgcj4kFJ1wGzEXEI+CPgTOAvlaza8Z2IeBPwEuCDkpokXzLvbesGKoR6o8k5Z6xS\n4y9rH//p+cUSz1LGv/ZST+t8QUuy4LozfrNRyVPjJyIOA4fbtr07c/u1XR73ZeCn1zLAjaDXBVzl\nzfiXWjeHd3J3YcV7ualWcY3fbIR85W4Oebp6FppRugXDW1MyA9SqFc6Yrg4l419R6plyqcdslBz4\nc+hUl86qpXP4lC3rP3l6ftnFWsOYtqHTxXAu9ZiNlgN/Dj3n6kkDf9nq/CdPNZbV44cxUVvXUo8z\nfrORceDPIc9cPVCujL/ZDJ7JnNwFhjI1c6drIjbVqq7xm42QA38PEUG90ew6Fz+UM+P/4VyDZrC8\n1DOUjL9Tjd+lHrNRcuDvYX4hiOi+7CKUM+NfnKdnS6bUs2Vtgb+x0GShGStKPdNVl3rMRsmBv4el\npQJXm48/eRsbJZq2YXGenmUZ/9pKPUtLWHbK+Mvz3pltdA78PSwGqwnr6slOydyybcsUz5yeH3hO\n/rlugb9WXdxnZuvPgb+Hbllq1mKNv0Rz8menZG7ZtnmKZiT1/0EsfYl26upxjd9sVBz4e6jP9y71\nlDHjb83CubzGX0v3DRr4W+9lpz5+Z/xmo+LA38PcQh8Zf4kCf+ca/9rm61n666kt459yO6fZKDnw\n99AKSKvX+JN9Zcr4W6We7AVcZy2uwjVgxj/frcaflHrKNuWF2UblwN9Dtyw1aynjL0/WevLUPGdM\nV6lVl/4TWevUzIulnhXTMldoRrn+YjLbyBz4e+hWl84qY43/5On5xQy/Zd1KPV5+0WykHPh7WCpP\nrNbHX8Yaf2PZiV1Yau1cc8bfoY8flk6km9n6yhX4Je2T9IikI5Ku7rB/k6SPpfvvkrQ3s++adPsj\nkl4/vKGPxsT28bfNzAmZOfkH7erpcr6k9UXgjN9sNHoGfklV4HrgDcBLgSskvbTtsLcDP4iIfwy8\nD/jD9LEvJVmq8SeBfcCfps9XGHlKPeXs418+QRvAVLXC1unqGjJ+l3rMNoI8Gf/FwJGIeDQi5oBb\ngP1tx+wHPpLevhX4OSVrMO4HbomIekR8CziSPl9h5Dm5W8qunlONxfV2s9YyUdtqffzZ/Wa2vvIs\nvbgLeCxz/yjwim7HpGv0Pg08J91+Z9tjdw082h5+4b99idNDrhM/lWa3eWbn/HefuI+t04X6g6ar\n7z51ilf/+M4V27dtqfHp+7/HV7/zVN/P2e29bJV+fuOjs2xe5QvWrOy2b53m4//qVev+e/IEfnXY\n1p7adjsmz2OTJ5AOAAcA9uzZk2NYK/2jnWcsXnA1TLvO3sL2rVNd97/kBWfxyzPn8kx9bVMWbyQ/\n/vyz+MWLVn5H/8Y/fzFfeOSJgZ/3hT+2heecMb1s20V7tvNLF+3m1Pza5vo3K7r282rrRb0umpH0\nKuAPIuL16f1rACLiP2aOuS095u8k1YDvATuBq7PHZo9b7XfOzMzE7OzswC/KzGzSSLonImbyHJun\nxn83cL6k8yRNk5ysPdR2zCHgyvT2W4DPR/KNcgi4PO36OQ84H/j7PAMzM7P10bPUk9bsrwJuA6rA\nwYh4UNJ1wGxEHAI+DPyZpCPACZIvB9LjPg48BDSAd0aEz+CZmY1Rz1LPOLjUY2bWn2GXeszMrEQc\n+M3MJowDv5nZhHHgNzObMA78ZmYTZkN29Ug6DvzDgA/fATw5xOEUwSS+ZpjM1z2Jrxkm83X3+5pf\nFBEr51npYEMG/rWQNJu3paksJvE1w2S+7kl8zTCZr3s9X7NLPWZmE8aB38xswpQx8N847gGMwSS+\nZpjM1z2Jrxkm83Wv22suXY3fzMxWV8aM38zMVlGawN9rQfiykHSupC9IeljSg5LelW4/R9Ltkr6R\n/rt93GMdNklVSV+V9Dfp/fMk3ZW+5o+l04aXiqSzJd0q6WvpZ/6qsn/Wkn4n/W/7AUk3S9pcxs9a\n0kFJT0h6ILOt42erxPvT+HafpIvW8rtLEfhzLghfFg3gdyPiJcArgXemr/Vq4HMRcT7wufR+2bwL\neDhz/w+B96Wv+QfA28cyqvX1X4HPRMQ/AV5O8vpL+1lL2gX8FjATET9FMhX85ZTzs74J2Ne2rdtn\n+waS9UzOJ1mp8ANr+cWlCPzkWxC+FCLi8Yj4Snr7GZJAsIvlC95/BHjzeEa4PiTtBv4l8KH0voCf\nBW5NDynja94G/AuS9S6IiLmIeIqSf9Yk64RsSVfz2wo8Tgk/64i4g2T9kqxun+1+4KORuBM4W9IL\nBv3dZQn8nRaEX7dF3TcKSXuBC4G7gOdFxOOQfDkAzx3fyNbFfwF+D2gtqvwc4KmIaC3UW8bP/MXA\nceB/pCWuD0k6gxJ/1hHxXeA/A98hCfhPA/dQ/s+6pdtnO9QYV5bAn3tR97KQdCbwCeC3I+LkuMez\nniT9PPBERNyT3dzh0LJ95jXgIuADEXEh8ENKVNbpJK1p7wfOA14InEFS5mhXts+6l6H+916WwH8U\nODdzfzdwbExjWXeSpkiC/p9HxCfTzf+v9adf+u8T4xrfOrgEeJOkb5OU8X6W5C+As9NyAJTzMz8K\nHI2Iu9L7t5J8EZT5s34t8K2IOB4R88AngX9G+T/rlm6f7VBjXFkCf54F4UshrW1/GHg4Iv44syu7\n4P2VwF+PemzrJSKuiYjdEbGX5LP9fES8FfgC8Jb0sFK9ZoCI+B7wmKSfSDf9HMn61aX9rElKPK+U\ntDX9b731mkv9WWd0+2wPAW9Lu3teCTzdKgkNJCJK8QO8Efg68E3g98c9nnV8nT9D8ifefcC96c8b\nSWrenwO+kf57zrjHuk6v/1Lgb9LbLwb+HjgC/CWwadzjW4fXewEwm37efwVsL/tnDfwH4GvAA8Cf\nAZvK+FkDN5Ocx5gnyejf3u2zJSn1XJ/Gt/tJup4G/t2+ctfMbMKUpdRjZmY5OfCbmU0YB34zswnj\nwG9mNmEc+M3MJowDv5nZhHHgNzObMA78ZmYT5v8DCfE3P+kCBIkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1296dd550>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(beta)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x14f71ec50>]"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x14f673940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(beta, beta_hat, 'o')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Coefficients are detectable to the degree that they are outside of the distribution of spurious coefficients. Some of these are, and some are not (SNR-limited, I believe):"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x14f9221d0>,\n",
" <matplotlib.lines.Line2D at 0x14f922390>,\n",
" <matplotlib.lines.Line2D at 0x14f965940>,\n",
" <matplotlib.lines.Line2D at 0x14f965a58>]"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x14f730128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1)\n",
"ax.hist(beta_hat[beta==0], bins=20)\n",
"ylim = ax.get_ylim()\n",
"ax.plot([beta_hat[beta>0], beta_hat[beta>0]], [0, ylim[1]], color='r')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How well can we reconstruct the original EEG signal?"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"y_hat = X @ beta_hat"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x14f743470>]"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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SzM20a1a13/Tqmp/9OzRl01MjcDoNszYcYNyg9tRPca8eLRqksvK3Q9m0/yTv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\nAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x14f743e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(y)\n",
"plt.plot(y_hat)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the variance explained:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.48233345429813224"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.corrcoef(y, y_hat)[0, 1]"
]
},
{
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