stacking_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "extra-bearing",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from stacking_fmri import stacking_CV_fmri, stacking_fmri\n",
    "from ridge_tools import R2\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "confidential-punch",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Set up or load features\n",
    "\n",
    "N_sample = 1000\n",
    "dim_X1 = 50\n",
    "dim_X2 = 100\n",
    "dim_X3 = 25\n",
    "\n",
    "X1 = np.random.randn(N_sample, dim_X1)\n",
    "X2 = np.random.randn(N_sample, dim_X2)\n",
    "X3 = np.random.randn(N_sample, dim_X3)\n",
    "\n",
    "#X1 = np.load('....')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "boring-occurrence",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Set up or load brain data (fMRI, EEG, ....)\n",
    "\n",
    "dim_Y = 10\n",
    "\n",
    "# Y = np.random.randn(N_sample, dim_Y)\n",
    "Y = 0.3 * X1.dot(np.random.randn(dim_X1, dim_Y)) + \\\n",
    "    0.3 * X2.dot(np.random.randn(dim_X2, dim_Y)) + \\\n",
    "    0.4 * X3.dot(np.random.randn(dim_X3, dim_Y))\n",
    "\n",
    "#Y = np.load('....')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "buried-charger",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 250)\n",
      "(3, 250)\n",
      "(3, 250)\n",
      "(3, 250)\n"
     ]
    }
   ],
   "source": [
    "### Run stacking using multiple features (Xs) and Y\n",
    "\n",
    "\n",
    "## with the outermost cross-validation\n",
    "r2s, stacked_r2s, _, _, _, S_average = stacking_CV_fmri(Y, [X1,X2,X3], method = 'cross_val_ridge',n_folds = 4,score_f=R2)",
    "\n",
    "\n",
    "## simple train-test setting (without the outermost cross-validation)\n",
    "# r2s, stacked_r2s, _, _, _, S_average = stacking_fmri(Y[0:700], Y[700:], [X1[0:700],X2[0:700],X3[0:700]], [X1[700:],X2[700:],X3[700:]], method = 'cross_val_ridge',score_f=R2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "chinese-sussex",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of r2s is (number of features, dim_Y), that is (3, 10)\n",
      "shape of stacked_r2s is (dim_Y, ), that is (10,)\n",
      "shape of S_average is (dim_Y, num of features), that is (10, 3)\n"
     ]
    }
   ],
   "source": [
    "### Results\n",
    "\n",
    "## r2s: voxelwise R2(predictions using only one feature, data)\n",
    "print('shape of r2s is (number of features, dim_Y), that is', r2s.shape)\n",
    "\n",
    "## stacked_r2s: voxelwise R2(stacking predictions using all features, data)\n",
    "print('shape of stacked_r2s is (dim_Y, ), that is', stacked_r2s.shape)\n",
    "\n",
    "## S_average: optimzed voxelwise stacking weights showing how different features are combined\n",
    "print('shape of S_average is (dim_Y, num of features), that is', S_average.shape)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "curious-blanket",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Prediction Performance')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "\n",
    "bar_width = 0.2\n",
    "index_0 = np.arange(dim_Y)\n",
    "index_1 = index_0 + bar_width\n",
    "index_2 = index_1 + bar_width\n",
    "index_3 = index_2 + bar_width\n",
    "\n",
    "\n",
    "plt.bar(index_0, stacked_r2s, width=bar_width, label='Stacking of X1,2,3')\n",
    "plt.bar(index_1, r2s[0,:], width=bar_width, label='X1')\n",
    "plt.bar(index_2, r2s[1,:], width=bar_width, label='X2')\n",
    "plt.bar(index_3, r2s[2,:], width=bar_width, label='X3')\n",
    "plt.legend()\n",
    "plt.xlabel('Voxel ID')\n",
    "plt.ylabel('R2')\n",
    "plt.title('Prediction Performance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "smoking-merchant",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.YTick at 0x7fd499373150>,\n",
       "  <matplotlib.axis.YTick at 0x7fd4a956ab50>,\n",
       "  <matplotlib.axis.YTick at 0x7fd4680841d0>],\n",
       " [Text(0, 0.5, 'X1'), Text(0, 1.5, 'X2'), Text(0, 2.5, 'X3')])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(S_average.T, vmin=0, vmax=1)\n",
    "plt.xlabel('Voxel ID')\n",
    "plt.ylabel('Feature')\n",
    "plt.yticks([0.5,1.5,2.5],['X1', 'X2', 'X3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "answering-fireplace",
   "metadata": {},
   "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}