Figures_Tables/main_text/Figure2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 2 \n",
    "## Variance of gene expression explained by IEAs as we variate the number of IEAs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"../../src/\")\n",
    "import IEA_model\n",
    "import numpy as np\n",
    "import torch\n",
    "import pandas as pd\n",
    "from torch.utils.data import DataLoader\n",
    "import utility\n",
    "\n",
    "from importlib import reload \n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from matplotlib import pyplot as plt "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/ocean/projects/asc170022p/juc91/anaconda/envs/IEA/lib/python3.7/site-packages/pandas/core/frame.py:3641: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  self[k1] = value[k2]\n"
     ]
    }
   ],
   "source": [
    "    data_train = utility.image_gene_dataset(train = True, cv = None)\n",
    "    data_test = utility.image_gene_dataset(train = False, cv = None)\n",
    "\n",
    "    train_loader = DataLoader(data_train)\n",
    "    test_loader = DataLoader(data_test)\n",
    "\n",
    "\n",
    "    sid_train, features_train, genes_train = data_train[:]\n",
    "    sid_test, features_test, genes_test = data_test[:]\n",
    "\n",
    "    sid_P1, features_P1 = utility.load_SSL_features_P1()\n",
    "    features_P1 = torch.tensor(features_P1)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "thold = 0.01\n",
    "\n",
    "df_genes = utility.load_gene_data()\n",
    "\n",
    "df = pd.read_csv(\"../../gene_list/THOLD_{}.txt\".format(thold))\n",
    "idx_gene = df[\"index\"].to_numpy()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_aligned_axes(L):\n",
    "    \"\"\"\n",
    "    Return the aligned axes.\n",
    "    L: The number of IEAs.\n",
    "    \"\"\"\n",
    "    \n",
    "    beta = .1\n",
    "    gamma = 1.0\n",
    "    \n",
    "    \n",
    "    Z_train_cv = []\n",
    "    Z_test_cv = []\n",
    "    Z_P1_cv = []\n",
    "\n",
    "\n",
    "    M = IEA_model.IEA( L = L,  idx_gene = idx_gene ).cuda()\n",
    "    # Generate the IEAs with the cross-valudation models\n",
    "\n",
    "    for cv in range(5):\n",
    "        filename = \"../../models/model_L{}_cv{}_beta{}_gamma{}_genes{}\".format(L, cv, beta, gamma, len(idx_gene))\n",
    "\n",
    "        M.load_state_dict( torch.load(filename) )\n",
    "\n",
    "        with torch.no_grad():\n",
    "            _, _, _, Z_train = M.forward( features_train.cuda(), non_prb = True )\n",
    "            Z_train_cv.append( Z_train.cpu().data.numpy() )\n",
    "\n",
    "            _, _, _, Z_test = M.forward( features_test.cuda(), non_prb = True  )\n",
    "            Z_test_cv.append( Z_test.cpu().data.numpy() )\n",
    "\n",
    "\n",
    "\n",
    "    Z_train_cv = np.array( Z_train_cv )\n",
    "    Z_test_cv = np.array( Z_test_cv )\n",
    "\n",
    "\n",
    "    Z_test_aligned = []\n",
    "    Z_train_aligned = []\n",
    "    \n",
    "    # Align the IEAs from models with different cross-validation.\n",
    "    for cv in range(0,5):\n",
    "        Z_cat = np.concatenate( [ Z_train_cv[ 0, :, : ], Z_train_cv[ cv, :, : ] ], axis = 1 )\n",
    "        corrcoef = np.corrcoef(Z_cat.T)\n",
    "\n",
    "\n",
    "        Z_test = []\n",
    "        Z_train = []\n",
    "        for lll in range(L):\n",
    "\n",
    "            corr_lll = corrcoef[lll, L:]\n",
    "            idx_lll = np.argmax( np.abs(corr_lll) )\n",
    "\n",
    "            mean = Z_train_cv[cv, :, idx_lll].mean()\n",
    "            std = Z_train_cv[cv, :, idx_lll].std()\n",
    "\n",
    "            if corr_lll[idx_lll]>0:\n",
    "                Z_train.append( ( Z_train_cv[cv, :, idx_lll] - mean ) / std  )\n",
    "                Z_test.append( ( Z_test_cv[cv, :, idx_lll] - mean ) / std  )\n",
    "            else:\n",
    "                Z_train.append( - ( Z_train_cv[cv, :, idx_lll] - mean ) / std  )                \n",
    "                Z_test.append( - ( Z_test_cv[cv, :, idx_lll] - mean) / std )\n",
    "\n",
    "        Z_train_aligned.append( np.array(Z_train).T  )\n",
    "        Z_test_aligned.append( np.array(Z_test).T )\n",
    "\n",
    "    Z_train_aligned = np.array(Z_train_aligned)\n",
    "    Z_test_aligned = np.array(Z_test_aligned)\n",
    "    \n",
    "    return Z_train_aligned, Z_test_aligned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_pairwise_corrcoef(axes, idx):\n",
    "    coef = np.corrcoef(axes[:, :, idx])\n",
    "    coef_off_diag = np.array( [coef[iii, jjj] for iii in range(5) for jjj in range(iii)] )\n",
    "    return coef_off_diag.mean(), coef_off_diag.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "L_list = list(range(1, 6))\n",
    "genelist = [ggg for ggg in df_genes.columns if \"ENSG\" in ggg]\n",
    "\n",
    "R2_all = []\n",
    "R2_selected = []\n",
    "\n",
    "for L in L_list:\n",
    "    df = pd.read_csv(\"../../gene_list/THOLD_{}.txt\".format(thold))\n",
    "    idx_gene = df[\"index\"].to_numpy()\n",
    "    res_row = [ str(thold) ]\n",
    "    \n",
    "    res_row.append( str(len(idx_gene)) )\n",
    "    \n",
    "    # Obtaining the final IEAs\n",
    "    \n",
    "    IEA_train, IEA_test = get_aligned_axes(L)\n",
    "    \n",
    "    final_IEA_train = IEA_train.sum(0)\n",
    "    final_IEA_test = IEA_test.sum(0)\n",
    "    \n",
    "    df_IEA_train = pd.DataFrame(final_IEA_train, index = sid_train , columns = [\"IEA{}\".format(iii) for iii in range(L)] )\n",
    "    df_IEA_test = pd.DataFrame(final_IEA_test, index = sid_test  , columns = [\"IEA{}\".format(iii) for iii in range(L)] )    \n",
    "    \n",
    "    df_IEA_genes_train = pd.merge(df_IEA_train, df_genes, left_index = True, right_index = True)\n",
    "    df_IEA_genes_test = pd.merge(df_IEA_test, df_genes, left_index = True, right_index = True)    \n",
    "    \n",
    "    \n",
    "    X_train = df_IEA_genes_train[ [\"IEA{}\".format(iii) for iii in range(L)] ]\n",
    "    y_train = df_IEA_genes_train[ genelist ].to_numpy()\n",
    "    X_test = df_IEA_genes_test[ [\"IEA{}\".format(iii) for iii in range(L)] ]\n",
    "    y_test = df_IEA_genes_test[ genelist ].to_numpy()\n",
    "    \n",
    "    \n",
    "    # Computing the R-squared scores for all genes\n",
    "    M = LinearRegression()\n",
    "    M.fit( X_train, y_train )\n",
    "    R2_all.append( M.score(X_test, y_test) )\n",
    "\n",
    "    # Computing the R-squared scores for all the selected genes\n",
    "    M.fit( X_train, y_train[:, idx_gene] )\n",
    "    R2_selected.append( M.score(X_test, y_test[:, idx_gene]) )\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting the total variance explained for the selected genes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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(range(1, 6), R2_selected, \"-s\", linewidth = 4, markersize = 12)\n",
    "plt.xlabel(\"Number of IEAs\", fontsize = 15)\n",
    "plt.ylabel(\"Total Variance Explained\", fontsize = 15)\n",
    "_ = plt.xticks( range(1,6), range(1,6), fontsize = 15 )\n",
    "_ = plt.yticks( fontsize = 15 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting the total variance explained for all genes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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(range(1, 6),  R2_all, \"-s\",  linewidth = 4, markersize = 12)\n",
    "plt.xlabel(\"Number of IEAs\", fontsize = 15)\n",
    "plt.ylabel(\"Total Variance Explained\", fontsize = 15)\n",
    "_ = plt.xticks( range(1,6), range(1,6), fontsize = 15 )\n",
    "\n",
    "_ = plt.yticks( fontsize = 15 )"
   ]
  }
 ],
 "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": "3.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}