examples/notebook_on_differentiable_imbalance.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial: Differentiable Information Imbalance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Differentiable Information Imbalance (DII) is used to select and optimally scale features (variables) to be informative of about a ground truth.\n",
    "\n",
    "DII is implemented in the 'FeatureWeighting' class. To see all the functions that you can call within this class, please refer to: The feature_weighting module in the DADApy documentation: https://dadapy.readthedocs.io/en/latest/modules.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from itertools import combinations_with_replacement\n",
    "\n",
    "from dadapy.metric_comparisons import MetricComparisons\n",
    "from dadapy.feature_weighting import FeatureWeighting\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison with the standard Information Imbalance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we show how to compute the differentiable Information Imbalance,\n",
    "\\begin{equation}\n",
    "DII(A\\rightarrow B) = \\frac{2}{N^2} \\sum_{i,j=1}^N\\, c_{ij}^A\\, r_{ij}^B\\, \\hspace{1cm} \\Bigg( c_{ij}^A = \\frac{\\exp(-d_{ij}^A/\\lambda)}{\\sum_{k(\\neq i)}{\\exp(-d_{ik}^A/\\lambda)}}\\Bigg),\n",
    "\\end{equation}\n",
    "for different choices of the softmax parameter $\\lambda$, and we see that the differentiable version tends to the standard Information Imbalance in the limit of small $\\lambda$. Qualitatively, this parameter decides how many neighbors are considered - for very small $\\lambda$, only the neigherest neighbor receives a weight of $~1$, all other neighbors weights close to $0$. We will define the distance spaces A and B using subsets of coordinates from a isotropic 3D Gaussian distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Included methods:\n",
    "- Prediction of distance space B from distance space A for a given value of $\\lambda$: return_dii"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sample dataset\n",
    "N = 1000\n",
    "cov = np.identity(3)\n",
    "mean = np.zeros(3)\n",
    "np.random.seed(9)\n",
    "X = np.random.multivariate_normal(mean=mean, cov=cov, size=(N))\n",
    "\n",
    "# define spaces A and B by subsets of coordinates\n",
    "coords1 = [0, 1]\n",
    "coords2 = [0, 1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/gs/c6kntl8s5z7b8jcdsd9xydww0000gp/T/ipykernel_64904/1281833669.py:8: UserWarning: maxk option not yet available for the FeatureWeighting class. It will be set to the number of data-1 (1000-1).\n",
      "  diff_imbs.append(f.return_dii(target_data=f_target, lambd=lambd))\n"
     ]
    }
   ],
   "source": [
    "# define an instance of the FeatureWeighting class\n",
    "f = FeatureWeighting(coordinates=X[:, coords1])\n",
    "f_target = FeatureWeighting(coordinates=X[:, coords2])\n",
    "\n",
    "diff_imbs = []\n",
    "lambdas = np.logspace(-7, -1, 10)  # uniformly spaced in [1e-7, 1e-1] in log scale\n",
    "for lambd in lambdas:\n",
    "    diff_imbs.append(f.return_dii(target_data=f_target, lambd=lambd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We compute for comparison purposes the standard Information Imbalance between the same distance spaces:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define an instance of the MetricComparisons class\n",
    "d = MetricComparisons(X, maxk=N - 1)\n",
    "imbs = d.return_inf_imb_two_selected_coords(coords1=coords1, coords2=coords2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lambdas, diff_imbs, \"o-\", label=\"Differentiable Information Imbalance\")\n",
    "plt.hlines(\n",
    "    imbs[0],\n",
    "    lambdas[0],\n",
    "    lambdas[-1],\n",
    "    color=\"black\",\n",
    "    label=\"Standard Information Imbalance\",\n",
    ")\n",
    "plt.xscale(\"log\")\n",
    "plt.xlabel(\"$\\\\lambda$\")\n",
    "plt.ylabel(\"Information Imbalance\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization on a 10D anisotropic Gaussian dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we show how to optimize the weights $\\{w_\\alpha\\}$ of the features $\\{X_\\alpha\\}$ in a space A $(\\alpha=1,...,D)$ in order to optimize the prediction of the distances measured in a target space B. We will construct space A using a 10D isotropic Gaussian distribution, and space B by reweighting its coordinates, resulting in a 10D anisotropic Gaussian.\n",
    "\n",
    "The weights appear in the distance function as\n",
    "\\begin{equation}\n",
    "d_{ij}^A(\\{w_\\alpha\\}) = \\Bigg[\\sum_{\\alpha=1}^D\\,(w_{\\alpha}X_\\alpha^i - w_{\\alpha}X_\\alpha^j) \\Bigg]^{1/2}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Included methods:\n",
    "- Gradient-descent optimization of the DII with respect to weights of features in space A, given a target distance space B: return_weights_optimize_dii"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sample datasets\n",
    "N = 500  # number of points\n",
    "d = 10  # dimension\n",
    "\n",
    "cov = np.identity(10)\n",
    "mean = np.zeros(10)\n",
    "X = np.random.multivariate_normal(mean=mean, cov=cov, size=(N))  # isotropic Gaussian\n",
    "\n",
    "weights = np.ones(10) * (0.01**2)\n",
    "weights[0:5] = [5, 2, 1, 1, 0.5]\n",
    "X_target = X * weights  # target space B constructed on this anisotropic Gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following block carries out the optimization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/romi/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:7: UserWarning: maxk option not yet available for the FeatureWeighting class. It will be set to the number of data-1 (500-1).\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 50  # number of training epochs\n",
    "\n",
    "f = FeatureWeighting(coordinates=X)\n",
    "f_target = FeatureWeighting(coordinates=X_target)\n",
    "final_weights = f.return_weights_optimize_dii(\n",
    "    target_data=f_target,\n",
    "    initial_weights=None,  # (default) automatic weights as inverse std.dev. of features\n",
    "    n_epochs=n_epochs,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the arguments 'lambd' and 'learning_rate' are not specified, these parameters are set automatically. After the optimization the FeatureWeighting object allows to access the values of the DII and the weights during the training, using the history:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dii_per_epoch = f.history[\"dii_per_epoch\"]\n",
    "weights_per_epoch = f.history[\"weights_per_epoch\"]\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n",
    "ax1.plot(np.arange(n_epochs + 1), dii_per_epoch)\n",
    "ax2.plot(np.arange(n_epochs + 1), weights_per_epoch[:, 0], label=\"$w_1$\")\n",
    "ax2.plot(np.arange(n_epochs + 1), weights_per_epoch[:, 1], label=\"$w_2$\")\n",
    "ax2.plot(np.arange(n_epochs + 1), weights_per_epoch[:, 2], label=\"$w_3$\")\n",
    "\n",
    "ax1.set(ylabel=\"Differentiable Information Imbalance\", xlabel=\"Epoch number\")\n",
    "ax2.set(ylabel=\"Sample weights\", xlabel=\"Epoch number\")\n",
    "ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visually compare the ground-truth weights of the anisotropic 10D Gaussian (i.e. the marginal standard deviations of the coordinates) and the optimal weights obtained from the optimization, after scaling them in the range [0,1]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "weights_names = (\n",
    "    \"$w_1$\",\n",
    "    \"$w_2$\",\n",
    "    \"$w_3$\",\n",
    "    \"$w_4$\",\n",
    "    \"$w_5$\",\n",
    "    \"$w_6$\",\n",
    "    \"$w_7$\",\n",
    "    \"$w_8$\",\n",
    "    \"$w_9$\",\n",
    "    \"$w_{10}$\",\n",
    ")\n",
    "weights_grouped = {\n",
    "    \"Ground-truth weights\": weights / max(weights),\n",
    "    \"Learnt weights (DII)\": final_weights / max(final_weights),\n",
    "}\n",
    "\n",
    "x = np.arange(len(weights_names))  # label locations\n",
    "width = 0.2  # bar widths\n",
    "multiplier = 0\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "for attribute, measurement in weights_grouped.items():\n",
    "    offset = width * multiplier\n",
    "    ax.bar(x + offset, measurement, width, label=attribute, edgecolor=\"white\")\n",
    "    multiplier += 1\n",
    "\n",
    "ax.set_ylabel(\"Weights (scaled in range [0,1])\")\n",
    "ax.set_xticks(x + width, weights_names)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the bar plot above we see that the scaled weights reproduce well the target standard deviations of the anisotropic Gaussian distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backward greedy elimination"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Backward greedy elimination is an efficient heuristic for selectin smaller features sets, given $\\leq$ 100 input features.\n",
    "\n",
    "In this example we illustrate, given a target space B and a starting set of $D$ candidate features in space A, all the optimal subsets of $D' (\\leq D)$ features to predict B are identified. At each step, the weights of the candidate features are optimized by minimizing the DII to the target space B, and after each optimization the feature associated to the lowest weight is discarded. The search stops when the optimal subset with a single feature is identified.\n",
    "\n",
    "For space A we employ 65 candidate features, given by all the monomials of degree up to 2 obtained from a set of 10 independent Gaussian features of zero mean and unit variance ($x_i \\sim \\mathcal{N}(0,1)$):\n",
    "\\begin{equation}\n",
    "\\underbrace{x_1, x_2, ...}_{\\text{order 1}},\\, \n",
    "\\underbrace{x_1^2, x_2^2, ..., x_1\\,x_2,\\, x_1\\,x_3, ...}_{\\text{order 2}}\\,.\n",
    "\\end{equation}\n",
    "The target distance B is constructed by selecting with different weights only 10 of the 65 monomials."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Included methods:\n",
    "- Stepwise backward greedy elimination: return_backward_greedy_dii_elimination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create all subsets of 10 elements with cardinality 1 or 2\n",
    "ncoords = range(10)\n",
    "monomials_list = []\n",
    "for degree in [1, 2]:\n",
    "    monomials_list += list(combinations_with_replacement(ncoords, degree))\n",
    "\n",
    "# use subsets to construct all possible monomials up to degree 2\n",
    "X_monomials = np.empty((X.shape[0], len(monomials_list)))\n",
    "for i_monomial, coords in enumerate(monomials_list):\n",
    "    monomial = np.prod(X[:, coords], axis=1)\n",
    "    X_monomials[:, i_monomial] = monomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected monomials in target space B:\n",
      "\t['X_6'] with weight 5.0\n",
      "\t['X_9'] with weight 5.0\n",
      "\t['X_1' 'X_3'] with weight 7.0\n",
      "\t['X_1' 'X_5'] with weight 2.0\n",
      "\t['X_2' 'X_2'] with weight 1.0\n",
      "\t['X_2' 'X_8'] with weight 4.0\n",
      "\t['X_3' 'X_9'] with weight 1.5\n",
      "\t['X_5' 'X_8'] with weight 1.0\n",
      "\t['X_8' 'X_8'] with weight 3.0\n",
      "\t['X_8' 'X_{10}'] with weight 6.0\n"
     ]
    }
   ],
   "source": [
    "# construct the target space B by selecting 10 monomials with different weights\n",
    "monomials_target = [5, 8, 12, 14, 20, 26, 35, 47, 59, 61]\n",
    "weights = np.zeros(len(monomials_list))\n",
    "weights[monomials_target] = [5, 5, 7, 2, 1, 4, 1.5, 1, 3, 6]\n",
    "\n",
    "coords_names = np.array(\n",
    "    [\"X_1\", \"X_2\", \"X_3\", \"X_4\", \"X_5\", \"X_6\", \"X_7\", \"X_8\", \"X_9\", \"X_{10}\"]\n",
    ")\n",
    "print(\"Selected monomials in target space B:\")\n",
    "for monomial_index in monomials_target:\n",
    "    monomial = monomials_list[monomial_index]\n",
    "    print(f\"\\t{coords_names[list(monomial)]} with weight {weights[monomial_index]}\")\n",
    "\n",
    "X_monomials_target = X_monomials * weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following block carries out the backward elimination starting from the whole space of the 65 features (monomials) in space A. This calculation might take ~20 min on a standard laptop; the progression state can be monitored by setting verbose=True when the FeatureWeighting object is initialized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/romi/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: maxk option not yet available for the FeatureWeighting class. It will be set to the number of data-1 (500-1).\n",
      "  # Remove the CWD from sys.path while we load stuff.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of nonzero weights: 65, execution time: 33.13 s.\n",
      "number of nonzero weights: 64, execution time: 34.30 s.\n",
      "number of nonzero weights: 63, execution time: 29.93 s.\n",
      "number of nonzero weights: 62, execution time: 29.55 s.\n",
      "number of nonzero weights: 61, execution time: 31.18 s.\n",
      "number of nonzero weights: 60, execution time: 29.06 s.\n",
      "number of nonzero weights: 59, execution time: 27.85 s.\n",
      "number of nonzero weights: 58, execution time: 26.99 s.\n",
      "number of nonzero weights: 57, execution time: 27.07 s.\n",
      "number of nonzero weights: 56, execution time: 25.89 s.\n",
      "number of nonzero weights: 55, execution time: 25.45 s.\n",
      "number of nonzero weights: 54, execution time: 24.73 s.\n",
      "number of nonzero weights: 53, execution time: 24.96 s.\n",
      "number of nonzero weights: 52, execution time: 24.30 s.\n",
      "number of nonzero weights: 51, execution time: 24.04 s.\n",
      "number of nonzero weights: 50, execution time: 24.47 s.\n",
      "number of nonzero weights: 49, execution time: 24.38 s.\n",
      "number of nonzero weights: 48, execution time: 18.13 s.\n",
      "number of nonzero weights: 47, execution time: 16.65 s.\n",
      "number of nonzero weights: 46, execution time: 16.37 s.\n",
      "number of nonzero weights: 45, execution time: 16.06 s.\n",
      "number of nonzero weights: 44, execution time: 15.81 s.\n",
      "number of nonzero weights: 43, execution time: 15.44 s.\n",
      "number of nonzero weights: 42, execution time: 15.32 s.\n",
      "number of nonzero weights: 41, execution time: 14.81 s.\n",
      "number of nonzero weights: 40, execution time: 14.51 s.\n",
      "number of nonzero weights: 39, execution time: 14.21 s.\n",
      "number of nonzero weights: 38, execution time: 13.95 s.\n",
      "number of nonzero weights: 37, execution time: 14.70 s.\n",
      "number of nonzero weights: 36, execution time: 15.57 s.\n",
      "number of nonzero weights: 35, execution time: 14.60 s.\n",
      "number of nonzero weights: 34, execution time: 12.80 s.\n",
      "number of nonzero weights: 33, execution time: 12.36 s.\n",
      "number of nonzero weights: 32, execution time: 12.09 s.\n",
      "number of nonzero weights: 31, execution time: 11.97 s.\n",
      "number of nonzero weights: 30, execution time: 11.49 s.\n",
      "number of nonzero weights: 29, execution time: 11.22 s.\n",
      "number of nonzero weights: 28, execution time: 10.90 s.\n",
      "number of nonzero weights: 27, execution time: 10.65 s.\n",
      "number of nonzero weights: 26, execution time: 10.36 s.\n",
      "number of nonzero weights: 25, execution time: 9.95 s.\n",
      "number of nonzero weights: 24, execution time: 9.71 s.\n",
      "number of nonzero weights: 23, execution time: 9.36 s.\n",
      "number of nonzero weights: 22, execution time: 9.07 s.\n",
      "number of nonzero weights: 21, execution time: 8.76 s.\n",
      "number of nonzero weights: 20, execution time: 8.48 s.\n",
      "number of nonzero weights: 19, execution time: 8.28 s.\n",
      "number of nonzero weights: 18, execution time: 7.86 s.\n",
      "number of nonzero weights: 17, execution time: 7.56 s.\n",
      "number of nonzero weights: 16, execution time: 7.27 s.\n",
      "number of nonzero weights: 15, execution time: 6.95 s.\n",
      "number of nonzero weights: 14, execution time: 6.62 s.\n",
      "number of nonzero weights: 13, execution time: 6.32 s.\n",
      "number of nonzero weights: 12, execution time: 6.04 s.\n",
      "number of nonzero weights: 11, execution time: 5.82 s.\n",
      "number of nonzero weights: 10, execution time: 5.41 s.\n",
      "number of nonzero weights: 9, execution time: 5.10 s.\n",
      "number of nonzero weights: 8, execution time: 4.80 s.\n",
      "number of nonzero weights: 7, execution time: 4.50 s.\n",
      "number of nonzero weights: 6, execution time: 4.20 s.\n",
      "number of nonzero weights: 5, execution time: 3.89 s.\n",
      "number of nonzero weights: 4, execution time: 3.59 s.\n",
      "number of nonzero weights: 3, execution time: 3.31 s.\n",
      "number of nonzero weights: 2, execution time: 3.07 s.\n",
      "number of nonzero weights: 1, execution time: 2.72 s.\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 80  # number of training epochs\n",
    "\n",
    "f = FeatureWeighting(coordinates=X_monomials, verbose=True)\n",
    "f_target = FeatureWeighting(coordinates=X_monomials_target)\n",
    "\n",
    "final_imbs, final_weights = f.return_backward_greedy_dii_elimination(\n",
    "    target_data=f_target,\n",
    "    initial_weights=None,  # set automatically (default)\n",
    "    n_epochs=n_epochs,\n",
    "    learning_rate=None,  # set automatically (default)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# optimized information imbalance vs number of non-zero features\n",
    "plt.plot(np.arange(X_monomials.shape[1], 0, -1), final_imbs, \".-\")\n",
    "plt.xlabel(\"Number of non-zero features\")\n",
    "plt.ylabel(\"DII\")\n",
    "plt.yscale(\"log\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot above we see that the optimized DII reaches a plateau after 9-10 features, which is consistent with the numbers of monomials included in the target space B. We can further verify that, for the subset with 10 non-zero features, both the selected features and their weights are mostly consistent with the ground-truth ones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_subset = 10\n",
    "monomials_learnt = np.where(final_weights[-n_subset] > 0)[0]\n",
    "union_set = list(set(monomials_target).union(monomials_learnt))\n",
    "\n",
    "weights_grouped = {\n",
    "    \"Ground-truth weights\": weights[union_set] / max(weights[union_set]),\n",
    "    \"Learnt weights (DII)\": final_weights[-n_subset][union_set]\n",
    "    / max(final_weights[-n_subset][union_set]),\n",
    "}\n",
    "weights_names = []\n",
    "for monomial_index in union_set:\n",
    "    monomial = monomials_list[monomial_index]\n",
    "    weights_names.append(f\"$w({''.join((coords_names[list(monomial)]))})$\")\n",
    "\n",
    "x = np.arange(len(weights_names))  # label locations\n",
    "width = 0.2  # bar widths\n",
    "multiplier = 0\n",
    "fig, ax = plt.subplots(figsize=(10, 4))\n",
    "for attribute, measurement in weights_grouped.items():\n",
    "    offset = width * multiplier\n",
    "    ax.bar(x + offset, measurement, width, label=attribute, edgecolor=\"white\")\n",
    "    multiplier += 1\n",
    "ax.set_ylabel(\"Weights (scaled in range [0,1])\")\n",
    "ax.set_xticks(x + width, weights_names)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## L1 regularization (lasso) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you need to select a small subset of features out of a very large input space ($\\geq$ 100 features), L1 regularization is your friend.\n",
    "\n",
    "In this section we show how to carry out a selection of optimal subsets of features in space A in order to predict a target space B, by optimizing the Differentiable Information Imbalance with a lasso (L1) regularization. Explicitely, the loss function which is minimized is\n",
    "\\begin{equation}\n",
    "\\mathcal{L} = DII(A(\\{w_\\alpha\\})\\rightarrow B) + \\beta \\sum_{\\alpha=1}^D\\, |w_\\alpha |\\,,\n",
    "\\end{equation}\n",
    "where $\\beta$ is the strength of the regularization, which determines the number of non-zero weights. To identify subsets with different numbers of non-zero features, a scan over different values of $\\beta$ is required.\n",
    "\n",
    "We will use the same dataset of monomials employed in the previous example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Included methods:\n",
    "- Search of optimal subsets of features by optimizing the DII with different strengths of the L1 regularization term : return_lasso_optimization_dii_search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create all subsets of 10 elements with cardinality 1 or 2\n",
    "ncoords = range(10)\n",
    "monomials_list = []\n",
    "for degree in [1, 2]:\n",
    "    monomials_list += list(combinations_with_replacement(ncoords, degree))\n",
    "\n",
    "# use subsets to construct all possible monomials up to degree 2\n",
    "X_monomials = np.empty((X.shape[0], len(monomials_list)))\n",
    "for i_monomial, coords in enumerate(monomials_list):\n",
    "    monomial = np.prod(X[:, coords], axis=1)\n",
    "    X_monomials[:, i_monomial] = monomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected monomials in target space B:\n",
      "\t['X_6'] with weight 5.0\n",
      "\t['X_9'] with weight 5.0\n",
      "\t['X_1' 'X_3'] with weight 7.0\n",
      "\t['X_1' 'X_5'] with weight 2.0\n",
      "\t['X_2' 'X_2'] with weight 1.0\n",
      "\t['X_2' 'X_8'] with weight 4.0\n",
      "\t['X_3' 'X_9'] with weight 1.5\n",
      "\t['X_5' 'X_8'] with weight 1.0\n",
      "\t['X_8' 'X_8'] with weight 3.0\n",
      "\t['X_8' 'X_{10}'] with weight 6.0\n"
     ]
    }
   ],
   "source": [
    "# construct space B by selecting 10 monomials with different weights\n",
    "monomials_target = [5, 8, 12, 14, 20, 26, 35, 47, 59, 61]\n",
    "weights = np.zeros(len(monomials_list))\n",
    "weights[monomials_target] = [5, 5, 7, 2, 1, 4, 1.5, 1, 3, 6]\n",
    "\n",
    "coords_names = np.array(\n",
    "    [\"X_1\", \"X_2\", \"X_3\", \"X_4\", \"X_5\", \"X_6\", \"X_7\", \"X_8\", \"X_9\", \"X_{10}\"]\n",
    ")\n",
    "print(\"Selected monomials in target space B:\")\n",
    "for monomial_index in monomials_target:\n",
    "    monomial = monomials_list[monomial_index]\n",
    "    print(f\"\\t{coords_names[list(monomial)]} with weight {weights[monomial_index]}\")\n",
    "\n",
    "X_monomials_target = X_monomials * weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following block optimizes the DII(A\\rightarrow B) with a L$_1$ regularization. By default, 10 optimizations for different values of the regularization strength $\\beta$ are carried out. If 'refine=True', additional values of $\\beta$ are tested in order to identify more subsets with a different number of non-zero features (This option leads to long calculations when the input feature space is large). Specific values of the parameters $\\beta$ to be tested can be set by the user with the argument 'l1_penalties'. As in the greedy search algorithm, the progress of the optimization can be monitored by setting verbose=True in the initalization of the FeatureWeighting object.\n",
    "\n",
    "(This calculation without refinement, can take ~5 min on a starndard laptop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/romi/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:17: UserWarning: maxk option not yet available for the FeatureWeighting class. It will be set to the number of data-1 (500-1).\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 l1-penalties to test:\n",
      "optimization with l1-penalty 1 of strength 0 took: 22.20 s.\n",
      "optimization with l1-penalty 2 of strength 1e-06 took: 27.58 s.\n",
      "optimization with l1-penalty 3 of strength 3.162e-06 took: 28.33 s.\n",
      "optimization with l1-penalty 4 of strength 1e-05 took: 21.80 s.\n",
      "optimization with l1-penalty 5 of strength 3.162e-05 took: 22.88 s.\n",
      "optimization with l1-penalty 6 of strength 0.0001 took: 18.24 s.\n",
      "optimization with l1-penalty 7 of strength 0.0003162 took: 11.75 s.\n",
      "optimization with l1-penalty 8 of strength 0.001 took: 6.44 s.\n",
      "optimization with l1-penalty 9 of strength 0.003162 took: 4.15 s.\n",
      "optimization with l1-penalty 10 of strength 0.01 took: 3.68 s.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 80  # number of training epochs\n",
    "\n",
    "f = FeatureWeighting(coordinates=X_monomials, verbose=True)\n",
    "f_target = FeatureWeighting(coordinates=X_monomials_target)\n",
    "\n",
    "(\n",
    "    num_nonzero_features,\n",
    "    l1_penalties_opt_per_nfeatures,\n",
    "    dii_opt_per_nfeatures,\n",
    "    weights_opt_per_nfeatures,\n",
    ") = f.return_lasso_optimization_dii_search(\n",
    "    target_data=f_target,\n",
    "    initial_weights=None,  # (default) set automatically\n",
    "    n_epochs=n_epochs,\n",
    "    learning_rate=None,  # (default) set automatically\n",
    "    refine=False,  # only 10 values of the L1 strength are tested\n",
    "    plotlasso=True,  # automatically show DII vs number of non-zero features\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot above shows the optimized DII reaches a pleateau after ~10 non-zero features. We can compare the optimal features identified in this set and their weights with the ground-truth values used to build the target space B:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# find number of non-zero features closest to 10 (ground-truth)\n",
    "n_subset = len(monomials_list) - np.nanargmin(np.abs(10 - num_nonzero_features))\n",
    "monomials_learnt = np.where(weights_opt_per_nfeatures[-9][-n_subset] > 1e-2)[0]\n",
    "union_set = list(set(monomials_target).union(monomials_learnt))\n",
    "\n",
    "weights_grouped = {\n",
    "    \"Ground-truth weights\": weights[union_set] / max(weights[union_set]),\n",
    "    \"Learnt weights (DII)\": weights_opt_per_nfeatures[-n_subset][union_set]\n",
    "    / max(weights_opt_per_nfeatures[-n_subset][union_set]),\n",
    "}\n",
    "weights_names = []\n",
    "for monomial_index in union_set:\n",
    "    monomial = monomials_list[monomial_index]\n",
    "    weights_names.append(f\"$w({''.join((coords_names[list(monomial)]))})$\")\n",
    "\n",
    "x = np.arange(len(weights_names))  # label locations\n",
    "width = 0.2  # bar widths\n",
    "multiplier = 0\n",
    "fig, ax = plt.subplots(figsize=(10, 4))\n",
    "for attribute, measurement in weights_grouped.items():\n",
    "    offset = width * multiplier\n",
    "    ax.bar(x + offset, measurement, width, label=attribute, edgecolor=\"white\")\n",
    "    multiplier += 1\n",
    "ax.set_ylabel(\"Weights (scaled in range [0,1])\")\n",
    "ax.set_xticks(x + width, weights_names)\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of our 10 default lasso strengths found a solution with 9 weights, including the eight biggest weights of the ground truth. If a different number of non-zero features is required, the L1 strenths per number of non-zero features can be inspected, and the user can specify additional L1 strenths in the region of interest for a new L1 search run. We see that the L1 strength to find 9 non-zero features was 1.00e-03:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([65., nan, 63., nan, nan, 60., nan, 58., nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, 48., nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan, 22., nan, nan, nan, nan, nan, nan, nan, nan,\n",
       "       nan, nan, nan, nan,  9., nan, nan, nan, nan,  4.,  3., nan, nan])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the number of nonzero features in the solutions found with various L1 strengths\n",
    "num_nonzero_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00e+00,      nan, 3.16e-06,      nan,      nan, 1.00e-05,\n",
       "            nan, 3.16e-05,      nan,      nan,      nan,      nan,\n",
       "            nan,      nan,      nan,      nan,      nan, 1.00e-04,\n",
       "            nan,      nan,      nan,      nan,      nan,      nan,\n",
       "            nan,      nan,      nan,      nan,      nan,      nan,\n",
       "            nan,      nan,      nan,      nan,      nan,      nan,\n",
       "            nan,      nan,      nan,      nan,      nan,      nan,\n",
       "            nan, 3.16e-04,      nan,      nan,      nan,      nan,\n",
       "            nan,      nan,      nan,      nan,      nan,      nan,\n",
       "            nan,      nan, 1.00e-03,      nan,      nan,      nan,\n",
       "            nan, 3.16e-03, 1.00e-02,      nan,      nan])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the according L1 strenths for the number of non-zero features as above\n",
    "l1_penalties_opt_per_nfeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02,  nan, 0.02,  nan,  nan, 0.02,  nan, 0.02,  nan,  nan,  nan,\n",
       "        nan,  nan,  nan,  nan,  nan,  nan, 0.01,  nan,  nan,  nan,  nan,\n",
       "        nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,\n",
       "        nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan, 0.01,\n",
       "        nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,  nan,\n",
       "        nan, 0.01,  nan,  nan,  nan,  nan, 0.13, 0.4 ,  nan,  nan])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The according DIIs for the number of non-zero features as above\n",
    "dii_opt_per_nfeatures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.28, 0.  , 0.  , 0.  , 1.49, 0.  , 0.  , 1.53, 0.  , 0.  ,\n",
       "       0.  , 2.28, 0.  , 0.49, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ,\n",
       "       0.  , 0.  , 0.  , 0.  , 1.22, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ,\n",
       "       0.  , 0.  , 0.38, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ,\n",
       "       0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ,\n",
       "       0.  , 0.  , 0.  , 0.  , 0.86, 0.  , 1.78, 0.  , 0.  , 0.  ])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Feature weights of the optimal solution with 9 non-zero features (see above))\n",
    "weights_opt_per_nfeatures[-9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00e+00, 1.00e-06, 3.16e-06, 1.00e-05, 3.16e-05, 1.00e-04,\n",
       "       3.16e-04, 1.00e-03, 3.16e-03, 1.00e-02])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# discover which L1 penalties were tested in the search\n",
    "f.history[\"l1_penalties\"]"
   ]
  }
 ],
 "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": "3.7.15"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}