{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a15f3302",
   "metadata": {},
   "source": [
    "# Density estimation with sparse transport maps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8888290b",
   "metadata": {},
   "source": [
    "In this example we demonstrate how MParT can be use to build map with certain sparse structure in order to characterize high dimensional densities with conditional independence."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed657c1",
   "metadata": {},
   "source": [
    "## Imports\n",
    "First, import MParT and other packages used in this notebook. Note that it is possible to specify the number of threads used by MParT by setting the `KOKKOS_NUM_THREADS` environment variable **before** importing MParT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b7bde703",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:50.525376Z",
     "iopub.status.busy": "2024-03-21T17:44:50.525208Z",
     "iopub.status.idle": "2024-03-21T17:44:52.360625Z",
     "shell.execute_reply": "2024-03-21T17:44:52.360094Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kokkos::OpenMP::initialize WARNING: You are likely oversubscribing your CPU cores.\n",
      "  process threads available :   4,  requested thread :   8\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Kokkos::OpenMP::initialize WARNING: You are likely oversubscribing your CPU cores.\n",
      "                                    Detected: 4 cores per node.\n",
      "                                    Detected: 1 MPI_ranks per node.\n",
      "                                    Requested: 8 threads per process.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kokkos is using 8 threads\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import multivariate_normal\n",
    "from tqdm import tqdm\n",
    "\n",
    "import os\n",
    "os.environ['KOKKOS_NUM_THREADS'] = '8'\n",
    "\n",
    "import mpart as mt\n",
    "print('Kokkos is using', mt.Concurrency(), 'threads')\n",
    "plt.rcParams['figure.dpi'] = 110"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23627b3c",
   "metadata": {},
   "source": [
    "## Stochastic volatility model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8c49968",
   "metadata": {},
   "source": [
    "### Problem description\n",
    "\n",
    "The problem considered here is a Markov process that describes the volatility on a financial asset overt time. The model depends on two hyperparamters $\\mu$ and $\\phi$ and state variable $Z_k$ represents log-volatility at times $k=1,...,T$. The log-volatility follows the order-one autoregressive process:\n",
    "$$Z_{k+1} = \\mu + \\phi(Z_k-\\mu) + \\epsilon_k, k>1, $$\n",
    "where\n",
    "$$\\mu \\sim \\mathcal{N}(0,1) $$\n",
    "$$ \\phi = 2\\frac{\\exp(\\phi^*)}{1+\\exp(\\phi^*)}, \\,\\,\\, \\phi^* \\sim \\mathcal{N}(3,1)$$\n",
    "$$ Z_0 | \\mu, \\phi \\sim \\mathcal{N}\\left(\\mu,\\frac{1}{1-\\phi^2}\\right)$$\n",
    "\n",
    "The objective is to characterize the joint density of\n",
    "$$\\mathbf{X}_T = (\\mu,\\phi,Z_1,...,Z_T), $$\n",
    "with $T$ being arbitrarly large. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b8403c5",
   "metadata": {},
   "source": [
    "The conditional independence property for this problem reads\n",
    "\n",
    "$$ \\pi(\\mathbf{x}_t|\\mathbf{x}_{<t}) = \\pi(\\mathbf{x}_t|\\mathbf{x}_{t-1},\\mu,\\phi)$$\n",
    "\n",
    "More details about this problem can be found in [[Baptista et al., 2022]](https://arxiv.org/pdf/2009.10303.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "776a5f48",
   "metadata": {},
   "source": [
    "### Sampling\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae4d6174",
   "metadata": {},
   "source": [
    "Drawing samples $(\\mu^i,\\phi^i,x_0^i,x_1^i,...,x_T^i)$ can be performed by the following function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c9fb981e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.363272Z",
     "iopub.status.busy": "2024-03-21T17:44:52.363016Z",
     "iopub.status.idle": "2024-03-21T17:44:52.366844Z",
     "shell.execute_reply": "2024-03-21T17:44:52.366427Z"
    }
   },
   "outputs": [],
   "source": [
    "def generate_SV_samples(d,N):\n",
    "    # Sample hyper-parameters\n",
    "    sigma = 0.25\n",
    "    mu = np.random.randn(1,N)\n",
    "    phis = 3+np.random.randn(1,N)\n",
    "    phi = 2*np.exp(phis)/(1+np.exp(phis))-1\n",
    "    X = np.vstack((mu,phi))\n",
    "    if d > 2:\n",
    "        # Sample Z0\n",
    "        Z = np.sqrt(1/(1-phi**2))*np.random.randn(1,N) + mu\n",
    "\n",
    "        # Sample auto-regressively\n",
    "        for i in range(d-3):\n",
    "            Zi = mu + phi * (Z[-1,:] - mu)+sigma*np.random.randn(1,N)\n",
    "            Z = np.vstack((Z,Zi))\n",
    "\n",
    "        X = np.vstack((X,Z))\n",
    "    return X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90687b5d",
   "metadata": {},
   "source": [
    "Set dimension of the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ada07ed8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.368600Z",
     "iopub.status.busy": "2024-03-21T17:44:52.368426Z",
     "iopub.status.idle": "2024-03-21T17:44:52.370787Z",
     "shell.execute_reply": "2024-03-21T17:44:52.370287Z"
    }
   },
   "outputs": [],
   "source": [
    "T = 30 #number of time steps including initial condition\n",
    "d = T+2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "915a2e2e",
   "metadata": {},
   "source": [
    "Few realizations of the process look like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "831253f0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.372566Z",
     "iopub.status.busy": "2024-03-21T17:44:52.372279Z",
     "iopub.status.idle": "2024-03-21T17:44:52.501341Z",
     "shell.execute_reply": "2024-03-21T17:44:52.500923Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 704x528 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Nvisu = 10 #Number of samples\n",
    "Xvisu = generate_SV_samples(d, Nvisu)\n",
    "\n",
    "Zvisu = Xvisu[2:,:]\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(Zvisu)\n",
    "plt.xlabel(\"Days (d)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97741aec",
   "metadata": {},
   "source": [
    "And corresponding realization of hyperparameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7e8562af",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.503402Z",
     "iopub.status.busy": "2024-03-21T17:44:52.503090Z",
     "iopub.status.idle": "2024-03-21T17:44:52.635559Z",
     "shell.execute_reply": "2024-03-21T17:44:52.635109Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:3: SyntaxWarning: invalid escape sequence '\\m'\n",
      "<>:4: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:3: SyntaxWarning: invalid escape sequence '\\m'\n",
      "<>:4: SyntaxWarning: invalid escape sequence '\\p'\n",
      "/tmp/ipykernel_268/2191412704.py:3: SyntaxWarning: invalid escape sequence '\\m'\n",
      "  plt.plot(range(1,Nvisu+1),Xvisu[1,:],label='$\\mu$')\n",
      "/tmp/ipykernel_268/2191412704.py:4: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  plt.plot(range(1,Nvisu+1),Xvisu[2,:],label='$\\phi$')\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 704x528 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hyper_params = Xvisu[:2,:]\n",
    "plt.figure()\n",
    "plt.plot(range(1,Nvisu+1),Xvisu[1,:],label='$\\mu$')\n",
    "plt.plot(range(1,Nvisu+1),Xvisu[2,:],label='$\\phi$')\n",
    "plt.xlabel('Samples')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e650f5d",
   "metadata": {},
   "source": [
    "### Probability density function\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "011bf987",
   "metadata": {},
   "source": [
    "The exact log-conditional densities used to define joint density $\\pi(\\mathbf{x}_T)$ are defined by the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "afa417f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.637622Z",
     "iopub.status.busy": "2024-03-21T17:44:52.637322Z",
     "iopub.status.idle": "2024-03-21T17:44:52.641903Z",
     "shell.execute_reply": "2024-03-21T17:44:52.641432Z"
    }
   },
   "outputs": [],
   "source": [
    "def SV_log_pdf(X):\n",
    "    \n",
    "    def normpdf(x,mu,sigma):\n",
    "        return  np.exp(-0.5 * ((x - mu)/sigma)**2) / (np.sqrt(2*np.pi) * sigma)\n",
    "    \n",
    "    sigma = 0.25\n",
    "\n",
    "    # Extract variables mu, phi and states\n",
    "    mu = X[0,:]\n",
    "    phi = X[1,:]\n",
    "    Z = X[2:,:]\n",
    "\n",
    "    # Compute density for mu\n",
    "    piMu = multivariate_normal(np.zeros(1),np.eye(1))\n",
    "    logPdfMu = piMu.logpdf(mu)\n",
    "    # Compute density for phi\n",
    "    phiRef = np.log((1+phi)/(1-phi))\n",
    "    dphiRef = 2/(1-phi**2)\n",
    "    piPhi = multivariate_normal(3*np.ones(1),np.eye(1))\n",
    "    logPdfPhi = piPhi.logpdf(phiRef)+np.log(dphiRef)\n",
    "    # Add piMu, piPhi to density\n",
    "    logPdf = np.vstack((logPdfMu,logPdfPhi))\n",
    "\n",
    "    # Number of time steps\n",
    "    dz = Z.shape[0]\n",
    "    if dz > 0:\n",
    "        # Conditonal density for Z_0\n",
    "        muZ0 = mu\n",
    "        stdZ0 = np.sqrt(1/(1-phi**2))\n",
    "        logPdfZ0 = np.log(normpdf(Z[0,:],muZ0,stdZ0))\n",
    "        logPdf = np.vstack((logPdf,logPdfZ0))\n",
    "\n",
    "        # Compute auto-regressive conditional densities for Z_i|Z_{1:i-1}\n",
    "        for i in range(1,dz):\n",
    "            meanZi = mu + phi * (Z[i-1,:]-mu)\n",
    "            stdZi = sigma\n",
    "            logPdfZi = np.log(normpdf(Z[i,:],meanZi,stdZi))\n",
    "            logPdf = np.vstack((logPdf,logPdfZi))\n",
    "    return logPdf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a239e0",
   "metadata": {},
   "source": [
    "## Transport map training"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be2f17fd",
   "metadata": {},
   "source": [
    "In the following we optimize each map component $S_k$, $k \\in \\{1,...,T+2\\}$:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2edcf214",
   "metadata": {},
   "source": [
    "* For $k=1$, map $S_1$ characterize marginal density $\\pi(\\mu)$\n",
    "* For $k=2$, map $S_2$ characterize conditional density $\\pi(\\phi|\\mu)$\n",
    "* For $k=3$, map $S_3$ characterize conditional density $\\pi(z_0|\\phi,\\mu)$\n",
    "* For $k>3$, map $S_k$ characterize conditional density $\\pi(z_{k-2}|z_{k-3},\\phi,\\mu)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33f7e124",
   "metadata": {},
   "source": [
    "Definition of log-conditional density from map component $S_k$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0b585e7d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.643967Z",
     "iopub.status.busy": "2024-03-21T17:44:52.643795Z",
     "iopub.status.idle": "2024-03-21T17:44:52.646522Z",
     "shell.execute_reply": "2024-03-21T17:44:52.646037Z"
    }
   },
   "outputs": [],
   "source": [
    "def log_cond_pullback_pdf(triMap,eta,x):\n",
    "    r = triMap.Evaluate(x)\n",
    "    log_pdf = eta.logpdf(r.T)+triMap.LogDeterminant(x)\n",
    "    return log_pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c4fe749",
   "metadata": {},
   "source": [
    "### Generating training and testing samples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f85583e3",
   "metadata": {},
   "source": [
    "From training samples generated with the known function we compare accuracy of the transport map induced density using different parameterization and a limited number of training samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "008f9150",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.648396Z",
     "iopub.status.busy": "2024-03-21T17:44:52.648229Z",
     "iopub.status.idle": "2024-03-21T17:44:52.658992Z",
     "shell.execute_reply": "2024-03-21T17:44:52.658600Z"
    }
   },
   "outputs": [],
   "source": [
    "N = 2000 #Number of training samples\n",
    "X = generate_SV_samples(d, N)\n",
    "\n",
    "Ntest = 5000 # Number of testing samples\n",
    "Xtest = generate_SV_samples(d,Ntest)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e197b2ec",
   "metadata": {},
   "source": [
    "### Objective function and gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe519be7",
   "metadata": {},
   "source": [
    "We use the minimization of negative log-likelihood to optimize map components."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "683d6e48",
   "metadata": {},
   "source": [
    "For map component $k$, the objective function is given by \n",
    "\n",
    "$$\n",
    "J_k(\\mathbf{w}_k) = - \\frac{1}{N}\\sum_{i=1}^N \\left( \\log\\eta\\left(S_k(\\mathbf{x}_{1:k}^i;\\mathbf{w}_k)\\right) + \\log \\frac{\\partial S_k(\\mathbf{x}_{1:k}^i;\\mathbf{w}_k)}{\\partial x_k}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b39fc53d",
   "metadata": {},
   "source": [
    "and corresponding gradient\n",
    "$$\n",
    "\\nabla_{\\mathbf{w}_k}J_k(\\mathbf{w}_k) = - \\frac{1}{N}\\sum_{i=1}^N \\left(\\left[\\nabla_{\\mathbf{w}_k}S_k(\\mathbf{x}_{1:k}^i;\\mathbf{w}_k)\\right]^T \\nabla_\\mathbf{r}\\log \\eta \\left(S_k\n",
    "(\\mathbf{x}_{1:k}^i;\\mathbf{w}_k)\\right) - \\frac{\\partial \\nabla_{\\mathbf{w}_k}S_k(\\mathbf{x}_{1:k}^i;\\mathbf{w}_k)}{\\partial x_k} \\left[\\frac{\\partial S_k(\\mathbf{x}_{1:k}^i;\\mathbf{w}_k)}{\\partial x_k}\\right]^{-1}\\right),\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f56c492c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.660872Z",
     "iopub.status.busy": "2024-03-21T17:44:52.660709Z",
     "iopub.status.idle": "2024-03-21T17:44:52.664105Z",
     "shell.execute_reply": "2024-03-21T17:44:52.663714Z"
    }
   },
   "outputs": [],
   "source": [
    "### Negative log likelihood objective\n",
    "def obj(coeffs, tri_map,x):\n",
    "    \"\"\" Evaluates the log-likelihood of the samples using the map-induced density. \"\"\"\n",
    "    num_points = x.shape[1]\n",
    "    tri_map.SetCoeffs(coeffs)\n",
    "\n",
    "    # Compute the map-induced density at each point \n",
    "    map_of_x = tri_map.Evaluate(x)\n",
    "\n",
    "    rho = multivariate_normal(np.zeros(tri_map.outputDim),np.eye(tri_map.outputDim))\n",
    "    rho_of_map_of_x = rho.logpdf(map_of_x.T)\n",
    "    log_det = tri_map.LogDeterminant(x)\n",
    "\n",
    "    # Return the negative log-likelihood of the entire dataset\n",
    "    return -np.sum(rho_of_map_of_x + log_det)/num_points\n",
    "\n",
    "def grad_obj(coeffs, tri_map, x):\n",
    "    \"\"\" Returns the gradient of the log-likelihood objective wrt the map parameters. \"\"\"\n",
    "    num_points = x.shape[1]\n",
    "    tri_map.SetCoeffs(coeffs)\n",
    "\n",
    "    # Evaluate the map\n",
    "    map_of_x = tri_map.Evaluate(x)\n",
    "\n",
    "    # Now compute the inner product of the map jacobian (\\nabla_w S) and the gradient (which is just -S(x) here)\n",
    "    grad_rho_of_map_of_x = -tri_map.CoeffGrad(x, map_of_x)\n",
    "\n",
    "    # Get the gradient of the log determinant with respect to the map coefficients\n",
    "    grad_log_det = tri_map.LogDeterminantCoeffGrad(x)\n",
    "    \n",
    "    return -np.sum(grad_rho_of_map_of_x + grad_log_det, 1)/num_points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d9ba8e3",
   "metadata": {},
   "source": [
    "### Training total order 1 map"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe73803",
   "metadata": {},
   "source": [
    "Here we use a total order 1 multivariate expansion to parameterize each component $S_k$, $k \\in \\{1,...,T+2\\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f84aa70c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.665947Z",
     "iopub.status.busy": "2024-03-21T17:44:52.665780Z",
     "iopub.status.idle": "2024-03-21T17:44:52.668196Z",
     "shell.execute_reply": "2024-03-21T17:44:52.667803Z"
    }
   },
   "outputs": [],
   "source": [
    "opts = mt.MapOptions()\n",
    "opts.basisType = mt.BasisTypes.HermiteFunctions "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aafe969",
   "metadata": {},
   "source": [
    "#### Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "327ead41",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:52.669877Z",
     "iopub.status.busy": "2024-03-21T17:44:52.669716Z",
     "iopub.status.idle": "2024-03-21T17:44:55.435018Z",
     "shell.execute_reply": "2024-03-21T17:44:55.434538Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   0%|          | 0/32 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  16%|█▌        | 5/32 [00:00<00:00, 43.34it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  31%|███▏      | 10/32 [00:00<00:01, 20.81it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  41%|████      | 13/32 [00:00<00:01, 16.84it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  50%|█████     | 16/32 [00:00<00:01, 14.87it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  56%|█████▋    | 18/32 [00:01<00:01, 13.71it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  62%|██████▎   | 20/32 [00:01<00:00, 12.83it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  69%|██████▉   | 22/32 [00:01<00:00, 11.62it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  75%|███████▌  | 24/32 [00:01<00:00, 10.76it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  81%|████████▏ | 26/32 [00:01<00:00, 10.03it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  88%|████████▊ | 28/32 [00:02<00:00,  9.34it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  91%|█████████ | 29/32 [00:02<00:00,  9.20it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  94%|█████████▍| 30/32 [00:02<00:00,  8.83it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  97%|█████████▋| 31/32 [00:02<00:00,  8.32it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component: 100%|██████████| 32/32 [00:02<00:00,  8.17it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component: 100%|██████████| 32/32 [00:02<00:00, 11.61it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Total order 1 approximation\n",
    "totalOrder = 1\n",
    "logPdfTM_to1 = np.zeros((d,Ntest))\n",
    "ListCoeffs_to1=np.zeros((d,))\n",
    "for dk in tqdm(range(1,d+1),desc=\"Map component\"):\n",
    "    fixed_mset= mt.FixedMultiIndexSet(dk,totalOrder)\n",
    "    S = mt.CreateComponent(fixed_mset,opts)\n",
    "    Xtrain = X[:dk,:]\n",
    "    Xtestk = Xtest[:dk,:]\n",
    "\n",
    "    ListCoeffs_to1[dk-1]=S.numCoeffs\n",
    "\n",
    "    options={'gtol': 1e-3, 'disp': False}\n",
    "    res = minimize(obj, S.CoeffMap(), args=(S, Xtrain), jac=grad_obj, method='BFGS', options=options)\n",
    "    \n",
    "    # Reference density\n",
    "    eta = multivariate_normal(np.zeros(S.outputDim),np.eye(S.outputDim))\n",
    "\n",
    "    # Compute log-conditional density at testing samples\n",
    "    logPdfTM_to1[dk-1,:]=log_cond_pullback_pdf(S,eta,Xtestk)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03e5c2cb",
   "metadata": {},
   "source": [
    "#### Compute KL divergence error\n",
    "\n",
    "Since we know what the true is for problem we can compute the KL divergence $D_{KL}(\\pi(\\mathbf{x}_t)||S^\\sharp \\eta)$ between the map-induced density and the true density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f3978f55",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:55.439182Z",
     "iopub.status.busy": "2024-03-21T17:44:55.437649Z",
     "iopub.status.idle": "2024-03-21T17:44:55.464197Z",
     "shell.execute_reply": "2024-03-21T17:44:55.463758Z"
    }
   },
   "outputs": [],
   "source": [
    "logPdfSV = SV_log_pdf(Xtest) # true log-pdf\n",
    "\n",
    "def compute_joint_KL(logPdfSV,logPdfTM):\n",
    "    KL = np.zeros((logPdfSV.shape[0],))\n",
    "    for k in range(1,d+1):\n",
    "        KL[k-1]=np.mean(np.sum(logPdfSV[:k,:],0)-np.sum(logPdfTM[:k,:],0))\n",
    "    return KL\n",
    "\n",
    "# Compute joint KL divergence for total order 1 approximation\n",
    "KL_to1 = compute_joint_KL(logPdfSV,logPdfTM_to1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6ec96db",
   "metadata": {},
   "source": [
    "### Training total order 2 map"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e23759e0",
   "metadata": {},
   "source": [
    "Here we use a total order 2 multivariate expansion to parameterize each component $S_k$, $k \\in \\{1,...,T+2\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7e2c419",
   "metadata": {},
   "source": [
    "#### Optimization\n",
    "\n",
    "This step can take few minutes depending on the number of time steps set at the definition of the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cec1039a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:44:55.468262Z",
     "iopub.status.busy": "2024-03-21T17:44:55.466959Z",
     "iopub.status.idle": "2024-03-21T17:50:36.996002Z",
     "shell.execute_reply": "2024-03-21T17:50:36.995509Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   0%|          | 0/32 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   6%|▋         | 2/32 [00:00<00:06,  5.00it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   9%|▉         | 3/32 [00:00<00:05,  4.86it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  12%|█▎        | 4/32 [00:01<00:08,  3.46it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  16%|█▌        | 5/32 [00:01<00:13,  2.01it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  19%|█▉        | 6/32 [00:03<00:18,  1.38it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  22%|██▏       | 7/32 [00:04<00:23,  1.09it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  25%|██▌       | 8/32 [00:05<00:22,  1.06it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  28%|██▊       | 9/32 [00:06<00:25,  1.13s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  31%|███▏      | 10/32 [00:09<00:34,  1.56s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  34%|███▍      | 11/32 [00:12<00:43,  2.06s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  38%|███▊      | 12/32 [00:15<00:48,  2.41s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  41%|████      | 13/32 [00:21<01:01,  3.25s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  44%|████▍     | 14/32 [00:25<01:02,  3.49s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  47%|████▋     | 15/32 [00:30<01:10,  4.17s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  50%|█████     | 16/32 [00:41<01:35,  5.99s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  53%|█████▎    | 17/32 [00:49<01:41,  6.80s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  56%|█████▋    | 18/32 [01:01<01:54,  8.16s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  59%|█████▉    | 19/32 [01:11<01:53,  8.76s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  62%|██████▎   | 20/32 [01:23<01:56,  9.70s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  66%|██████▌   | 21/32 [01:34<01:53, 10.29s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  69%|██████▉   | 22/32 [01:46<01:45, 10.57s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  72%|███████▏  | 23/32 [02:00<01:46, 11.79s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  75%|███████▌  | 24/32 [02:14<01:38, 12.25s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  78%|███████▊  | 25/32 [02:33<01:40, 14.42s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  81%|████████▏ | 26/32 [02:53<01:37, 16.23s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  84%|████████▍ | 27/32 [03:13<01:26, 17.24s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  88%|████████▊ | 28/32 [03:41<01:22, 20.52s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  91%|█████████ | 29/32 [04:03<01:02, 20.93s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  94%|█████████▍| 30/32 [04:39<00:50, 25.34s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  97%|█████████▋| 31/32 [05:11<00:27, 27.39s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component: 100%|██████████| 32/32 [05:41<00:00, 28.19s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component: 100%|██████████| 32/32 [05:41<00:00, 10.67s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "# Total order 2 approximation\n",
    "totalOrder = 2\n",
    "logPdfTM_to2 = np.zeros((d,Ntest))\n",
    "ListCoeffs_to2=np.zeros((d,))\n",
    "for dk in tqdm(range(1,d+1),desc=\"Map component\"):\n",
    "    fixed_mset= mt.FixedMultiIndexSet(dk,totalOrder)\n",
    "    S = mt.CreateComponent(fixed_mset,opts)\n",
    "    Xtrain = X[:dk,:]\n",
    "    Xtestk = Xtest[:dk,:]\n",
    "\n",
    "    ListCoeffs_to2[dk-1]=S.numCoeffs\n",
    "\n",
    "    options={'gtol': 1e-3, 'disp': False}\n",
    "    res = minimize(obj, S.CoeffMap(), args=(S, Xtrain), jac=grad_obj, method='BFGS', options=options)\n",
    "    \n",
    "    # Reference density\n",
    "    eta = multivariate_normal(np.zeros(S.outputDim),np.eye(S.outputDim))\n",
    "\n",
    "    # Compute log-conditional density at testing samples\n",
    "    logPdfTM_to2[dk-1,:]=log_cond_pullback_pdf(S,eta,Xtestk)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e9896a1",
   "metadata": {},
   "source": [
    "#### Compute KL divergence error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b2adb05f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:50:36.998589Z",
     "iopub.status.busy": "2024-03-21T17:50:36.998234Z",
     "iopub.status.idle": "2024-03-21T17:50:37.007007Z",
     "shell.execute_reply": "2024-03-21T17:50:37.006580Z"
    }
   },
   "outputs": [],
   "source": [
    "# Compute joint KL divergence for total order 2 approximation\n",
    "KL_to2 = compute_joint_KL(logPdfSV,logPdfTM_to2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3456546",
   "metadata": {},
   "source": [
    "### Training sparse map"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0361302",
   "metadata": {},
   "source": [
    "Here we use the prior knowledge of the conditional independence property of the target density $\\pi(\\mathbf{x}_T)$ to parameterize map components with a map structure."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57f56da8",
   "metadata": {},
   "source": [
    "#### Prior knowledge used to parameterize map components"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ceaac4",
   "metadata": {},
   "source": [
    "From the independence structure mentionned in the problem formulation we have:\n",
    "\n",
    "\n",
    "*   $\\pi(\\mu,\\phi)=\\pi(\\mu)\\pi(\\phi)$, meaning $S_2$ only dependes on $\\phi$\n",
    "*   $\\pi(z_{k-2}|z_{k-3},...,z_{0},\\phi,\\mu)=\\pi(z_{k-2}|z_{k-3},\\phi,\\mu),\\,\\, k>3$,  meaning $S_k$, only depends on $z_{k-2}$,$z_{k-3}$, $\\phi$ and $\\mu$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "521e1225",
   "metadata": {},
   "source": [
    "Complexity of map component can also be deducted from problem formulation:\n",
    "\n",
    "\n",
    "*   $\\pi(\\mu)$ being a normal distribution, $S_1$ should be of order 1.\n",
    "*  $\\pi(\\phi)$ is non-Gaussian such that $S_2$ should be nonlinear.\n",
    "*  $\\pi(z_{k-2}|z_{k-3},\\phi,\\mu)$ can be represented by a total order 2 parameterization due to the linear autoregressive model.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6faabf94",
   "metadata": {},
   "source": [
    "Hence multi-index sets used for this problem are:\n",
    "\n",
    "\n",
    "*   $k=1$: 1D expansion of order $\\geq$ 1\n",
    "*   $k=2$: 1D expansion (depending on last component) of high order $>1$\n",
    "*   $k=3$: 3D expansion of total order 2\n",
    "*   $k>3$: 4D expansion (depending on first two and last two components) of total order 2\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac245384",
   "metadata": {},
   "source": [
    "#### Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "afb95e31",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:50:37.009776Z",
     "iopub.status.busy": "2024-03-21T17:50:37.009459Z",
     "iopub.status.idle": "2024-03-21T17:50:52.384923Z",
     "shell.execute_reply": "2024-03-21T17:50:52.384450Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   0%|          | 0/32 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   6%|▋         | 2/32 [00:03<00:55,  1.86s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:   9%|▉         | 3/32 [00:03<00:34,  1.18s/it]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  12%|█▎        | 4/32 [00:04<00:25,  1.11it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  16%|█▌        | 5/32 [00:04<00:19,  1.41it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  19%|█▉        | 6/32 [00:05<00:15,  1.72it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  22%|██▏       | 7/32 [00:05<00:12,  1.94it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  25%|██▌       | 8/32 [00:05<00:10,  2.31it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  28%|██▊       | 9/32 [00:06<00:10,  2.21it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  31%|███▏      | 10/32 [00:06<00:09,  2.42it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  34%|███▍      | 11/32 [00:07<00:09,  2.24it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  38%|███▊      | 12/32 [00:07<00:10,  1.96it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  41%|████      | 13/32 [00:08<00:09,  2.07it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  44%|████▍     | 14/32 [00:08<00:08,  2.18it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  47%|████▋     | 15/32 [00:08<00:07,  2.16it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  50%|█████     | 16/32 [00:09<00:06,  2.49it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  53%|█████▎    | 17/32 [00:09<00:05,  2.56it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  56%|█████▋    | 18/32 [00:10<00:05,  2.51it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  59%|█████▉    | 19/32 [00:10<00:04,  2.84it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  62%|██████▎   | 20/32 [00:10<00:04,  2.73it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  66%|██████▌   | 21/32 [00:10<00:03,  2.88it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  69%|██████▉   | 22/32 [00:11<00:03,  2.79it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  72%|███████▏  | 23/32 [00:11<00:03,  2.98it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  75%|███████▌  | 24/32 [00:12<00:03,  2.58it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  78%|███████▊  | 25/32 [00:12<00:02,  2.62it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  81%|████████▏ | 26/32 [00:12<00:02,  2.55it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  84%|████████▍ | 27/32 [00:13<00:01,  2.85it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  88%|████████▊ | 28/32 [00:13<00:01,  2.76it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  91%|█████████ | 29/32 [00:13<00:00,  3.01it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  94%|█████████▍| 30/32 [00:14<00:00,  2.13it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component:  97%|█████████▋| 31/32 [00:14<00:00,  2.27it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component: 100%|██████████| 32/32 [00:15<00:00,  2.40it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\r",
      "Map component: 100%|██████████| 32/32 [00:15<00:00,  2.08it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "totalOrder = 2\n",
    "logPdfTM_sa = np.zeros((d,Ntest))\n",
    "ListCoeffs_sa = np.zeros((d,))\n",
    "\n",
    "# MultiIndexSet for map S_k, k>3\n",
    "mset_to= mt.MultiIndexSet.CreateTotalOrder(4,totalOrder,mt.NoneLim()) \n",
    "\n",
    "maxOrder=9 # order for map S_2\n",
    "for dk in tqdm(range(1,d+1),desc=\"Map component\"):\n",
    "    if dk == 1:\n",
    "        fixed_mset= mt.FixedMultiIndexSet(1,totalOrder)\n",
    "        S = mt.CreateComponent(fixed_mset,opts)\n",
    "        Xtrain = X[dk-1,:].reshape(1,-1)\n",
    "        Xtestk = Xtest[dk-1,:].reshape(1,-1)\n",
    "    elif dk == 2:\n",
    "        fixed_mset= mt.FixedMultiIndexSet(1,maxOrder)\n",
    "        S = mt.CreateComponent(fixed_mset,opts)\n",
    "        Xtrain = X[dk-1,:].reshape(1,-1)\n",
    "        Xtestk = Xtest[dk-1,:].reshape(1,-1) \n",
    "    elif dk==3:\n",
    "        fixed_mset= mt.FixedMultiIndexSet(dk,totalOrder)\n",
    "        S = mt.CreateComponent(fixed_mset,opts)\n",
    "        Xtrain = X[:dk,:]\n",
    "        Xtestk = Xtest[:dk,:]\n",
    "    else:\n",
    "        multis=np.zeros((mset_to.Size(),dk))\n",
    "        for s in range(mset_to.Size()):\n",
    "            multis_to = np.array([mset_to[s].tolist()])\n",
    "            multis[s,:2]=multis_to[0,:2]\n",
    "            multis[s,-2:]=multis_to[0,-2:]\n",
    "        mset = mt.MultiIndexSet(multis)\n",
    "        fixed_mset = mset.fix(True)\n",
    "        S = mt.CreateComponent(fixed_mset,opts)\n",
    "        Xtrain = X[:dk,:]\n",
    "        Xtestk = Xtest[:dk,:]\n",
    "\n",
    "    ListCoeffs_sa[dk-1]=S.numCoeffs\n",
    "\n",
    "    options={'gtol': 1e-3, 'disp': False}\n",
    "    res = minimize(obj, S.CoeffMap(), args=(S, Xtrain), jac=grad_obj, method='BFGS', options=options)\n",
    "    rho = multivariate_normal(np.zeros(S.outputDim),np.eye(S.outputDim))    \n",
    "    \n",
    "    logPdfTM_sa[dk-1,:]=log_cond_pullback_pdf(S,rho,Xtestk)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "720a1587",
   "metadata": {},
   "source": [
    "#### Compute KL divergence error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "26cccf8a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:50:52.389243Z",
     "iopub.status.busy": "2024-03-21T17:50:52.387877Z",
     "iopub.status.idle": "2024-03-21T17:50:52.398310Z",
     "shell.execute_reply": "2024-03-21T17:50:52.397871Z"
    }
   },
   "outputs": [],
   "source": [
    "# Compute joint KL divergence\n",
    "KL_sa = compute_joint_KL(logPdfSV,logPdfTM_sa)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf87687c",
   "metadata": {},
   "source": [
    "## Compare approximations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bb992a5",
   "metadata": {},
   "source": [
    "### KL divergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "01889136",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:50:52.414360Z",
     "iopub.status.busy": "2024-03-21T17:50:52.401024Z",
     "iopub.status.idle": "2024-03-21T17:50:52.759746Z",
     "shell.execute_reply": "2024-03-21T17:50:52.759315Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:8: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:8: SyntaxWarning: invalid escape sequence '\\p'\n",
      "/tmp/ipykernel_268/1071692651.py:8: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  ax.set_ylabel('$D_{KL}(\\pi(\\mathbf{x}_t)||S^\\sharp \\eta)$')\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 704x528 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare map approximations \n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(range(1,d+1),KL_to1,'-o',label='Total order 1')\n",
    "ax.plot(range(1,d+1),KL_to2,'-o',label='Total order 2')\n",
    "ax.plot(range(1,d+1),KL_sa,'-o',label='Sparse MultiIndexSet')\n",
    "ax.set_yscale('log')\n",
    "ax.set_xlabel('d')\n",
    "ax.set_ylabel('$D_{KL}(\\pi(\\mathbf{x}_t)||S^\\sharp \\eta)$')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b8e9f34",
   "metadata": {},
   "source": [
    "Usually increasing map complexity will improve map approximation. However when the number of parameters increases too much compared to the number of samples, computed map overfits the data which lead to worst approximation. This overfitting can be seen in this examples when looking at the total order 2 approximation that rapidly loses accuracy when the dimension increases.\n",
    "\n",
    "Using sparse multi-index sets help reduces the increase of parameters when the dimension increases leading to better approximation for all dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6d2147d",
   "metadata": {},
   "source": [
    "### Map coefficients"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d84783",
   "metadata": {},
   "source": [
    "To complement observations made above, we visualize the number of parameters (polyniomal coefficients) for each map parameterization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "17062a2f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-21T17:50:52.761921Z",
     "iopub.status.busy": "2024-03-21T17:50:52.761576Z",
     "iopub.status.idle": "2024-03-21T17:50:52.954225Z",
     "shell.execute_reply": "2024-03-21T17:50:52.953710Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 704x528 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax =plt.subplots()\n",
    "ax.plot(range(1,d+1),ListCoeffs_to1,'-o',label='Total order 1')\n",
    "ax.plot(range(1,d+1),ListCoeffs_to2,'-o',label='Total order 2')\n",
    "ax.plot(range(1,d+1),ListCoeffs_sa,'-o',label='Sparse MultiIndexSet')\n",
    "ax.set_xlabel('d')\n",
    "ax.set_ylabel('# coefficients')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d36fada3",
   "metadata": {},
   "source": [
    "We can observe the exponential growth of the number coefficients for the total order 2 approximation. Chosen sparse multi-index sets have a fixed number of parameters which become smaller than the number of parameters of the total order 1 approximation when dimension is 15."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c3496fd",
   "metadata": {},
   "source": [
    "Using less parameters helps error scaling with dimension but aslo helps reducing computation time for the optimization and the evaluation the transport maps."
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": "ipynb,py"
  },
  "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": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}