intro.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from chmm_actions import CHMM, forwardE, datagen_structured_obs_room\n",
    "import matplotlib.pyplot as plt\n",
    "import igraph\n",
    "from matplotlib import cm, colors\n",
    "import os\n",
    "\n",
    "custom_colors = (\n",
    "    np.array(\n",
    "        [\n",
    "            [214, 214, 214],\n",
    "            [85, 35, 157],\n",
    "            [253, 252, 144],\n",
    "            [114, 245, 144],\n",
    "            [151, 38, 20],\n",
    "            [239, 142, 192],\n",
    "            [214, 134, 48],\n",
    "            [140, 194, 250],\n",
    "            [72, 160, 162],\n",
    "        ]\n",
    "    )\n",
    "    / 256\n",
    ")\n",
    "if not os.path.exists(\"figures\"):\n",
    "    os.makedirs(\"figures\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_graph(\n",
    "    chmm, x, a, output_file, cmap=cm.Spectral, multiple_episodes=False, vertex_size=30\n",
    "):\n",
    "    states = chmm.decode(x, a)[1]\n",
    "\n",
    "    v = np.unique(states)\n",
    "    if multiple_episodes:\n",
    "        T = chmm.C[:, v][:, :, v][:-1, 1:, 1:]\n",
    "        v = v[1:]\n",
    "    else:\n",
    "        T = chmm.C[:, v][:, :, v]\n",
    "    A = T.sum(0)\n",
    "    A /= A.sum(1, keepdims=True)\n",
    "\n",
    "    g = igraph.Graph.Adjacency((A > 0).tolist())\n",
    "    node_labels = np.arange(x.max() + 1).repeat(n_clones)[v]\n",
    "    if multiple_episodes:\n",
    "        node_labels -= 1\n",
    "    colors = [cmap(nl)[:3] for nl in node_labels / node_labels.max()]\n",
    "    out = igraph.plot(\n",
    "        g,\n",
    "        output_file,\n",
    "        layout=g.layout(\"kamada_kawai\"),\n",
    "        vertex_color=colors,\n",
    "        vertex_label=v,\n",
    "        vertex_size=vertex_size,\n",
    "        margin=50,\n",
    "    )\n",
    "\n",
    "    return out\n",
    "\n",
    "\n",
    "def get_mess_fwd(chmm, x, pseudocount=0.0, pseudocount_E=0.0):\n",
    "    n_clones = chmm.n_clones\n",
    "    E = np.zeros((n_clones.sum(), len(n_clones)))\n",
    "    last = 0\n",
    "    for c in range(len(n_clones)):\n",
    "        E[last : last + n_clones[c], c] = 1\n",
    "        last += n_clones[c]\n",
    "    E += pseudocount_E\n",
    "    norm = E.sum(1, keepdims=True)\n",
    "    norm[norm == 0] = 1\n",
    "    E /= norm\n",
    "    T = chmm.C + pseudocount\n",
    "    norm = T.sum(2, keepdims=True)\n",
    "    norm[norm == 0] = 1\n",
    "    T /= norm\n",
    "    T = T.mean(0, keepdims=True)\n",
    "    log2_lik, mess_fwd = forwardE(\n",
    "        T.transpose(0, 2, 1), E, chmm.Pi_x, chmm.n_clones, x, x * 0, store_messages=True\n",
    "    )\n",
    "    return mess_fwd\n",
    "\n",
    "\n",
    "def place_field(mess_fwd, rc, clone):\n",
    "    assert mess_fwd.shape[0] == rc.shape[0] and clone < mess_fwd.shape[1]\n",
    "    field = np.zeros(rc.max(0) + 1)\n",
    "    count = np.zeros(rc.max(0) + 1, int)\n",
    "    for t in range(mess_fwd.shape[0]):\n",
    "        r, c = rc[t]\n",
    "        field[r, c] += mess_fwd[t, clone]\n",
    "        count[r, c] += 1\n",
    "    count[count == 0] = 1\n",
    "    return field / count\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training a CHMM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of clones: 5.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|█████████████████████████| 100/100 [00:01<00:00, 56.83it/s, train_bps=0.99]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.49545668131679943\n"
     ]
    }
   ],
   "source": [
    "# Train CHMM on random data\n",
    "TIMESTEPS = 1000\n",
    "OBS = 2\n",
    "x = np.random.randint(OBS, size=(1000,))  # Observations. Replace with your data.\n",
    "a = np.zeros(\n",
    "    1000, dtype=np.int64\n",
    ")  # If there are actions in your domain replace this. If not, keep the vector of zeros.\n",
    "n_clones = (\n",
    "    np.ones(OBS, dtype=np.int64) * 5\n",
    ")  # Number of clones specifies the capacity for each observation.\n",
    "\n",
    "x_test = np.random.randint(\n",
    "    OBS, size=(1000,)\n",
    ")  # Test observations. Replace with your data.\n",
    "a_test = np.zeros(1000, dtype=np.int64)\n",
    "\n",
    "chmm = CHMM(n_clones=n_clones, pseudocount=1e-10, x=x, a=a)  # Initialize the model\n",
    "progression = chmm.learn_em_T(x, a, n_iter=100, term_early=False)  # Training\n",
    "\n",
    "nll_per_prediction = chmm.bps(\n",
    "    x_test, a_test\n",
    ")  # Evaluate negative log-likelihood (base 2 log)\n",
    "avg_nll = np.mean(nll_per_prediction)\n",
    "avg_prediction_probability = 2 ** (-avg_nll)\n",
    "print(avg_prediction_probability)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rectangular room datagen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of clones: 70.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 98%|████████████████████▋| 985/1000 [18:20<00:16,  1.12s/it, train_bps=0.00329]\n"
     ]
    }
   ],
   "source": [
    "room = np.array(\n",
    "    [\n",
    "        [1, 2, 3, 0, 3, 1, 1, 1],\n",
    "        [1, 1, 3, 2, 3, 2, 3, 1],\n",
    "        [1, 1, 2, 0, 1, 2, 1, 0],\n",
    "        [0, 2, 1, 1, 3, 0, 0, 2],\n",
    "        [3, 3, 1, 0, 1, 0, 3, 0],\n",
    "        [2, 1, 2, 3, 3, 3, 2, 0],\n",
    "    ]\n",
    ")\n",
    "n_emissions = room.max() + 1\n",
    "\n",
    "a, x, rc = datagen_structured_obs_room(room, length=50000)\n",
    "\n",
    "n_clones = np.ones(n_emissions, dtype=np.int64) * 70\n",
    "chmm = CHMM(n_clones=n_clones, pseudocount=2e-3, x=x, a=a, seed=42)  # Initialize the model\n",
    "progression = chmm.learn_em_T(x, a, n_iter=1000)  # Training\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  2%|▍                      | 2/100 [00:03<02:37,  1.61s/it, train_bps=0.000163]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.0077761025, 0.00016258565, 0.00016258565]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# refine learning\n",
    "chmm.pseudocount = 0.0\n",
    "chmm.learn_viterbi_T(x, a, n_iter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 384x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cmap = colors.ListedColormap(custom_colors[-4:])\n",
    "plt.matshow(room, cmap=cmap)\n",
    "plt.savefig(\"figures/rectangular_room_layout.pdf\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<igraph.drawing.Plot at 0x14d7966a0>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = plot_graph(\n",
    "    chmm, x, a, output_file=\"figures/rectangular_room_graph.pdf\", cmap=cmap\n",
    ")\n",
    "graph\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "mess_fwd = get_mess_fwd(chmm, x, pseudocount_E=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 384x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clone = 114\n",
    "plt.matshow(place_field(mess_fwd, rc, clone))\n",
    "plt.savefig(\"figures/rectangular_room_place_field.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empty rectangular room datagen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of clones: 70.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 63%|█████████████▏       | 630/1000 [11:27<06:43,  1.09s/it, train_bps=0.00713]\n"
     ]
    }
   ],
   "source": [
    "H, W = 6, 8\n",
    "room = np.zeros((H, W), dtype=np.int64)\n",
    "room[:] = 0\n",
    "room[0] = 5\n",
    "room[-1] = 6\n",
    "room[:, 0] = 7\n",
    "room[:, -1] = 8\n",
    "room[0, 0] = 1\n",
    "room[0, -1] = 2\n",
    "room[-1, 0] = 3\n",
    "room[-1, -1] = 4\n",
    "n_emissions = room.max() + 1\n",
    "\n",
    "a, x, rc = datagen_structured_obs_room(room, length=50000)\n",
    "\n",
    "n_clones = np.ones(n_emissions, dtype=np.int64) * 70\n",
    "chmm = CHMM(n_clones=n_clones, pseudocount=2e-3, x=x, a=a, seed=4)  # Initialize the model\n",
    "progression = chmm.learn_em_T(x, a, n_iter=1000)  # Training\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  2%|▍                      | 2/100 [00:02<01:47,  1.10s/it, train_bps=0.000186]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.0071397107, 0.00018598416, 0.00018598416]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# refine learning\n",
    "chmm.pseudocount = 0.0\n",
    "chmm.learn_viterbi_T(x, a, n_iter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 384x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cmap = colors.ListedColormap(custom_colors)\n",
    "plt.matshow(room, cmap=cmap)\n",
    "plt.savefig(\"figures/empty_rectangular_room_layout.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600pt\" height=\"600pt\" viewBox=\"0 0 600 600\" version=\"1.1\">\n",
       "<defs>\n",
       "<g>\n",
       "<symbol overflow=\"visible\" id=\"glyph0-0\">\n",
       "<path style=\"stroke:none;\" d=\"M 0.453125 0 L 0.453125 -10.042969 L 8.421875 -10.042969 L 8.421875 0 Z M 7.164062 -1.257812 L 7.164062 -8.785156 L 1.710938 -8.785156 L 1.710938 -1.257812 Z M 7.164062 -1.257812 \"/>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<igraph.drawing.Plot at 0x14daefe20>"
      ]
     },
     "execution_count": 13,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = plot_graph(\n",
    "    chmm, x, a, output_file=\"figures/empty_rectangular_room_graph.pdf\", cmap=cmap, vertex_size=30\n",
    ")\n",
    "graph\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "mess_fwd = get_mess_fwd(chmm, x, pseudocount_E=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 384x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clone = 58\n",
    "plt.matshow(place_field(mess_fwd, rc, clone))\n",
    "plt.savefig(\"figures/empty_rectangular_room_place_field.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5x5 mazes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of clones: 10.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 12%|██▋                   | 120/1000 [00:01<00:10, 82.03it/s, train_bps=0.0363]\n"
     ]
    }
   ],
   "source": [
    "room = np.random.permutation(25).reshape(5, 5)\n",
    "\n",
    "a, x, rc = datagen_structured_obs_room(room, length=10000)\n",
    "\n",
    "n_clones = np.ones(25, dtype=np.int64) * 10\n",
    "chmm = CHMM(n_clones=n_clones, pseudocount=1e-2, x=x, a=a, seed=4)  # Initialize the model\n",
    "progression = chmm.learn_em_T(x, a, n_iter=1000)  # Training\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  2%|▍                      | 2/100 [00:00<00:03, 27.86it/s, train_bps=0.000797]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0.036278766, 0.0007965784, 0.0007965784]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# refine learning\n",
    "chmm.pseudocount = 0.0\n",
    "chmm.learn_viterbi_T(x, a, n_iter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(room, cmap=\"Reds\")\n",
    "plt.savefig(\"figures/square_room_layout.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<igraph.drawing.Plot at 0x150473640>"
      ]
     },
     "execution_count": 23,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
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     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = plot_graph(\n",
    "    chmm, x, a, output_file=\"figures/square_room_graph.pdf\", cmap=cm.Reds\n",
    ")\n",
    "graph\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "mess_fwd = get_mess_fwd(chmm, x, pseudocount_E=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clone = 75\n",
    "plt.matshow(place_field(mess_fwd, rc, clone))\n",
    "plt.savefig(\"figures/square_room_place_field.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two Rooms Stitched Together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of clones: 18.8125\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 18%|████                  | 182/1000 [00:39<02:59,  4.56it/s, train_bps=0.0262]\n"
     ]
    }
   ],
   "source": [
    "room1 = np.array(\n",
    "    [\n",
    "        [12, 4, 0, 1, 13, 2],\n",
    "        [7, 3, 12, 11, 0, 10],\n",
    "        [5, 12, 14, 12, 9, 4],\n",
    "        [5, 0, 14, 7, 4, 8],\n",
    "        [4, 10, 7, 2, 13, 1],\n",
    "        [3, 14, 8, 3, 12, 11],\n",
    "        [1, 1, 5, 12, 14, 12],\n",
    "        [5, 9, 3, 0, 14, 7],\n",
    "    ]\n",
    ")\n",
    "\n",
    "room2 = np.array(\n",
    "    [\n",
    "        [3, 12, 11, 4, 11, 11],\n",
    "        [12, 14, 12, 11, 9, 1],\n",
    "        [0, 14, 7, 2, 4, 9],\n",
    "        [0, 0, 9, 8, 2, 11],\n",
    "        [8, 13, 8, 6, 9, 2],\n",
    "        [0, 5, 4, 13, 2, 14],\n",
    "        [14, 4, 13, 7, 9, 14],\n",
    "        [11, 1, 3, 13, 3, 0],\n",
    "    ]\n",
    ")\n",
    "\n",
    "H, W = room1.shape\n",
    "\n",
    "no_left = [(r, 0) for r in range(H)]\n",
    "no_right = [(r, W-1) for r in range(H)]\n",
    "no_up = [(0, c) for c in range(W)]\n",
    "no_down = [(H-1, c) for c in range(W)]\n",
    "\n",
    "a1, x1, rc1 = datagen_structured_obs_room(room1, None, None, no_left, no_right, no_up, no_down, length=50000)\n",
    "a2, x2, rc2 = datagen_structured_obs_room(room2, None, None, no_left, no_right, no_up, no_down, length=50000)\n",
    "\n",
    "x = np.hstack((0, x1 + 1, 0, x2 + 1))\n",
    "a = np.hstack((4, a1[:-1], 4, 4, a2))\n",
    "\n",
    "n_emissions = x.max() + 1\n",
    "\n",
    "n_clones = 20 * np.ones(n_emissions, int)\n",
    "n_clones[0] = 1\n",
    "chmm = CHMM(n_clones=n_clones, pseudocount=2e-2, x=x, a=a, seed=19)  # Initialize the model\n",
    "progression = chmm.learn_em_T(x, a, n_iter=1000)  # Training\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  2%|▍                      | 2/100 [00:00<00:42,  2.30it/s, train_bps=0.000102]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_states: 88 (88 for perfect recovery), bps: [ 8.23362  1.      -0.      ... -0.      -0.      -0.     ]\n"
     ]
    }
   ],
   "source": [
    "# refine learning\n",
    "chmm.pseudocount = 0.0\n",
    "chmm.learn_viterbi_T(x, a, n_iter=100)\n",
    "bps = chmm.bps(x, a)\n",
    "states = chmm.decode(x, a)[1]\n",
    "n_states = len(np.unique(states))\n",
    "print(\"n_states: {} (88 for perfect recovery), bps: {}\".format(n_states, bps))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
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      ],
      "text/plain": [
       "<igraph.drawing.Plot at 0x14c9dac70>"
      ]
     },
     "execution_count": 28,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = plot_graph(chmm, x, a, output_file=\"figures/stitched_rooms.pdf\", multiple_episodes=True)\n",
    "graph\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "mess_fwd = get_mess_fwd(chmm, x, pseudocount_E=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 288x416 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clone = 229\n",
    "rc = np.vstack(((0, 8), rc1, (0, 8), rc2 + (5, 3)))\n",
    "pf = place_field(mess_fwd, rc, clone)\n",
    "pf[0, 8] = 0.0\n",
    "plt.matshow(pf)\n",
    "plt.savefig(\"figures/stitched_rooms_place_field.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Three pentagonal cliques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average number of clones: 5.0\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  9%|██                      | 86/1000 [00:00<00:05, 153.44it/s, train_bps=2.06]\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = np.zeros((15, 15))\n",
    "# Connect cliques\n",
    "for i in range(0, 4 + 1):\n",
    "    for j in range(0, 4 + 1):\n",
    "        if i != j:\n",
    "            T[i, j] = 1.0\n",
    "for i in range(5, 9 + 1):\n",
    "    for j in range(5, 9 + 1):\n",
    "        if i != j:\n",
    "            T[i, j] = 1.0\n",
    "for i in range(10, 14 + 1):\n",
    "    for j in range(10, 14 + 1):\n",
    "        if i != j:\n",
    "            T[i, j] = 1.0\n",
    "# Disconnect in clique connector nodes\n",
    "T[0, 4] = 0.0\n",
    "T[4, 0] = 0.0\n",
    "T[5, 9] = 0.0\n",
    "T[9, 5] = 0.0\n",
    "T[10, 14] = 0.0\n",
    "T[14, 10] = 0.0\n",
    "# Connect cross clique connector nodes\n",
    "T[4, 5] = 1.0\n",
    "T[5, 4] = 1.0\n",
    "T[9, 10] = 1.0\n",
    "T[10, 9] = 1.0\n",
    "T[14, 0] = 1.0\n",
    "T[0, 14] = 1.0\n",
    "plt.matshow(T)\n",
    "\n",
    "# Draw data\n",
    "states = [0]\n",
    "for _ in range(10000):\n",
    "    prev_state = states[-1]\n",
    "\n",
    "    possible_next_states = np.where(T[prev_state, :])[0]\n",
    "    next_state = np.random.choice(possible_next_states)\n",
    "    states.append(next_state)\n",
    "states = np.array(states)\n",
    "\n",
    "state_to_obs = (\n",
    "    np.array([1, 2, 3, 4, 5, 6, 1, 4, 5, 2, 8, 2, 3, 5, 7], dtype=int) - 1\n",
    ")  # Aliasing version\n",
    "\n",
    "# Create observation data\n",
    "x = state_to_obs[states]\n",
    "a = np.zeros(len(x), dtype=int)\n",
    "\n",
    "n_clones = np.ones(8, dtype=np.int64) * 5\n",
    "chmm = CHMM(n_clones=n_clones, pseudocount=1.0, x=x, a=a)  # Initialize the model\n",
    "progression = chmm.learn_em_T(x, a, n_iter=1000)  # Training\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  3%|▊                          | 3/100 [00:00<00:12,  7.72it/s, train_bps=1.99]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# refine learning\n",
    "chmm.pseudocount = 0.0\n",
    "chmm.learn_viterbi_T(x, a, n_iter=100)\n",
    "states = chmm.decode(x, a)[1]\n",
    "n_states = len(np.unique(states))\n",
    "n_states\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<igraph.drawing.Plot at 0x14d670c70>"
      ]
     },
     "execution_count": 33,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cmap = colors.ListedColormap(custom_colors[[7, 3, 2, 1, 5, 0, 4, 6]])\n",
    "graph = plot_graph(chmm, x, a, output_file=\"figures/pentagonal_cliques.pdf\", cmap=cmap)\n",
    "graph\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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