GLM_kay.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "GLM_kay.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "ot_9b6_0H6o4",
        "N4u1DyTvIx0u",
        "VRNH_HwLfTj2"
      ],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Aburas98/NMA-kay-V_cortex_Modelling/blob/main/GLM_kay.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ot_9b6_0H6o4"
      },
      "source": [
        "#Import dataset and libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JndvoS7XIE0V"
      },
      "source": [
        "import os\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HBFpMpr-IKHM"
      },
      "source": [
        "fname = \"kay_labels.npy\"\n",
        "if not os.path.exists(fname):\n",
        "  !wget -qO $fname https://osf.io/r638s/download\n",
        "fname = \"kay_labels_val.npy\"\n",
        "if not os.path.exists(fname):\n",
        "  !wget -qO $fname https://osf.io/yqb3e/download\n",
        "fname = \"kay_images.npz\"\n",
        "if not os.path.exists(fname):\n",
        "  !wget -qO $fname https://osf.io/ymnjv/download"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KwsAPXlXIMvb"
      },
      "source": [
        "with np.load(fname) as dobj:\n",
        "    dat = dict(**dobj)\n",
        "labels = np.load('kay_labels.npy')\n",
        "val_labels = np.load('kay_labels_val.npy')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o2UR46OW8RHt"
      },
      "source": [
        "\n",
        "`labels` is a 4 by stim array of class names:  \n",
        "- row 3 has the labels predicted by a deep neural network (DNN) trained on Imagenet\n",
        "- rows 0-2 correspond to different levels of the wordnet hierarchy for the DNN predictions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o_P2QFoM7NJe"
      },
      "source": [
        "`dat` has the following fields:  \n",
        "- `stimuli`: stim x i x j array of grayscale stimulus images\n",
        "- `stimuli_test`: stim x i x j array of grayscale stimulus images in the test set  \n",
        "- `responses`: stim x voxel array of z-scored BOLD response amplitude\n",
        "- `responses_test`:  stim x voxel array of z-scored BOLD response amplitude in the test set  \n",
        "- `roi`: array of voxel labels\n",
        "- `roi_names`: array of names corresponding to voxel labels"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N4u1DyTvIx0u"
      },
      "source": [
        "# Divide ROIs for training set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H3I5jaKpJpuc"
      },
      "source": [
        "roi_responses_list = []\n",
        "for roi_index in range(1,8):\n",
        "    bold_index = dat['roi'] == roi_index\n",
        "    roi_responses_list.append(\n",
        "        np.array([ bold[bold_index] for bold in dat['responses']]))\n",
        "np_v1, np_v2, np_v3, np_v3a, np_v3b, np_v4, np_latocc = roi_responses_list\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VRNH_HwLfTj2"
      },
      "source": [
        "# Divide ROIs for test set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wumx9NzMJ3Le"
      },
      "source": [
        "# I did not use this for prediction as I initially intended, because test set has less labels than training set (less categorical variables)\n",
        "troi_responses_list = []\n",
        "for roi_index in range(1,8):\n",
        "    bold_index = dat['roi'] == roi_index\n",
        "    troi_responses_list.append(\n",
        "        np.array([ bold[bold_index] for bold in dat['responses_test']]))\n",
        "np_v1test, np_v2test, np_v3test, np_v3atest, np_v3btest, np_v4test, np_latocctest = troi_responses_list "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lz_S47fdyBuo"
      },
      "source": [
        "# Encode labels and construct the design matrix X"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Sfzk_LmgyaU4",
        "outputId": "f99bfefe-dd94-415b-c721-1d7ef9760c5f"
      },
      "source": [
        "level1 = labels[0,:]\n",
        "print(level1.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1750,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MuHnjX4bjRMe"
      },
      "source": [
        "from numpy import array\n",
        "from numpy import argmax\n",
        "from sklearn.preprocessing import LabelEncoder\n",
        "from sklearn.preprocessing import OneHotEncoder"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_uuLtmpWyyln",
        "outputId": "9b056d98-78dd-459a-c5ff-abb46818a340"
      },
      "source": [
        "# integer encode\n",
        "label_encoder = LabelEncoder()\n",
        "integer_encoded = label_encoder.fit_transform(level1)\n",
        "print(integer_encoded.shape)\n",
        "# binary encode\n",
        "onehot_encoder = OneHotEncoder(sparse=False)\n",
        "integer_encoded = integer_encoded.reshape(len(integer_encoded), 1)\n",
        "X = onehot_encoder.fit_transform(integer_encoded)\n",
        "print(X.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1750,)\n",
            "(1750, 8)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sfq0-6awg55F",
        "outputId": "4d9fb79d-2683-4b6c-daa0-d9ba1e3fb385"
      },
      "source": [
        "X_t = np.transpose(X)\n",
        "mult = np.dot(X_t,X)\n",
        "print(mult.shape)\n",
        "# check for multicollinearity\n",
        "np.linalg.det(mult) == 0 "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(8, 8)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dyL33hKQOk0T",
        "outputId": "50401560-e306-4099-ed88-865eb8d9c7db"
      },
      "source": [
        "print(level1[10:20])\n",
        "print(X[10:20])\n",
        "x = np.where()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['artifact' 'artifact' 'artifact' 'animal' 'geological formation' 'entity'\n",
            " 'artifact' 'animal' 'animal' 'artifact']\n",
            "[[0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XRKX3BpZDA8L"
      },
      "source": [
        "Y = dat[\"responses\"]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nPY1KI68NljB",
        "outputId": "63aab751-39b0-40f0-9ea9-85571601698d"
      },
      "source": [
        "Y.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1750, 8428)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bH-wwbIZzZvN"
      },
      "source": [
        "#Import model and fit to data\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rMm3O1LDhgUC"
      },
      "source": [
        "import sklearn as sk\n",
        "from sklearn import linear_model\n",
        "from sklearn.metrics import r2_score"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h4zwysUKVYN6"
      },
      "source": [
        "## Model fitting for V1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mv8biI-ozArH"
      },
      "source": [
        "model1 = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_v1)\n",
        "v1_score = r2_score(np_v1, model1.predict(X))\n",
        "print(f\"R2 score for V1 is {v1_score}\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EyA2UBZ9jjQk"
      },
      "source": [
        "## Model fitting for V2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iBPBtyXIjhPN",
        "outputId": "4b7a2004-bd43-41a7-93ac-67e1aa1b061a"
      },
      "source": [
        "model2 = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_v2)\n",
        "v2_score = r2_score(np_v2, model2.predict(X))\n",
        "print(f\"R2 score for V2 is {v2_score}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score for V2 is 0.0008442358838341754\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cp6--V-Kj5hm"
      },
      "source": [
        "## Model fitting for V3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6KQYDpfQkXDz",
        "outputId": "7c70622d-a9c2-4a10-bd1f-8a1b31b75f22"
      },
      "source": [
        "model3 = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_v3)\n",
        "v3_score = r2_score(np_v3, model3.predict(X))\n",
        "print(f\"R2 score for V3 is {v3_score}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score for V3 is 0.001023488631134326\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z343PVVNj5v1"
      },
      "source": [
        "## Model fitting for V3A"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "28d8fQT3kico",
        "outputId": "2fd2ab5e-0d79-4791-80d8-9c1de43fa471"
      },
      "source": [
        "model3a = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_v3a)\n",
        "v3a_score = r2_score(np_v3a, model3a.predict(X))\n",
        "print(f\"R2 score for V3a is {v3a_score}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score for V3a is 0.0024178710597828005\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vEwHFczjj6jL"
      },
      "source": [
        "## Model fitting for V3B"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JEPWAM3kktob",
        "outputId": "7e24306f-1d98-4b7c-db6b-b69c139f479e"
      },
      "source": [
        "model3b = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_v3b)\n",
        "v3b_score = r2_score(np_v3b, model3b.predict(X))\n",
        "print(f\"R2 score for V3b is {v3b_score}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score for V3b is 0.005073717254267692\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vfrgkGKdaLuz"
      },
      "source": [
        "model4 = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_v4)\n",
        "v4_score = r2_score(np_v4, model4.predict(X))\n",
        "print(f\"R2 score for V4 is {v4_score}\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ux9b3bnj6qk"
      },
      "source": [
        "## Model fitting for LO"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BBZFestNkTK4",
        "outputId": "a538c86f-b7c9-43ca-d5cf-a0df1da652da"
      },
      "source": [
        "model_lo = linear_model.MultiTaskLassoCV(cv=6, random_state=0).fit(X,np_latocc)\n",
        "lo_score = r2_score(np_latocc, model_lo.predict(X))\n",
        "print(f\"R2 score for LO is {lo_score}\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 score for LO is 0.005980201825683018\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C-8tBvI_o5Vk"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z33wNT9cCbHp"
      },
      "source": [
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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pbwxj5r8Cmi6"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}