central_concepts_in_ML_for_decoding.ipynb

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  "metadata": {
    "colab": {
      "name": "Neural decoding.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/KordingLab/Neural_Decoding/blob/classifiers/central_concepts_in_ML_for_decoding.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w2FCVtm3EhuL",
        "colab_type": "text"
      },
      "source": [
        "# Decoding neural activity\n",
        "_Machine learning for mind reading_\n",
        "\n",
        "This tutorial introduces concepts that are central to the practice of decoding neural activity using machine learning (or any method). We will make heavy use of our [Python package for neural decoding](https://github.com/KordingLab/Neural_Decoding).\n",
        "\n",
        "This tutorial accompanies these [lecture slides](https://).\n",
        "\n",
        "The solutions to the exercises can be found in [this completed Colab](https://colab.research.google.com/drive/1SxXwmTgW2Ro34BQEy91zOXHs9JhMqcBJ).\n",
        "\n",
        "### Outline\n",
        "\n",
        "1. Overfitting\n",
        "2. Crossvalidation\n",
        "3. Regularization\n",
        "4. Applying recurrent neural networks\n",
        "5. What methods work best and when?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ufp0LsaTwe5B",
        "colab_type": "text"
      },
      "source": [
        "## Preliminaries\n",
        "\n",
        "Import modules and simulate data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ih_NKq_Xn98m",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6zqKK3iOwK6X",
        "colab_type": "text"
      },
      "source": [
        "### Let's simulate some data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aKOAseCQmd5U",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Generate some fake trial data\n",
        "n_trials = 250\n",
        "n_neurons = 10\n",
        "n_bins_per_trial = 50\n",
        "\n",
        "# And generate some fake neural recordings\n",
        "# We'll pretend we have a drift diffusion model\n",
        "\n",
        "def generate_neural_data(n_trials, n_neurons = 25, n_bins_per_trial = 50,\n",
        "                         noise_variance = 1, drift_rate = 0.07,\n",
        "                         mean_rate = 25):\n",
        "  \"\"\"Generates fake neural data of shape (n_trials, n_neurons, n_bins_per_trial\n",
        "        according to a drift diffusion process with given parameters.\n",
        "     Also generates decisions, which is 0 or 1 depending on the \"animal's decision\"\n",
        "        and is returned as an array of shape (n_trials,) \n",
        "        \n",
        "    Returns: (neural_data, decisions)\n",
        "  \"\"\"\n",
        "\n",
        "  decisions = np.random.binomial(1,.5,size = n_trials)\n",
        "  \n",
        "  neural_recordings = np.zeros((n_trials,n_neurons,n_bins_per_trial))\n",
        "\n",
        "  for t in range(n_bins_per_trial):\n",
        "    if t==0:\n",
        "      neural_recordings[:,:,t] = mean_rate + np.random.randn(n_trials,n_neurons) * noise_variance\n",
        "    else:\n",
        "      neural_recordings[:,:,t] = neural_recordings[:,:,t-1] \\\n",
        "                      + np.reshape(drift_rate*(decisions*2-1),(len(decisions),1)) \\\n",
        "                      + np.random.randn(n_trials,n_neurons) * noise_variance\n",
        "      \n",
        "  return neural_recordings, decisions\n",
        "\n",
        "neural_recordings, decisions = generate_neural_data(n_trials, \n",
        "                                         n_neurons, n_bins_per_trial)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bN82ZMD7q0X1",
        "colab_type": "code",
        "outputId": "86300c04-0da6-4d08-9e92-9388bac8e82f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "source": [
        "# plot out some trials for one neuron\n",
        "\n",
        "neuron_id = 0\n",
        "\n",
        "plt.figure(figsize=(10,5))\n",
        "plt.plot(np.arange(0,500,10),neural_recordings[:10,neuron_id,:].T)\n",
        "plt.xlabel(\"Time (ms)\")\n",
        "plt.ylabel(\"Spike rate (Hz)\")\n",
        "plt.legend([\"Trial {}\".format(i) for i in range(1,6)])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f97c8214da0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
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acnx97jPFixFkIzLyua+Gc6u6GJFlIwqFOWq1L2pLU7KlVvugVFq1Sbw3ijYdiJVMKXI8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Gs9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\nTAghhBDCBiQJE0IIIYSwgf8HtxHWXJ9M08oAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "euk_r7MYJ9PS",
        "colab_type": "text"
      },
      "source": [
        "#### Exercise 0: Look at the distribution of neural activity \n",
        "\n",
        "Let's gain an intuition for the data. Plot out the average neural activity for each of the two choices. \n",
        "\n",
        "Average across trials **and** neurons — we're going to assume they have the same response properties. Then, plot out the averages for trials with a choices of 0 vs a choice of 1.\n",
        "\n",
        "If you have extra time, overlay the standard deviations."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3r6MNcOQN7Kc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JhQtKkGZgrvB",
        "colab_type": "text"
      },
      "source": [
        "## 1. Overfitting\n",
        "\n",
        "<img src='https://cdn-images-1.medium.com/max/1600/1*SBUK2QEfCP-zvJmKm14wGQ.png' />\n",
        "\n",
        "In common parlance, we call a classifier or regressor 'overfit' when it has learned to explain noise in the training set at the expense of its ability to generalize to new data.\n",
        "\n",
        "In that one-sentence description, we invoked the concepts of _training set_ and _generalization_. These are absolutely key to any modeling effort, including decoding.\n",
        "\n",
        "##### Training sets vs. testing sets\n",
        "You need to train your decoder, obviously, and for that you'll need training data. No one cares how well your decoder works on your training data, though. What we care about is its _performance on data not used for training_.  That is, we are interested in how well your decoder **generalizes** to new data. The only way to rigorously know how well your decoder generalizes is to test it on data not used for training. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8ge2NEhXUD8E",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn import linear_model"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u1EhoS2kgsZT",
        "colab_type": "code",
        "outputId": "2b9cc4fa-06ba-489d-8b1a-8f78e04da00a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "## Fit a decoder using all your data\n",
        "\n",
        "# We'll predict each decision using all neurons's activity throughout the trials\n",
        "X = np.reshape(neural_recordings, (n_trials,-1))\n",
        "\n",
        "# initalize the model\n",
        "my_naive_model = linear_model.LinearRegression()\n",
        "\n",
        "#fit\n",
        "my_naive_model.fit(X, decisions)\n",
        "\n",
        "# And see how we did on our data set,\n",
        "print(\"R2 was\",my_naive_model.score(X,decisions))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R2 was 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aATf_EwnnQyC",
        "colab_type": "text"
      },
      "source": [
        "**Looks great!** \n",
        "\n",
        "#### Exercise 1.1: \n",
        "Now, suppose you release your decoder in the world. Will it work? Can't be better than perfect, right?\n",
        "\n",
        "Create some new data and use the `score` function to see the $R^2$ of your model on new data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3OmY3-jDnWjR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Let's do new electrophysiology and take new data. This cost $2,000,000 in \n",
        "# NIH funding so it better work.\n",
        "new_neural_recordings, new_decisions = generate_neural_data(n_trials, \n",
        "                                             n_neurons, n_bins_per_trial)\n",
        "new_X = np.reshape(new_neural_recordings, (n_trials,-1))\n",
        "\n",
        "\n",
        "# Now you: score the model on this new data\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iBrTBP3oZ16v",
        "colab_type": "text"
      },
      "source": [
        "#### Exercise 1.2: \n",
        "You may have noticed that we're using linear *regression*, even though we have a classification problem.\n",
        "It'd be better to use logistic regression. \n",
        "\n",
        "Fit and score this logistic regression method using your original data.\n",
        "\n",
        "Then, also score this method with the new data you just obtained with your R01 funds. (That is, print both the test and train accuracy.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C13c7lGIYZZa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "log_reg = linear_model.LogisticRegression(penalty='none', solver = 'lbfgs',\n",
        "                                          max_iter = 1000)\n",
        "\n",
        "# fit\n",
        "\n",
        "# now score on both test and train"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aYdsXI596Gck",
        "colab_type": "text"
      },
      "source": [
        "Once you've completed that, just run this next cell. \n",
        "\n",
        "It shows the coefficients of the fit you just made. Does it match your intuitions? "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dMYFYr5VzPXy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "\n",
        "def plot_coefs(fit_model):\n",
        "  \"\"\"Makes a nice plot of the coefficients. fit_model is the model instance after fitting.\"\"\"\n",
        "  # get the coefficients of your fit\n",
        "  coefficients = fit_model.coef_.reshape(n_neurons, n_bins_per_trial)\n",
        "  \n",
        "\n",
        "  # show them\n",
        "  plt.figure(figsize = (10,5))\n",
        "  plt.imshow(coefficients, cmap = 'coolwarm', vmin = -np.max(coefficients), \n",
        "                                              vmax = np.max(coefficients))\n",
        "\n",
        "  #make it pretty\n",
        "  plt.ylabel(\"Neuron #\", fontsize = 14)\n",
        "  plt.xlabel(\"Time (ms)\", fontsize = 14)\n",
        "  plt.colorbar(orientation = 'horizontal', shrink = .6, \n",
        "               label=\"Contribution of bin to decision; its 'Vote' towards a positive decision.\")\n",
        "  plt.tight_layout()\n",
        "  plt.show()\n",
        "  \n",
        "plot_coefs(log_reg)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ED41_d9dniIE",
        "colab_type": "text"
      },
      "source": [
        "## 2. Crossvalidation\n",
        "\n",
        "We saw in the last section that if we used all of our training data to fit a method, we have no idea how our method will work \n",
        "on new data. This a problem for any engineering purpose.\n",
        "\n",
        "We also have no idea if our coefficients are meaningful or reflect random noise in the data. This is a problem for the science.\n",
        "\n",
        "The way to address this problem is to **split your data into a training segment and a validation segment**. We'll try an 80%/20% split."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZwRNhIco_nrS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "split = int(n_trials*4/5)\n",
        "\n",
        "training_data = \n",
        "validation_data = \n",
        "\n",
        "training_decisions = \n",
        "validation_decisions = "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xii4Ow-nAQVV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# fit on the training data. (Don't forget to reinitialize your decoder first.)\n",
        "log_reg = \n",
        "\n",
        "\n",
        "# fit and score on training\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SeUInXtmAQYQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# score on the validation data"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bo94tWYoAQbF",
        "colab_type": "text"
      },
      "source": [
        "But right now we're only testing on 20% of the data! Small data means high variance, so maybe we can't trust these scores much.\n",
        "\n",
        "A common practice is therefore to perform __k-fold crossvalidation__. This just means we rotate which segment of the original data is the validation set. We can then average the scores."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CK6-aoITAQel",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Just run this.\n",
        "def get_test_train_splits(data, decisions, n_folds=5):\n",
        "  \"\"\"\n",
        "  Returns a tuple of matched train sets and validation sets, rotating through the data.\n",
        "  \n",
        "  Note that there are scikit-learn functions that do this, too.\"\"\"\n",
        "  \n",
        "  fold_size = len(data)//n_folds\n",
        "  \n",
        "  training_sets = [np.roll(data,fold_size*i, axis=0)[fold_size:] for i in range(n_folds)]\n",
        "  val_sets = [np.roll(data,fold_size*i, axis=0)[:fold_size] for i in range(n_folds)]\n",
        "  \n",
        "  training_Y = [np.roll(decisions,fold_size*i, axis=0)[fold_size:] for i in range(n_folds)]\n",
        "  val_Y = [np.roll(decisions,fold_size*i, axis=0)[:fold_size] for i in range(n_folds)]\n",
        "  \n",
        "\n",
        "  return (training_sets, training_Y), (val_sets, val_Y)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0EVx8pdAI7aB",
        "colab_type": "text"
      },
      "source": [
        "#### Excercise 2\n",
        "\n",
        "Fill out the missing gaps in the script below. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j3KLNF9vGDnb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "(training_sets, training_Ys), (val_sets, val_Ys) = get_test_train_splits(X, decisions)\n",
        "\n",
        "scores = []\n",
        "\n",
        "# Iterate through the k=5 folds\n",
        "for fold in range(5):\n",
        "  print(\"Fold {} of 5\".format(fold))\n",
        "  \n",
        "  training_X = training_sets[fold]\n",
        "  training_Y = training_Ys[fold]\n",
        "  \n",
        "  validation_X = val_sets[fold]\n",
        "  validation_Y = val_Ys[fold]\n",
        "  \n",
        "  # Redefine the logistic regression model. (important to do this inside the loop)\n",
        "  this_model = \n",
        "  \n",
        "  # Now fit on the training data\n",
        "  \n",
        "  \n",
        "  # score on the validation data\n",
        "  this_accuracy = \n",
        "  \n",
        "  scores.append(this_accuracy)\n",
        "  \n",
        "  # score on the new dataset (new_X, new_decisions from above)\n",
        "  accuracy_on_test_data = \n",
        "  \n",
        "  print(\"   Validation accuracy of {}\".format( this_accuracy ))\n",
        "  print(\"   True test set accuracy of {}\".format( accuracy_on_test_data ))\n",
        "  plot_coefs(this_model)\n",
        "  \n",
        "print(\"Mean validation accuracy: {}\".format(np.mean(scores)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ItAke3ZhGDpt",
        "colab_type": "text"
      },
      "source": [
        "How close is the validation accuracy to the test set accuracy? \n",
        "\n",
        "How much did using 80% of the data affect the test set accuracy?\n",
        "\n",
        "## 3. Regularization\n",
        "\n",
        "Here we'll apply regularization, as talked about in the lecture.\n",
        "\n",
        "\n",
        "#### Exercise 3.1\n",
        "\n",
        "Go to the [scikit-learn docs](https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression) and decide which form of regularization you would like to use with logistic regression.\n",
        "\n",
        "#### Exercise 3.2\n",
        "\n",
        "Copy and paste the cell from _Excercise 2_, but this time change the `penalty` flag in the `LogisticRegression` call to the form of regularization you chose. \n",
        "\n",
        "\n",
        "First all other default parameters. Then set `C=1e-6` and see what happens.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rkVb9JB3GDrq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# copy, paste, and regularize Exercise 2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fBksWszaLgi5",
        "colab_type": "text"
      },
      "source": [
        "#### Exercise 3.3: Choose the best regularization penalty\n",
        "\n",
        "Let's automate the above process so that we can choose the best performing value of `C`.\n",
        "\n",
        "First, write a function (largely copy and paste from the last exercise) that returns the mean validation accuracy for\n",
        "an arbitrary value of `C`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UXsa18cbqt67",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# First complete this function that takes data (e.g. X) \n",
        "# and a model, and returns the average validation accuracy from 5-fold CV\n",
        "# (Largely copy and past from above, but deleting print statements)\n",
        "def get_kfold_validation_score(data, decisions, C):\n",
        "  \n",
        "  \n",
        "  \n",
        "  return mean_validation_accuracy"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7QFQQAj-rFIF",
        "colab_type": "text"
      },
      "source": [
        "Now let's create a loop for various values of `C` and see what's the best.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4cobrMeXLgoZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# decide on a logarithmic schedule of Cs. \n",
        "Cs_to_test = \n",
        "\n",
        "validation_accuracy_vs_C = []\n",
        "for C in Cs_to_test:\n",
        "  \n",
        "  # get the mean score on k-fold cross-validation using your function above\n",
        "  mean_validation_accuracy = \n",
        "  \n",
        "  validation_accuracy_vs_C.append(mean_validation_accuracy)\n",
        "  \n",
        "  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "30dujMtRNSFP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Now plot the lists you just made. (Just run this.)\n",
        "plt.semilogx(Cs_to_test, validation_accuracy_vs_C,\"o-\")\n",
        "plt.xlabel(\"C\",fontsize=16)\n",
        "plt.ylabel(\"validation acc.\",fontsize=16)\n",
        "plt.ylim([.8,1])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KiuHUp2QSqvy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "zaPCPWdJSqSf"
      },
      "source": [
        "## 4. Applying recurrent neural networks\n",
        "\n",
        "This section is going to be a bit of an introduction to our [python package for neural decoding](https://github.com/KordingLab/Neural_Decoding).\n",
        "\n",
        "First let's install the package. This will also install all the dependencies we need."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "nIwIoxB3SqSg",
        "colab": {}
      },
      "source": [
        "!pip install Neural-Decoding --upgrade"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "n7R8Wu-iSqSk",
        "colab": {}
      },
      "source": [
        "from Neural_Decoding import decoders\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "mNRHoZ8kSqSm"
      },
      "source": [
        "Let's take a look at the documentation of the decoder we'll use."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "PfPChxogSqSo",
        "colab": {}
      },
      "source": [
        "# Run me\n",
        "?decoders.SimpleRNNClassification"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CWLHbPsR_-rb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "?decoders.SimpleRNNClassification.fit"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sLQd5QKsaKdz",
        "colab_type": "text"
      },
      "source": [
        "You'll notice that the shape of the training inputs is now **3-dimensional**. This is because we can now explitly model the effect of time! Hooray! \n",
        "\n",
        "Recall that recurrent neural networks contain a \"hidden state\". The way this decoder works is that it reads all the neural activities in at the first time bin (out of `n_time_bins`) and then updates its hidden state accordingly. The value of this hidden state informs how the hidden state will evolve over time in each trial. After the hidden state updates `n_time_bin` times, it outputs its prediction for the animal's choice.\n",
        "\n",
        "\n",
        "Lets apply this classifier to the data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZGDcn7g6AVeN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# lets re-split our original 3-dimensional trials/neurons/time input data.\n",
        "split = int(n_trials*4/5)\n",
        "\n",
        "training_data = neural_recordings[:split]\n",
        "validation_data = neural_recordings[split:]\n",
        "\n",
        "training_decisions = decisions[:split]\n",
        "validation_decisions = decisions[split:]\n",
        "\n",
        "training_data = np.swapaxes(training_data, 1, 2)\n",
        "validation_data = np.swapaxes(validation_data, 1, 2)\n",
        "\n",
        "print(\"Training input data is of shape\", training_data.shape)\n",
        "print(\"Validation input data is of shape\", validation_data.shape)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D5CLevam9m6N",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "\n",
        "# first we instantiate the decoder\n",
        "my_RNN_classifier = decoders.SimpleRNNClassification(units = 50,\n",
        "                                                    dropout = 0,\n",
        "                                                    num_epochs =250,\n",
        "                                                    verbose = 1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g2V2ttwE-SG9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# now we fit to our training data, like before\n",
        "my_RNN_classifier.fit(training_data, training_decisions)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p7kc5I2xB5ya",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# predict on the validation data\n",
        "\n",
        "predictions = my_RNN_classifier.predict(validation_data)\n",
        "predictions"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l9ihnQ0zHS6Z",
        "colab_type": "text"
      },
      "source": [
        "##### Excercise 4.0\n",
        "\n",
        "Get the percentage of the predictions that were made correctly."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vZyVFSJDF6hD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MUU4_IKwGh4n",
        "colab_type": "text"
      },
      "source": [
        "This is not as quite as good as logistic regression yet. There are a lot of parameters to choose for RNNs, and we haven't tried that yet.\n",
        "\n",
        "\n",
        "#### Looking inside the model\n",
        "\n",
        "Within the `my_RNN_classifier` object you just fit, there is an actual Keras model. We can look at it, change its parameters, and use Keras methods."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cEu_9fToHM_g",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Put the cursor after model, and press tab to see the methods we can call\n",
        "my_RNN_classifier.model."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J9Z-T3diH9ze",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# for example, we can use Keras's in-built method for calculating accuracy\n",
        "from keras.utils import np_utils\n",
        "acc = my_RNN_classifier.model.test_on_batch(validation_data, \n",
        "                                      np_utils.to_categorical(validation_decisions))\n",
        "print(\"Accuracy is {} %\".format(100*acc[1]))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IPVi_UFOLOM6",
        "colab_type": "text"
      },
      "source": [
        "#### Excercise 4.1: Tuning the RNN\n",
        "\n",
        "Train an RNN decoder again, but this time use 1000 hidden units instead of 50."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i3IIljjbLfRD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "aQSc7xswSqTZ"
      },
      "source": [
        "## 5. Compare many methods on actual neural data\n",
        "\n",
        "### Preliminaries\n",
        "\n",
        "**STOP** Make sure you're running a **GPU runtime** for this section. (Runtime -> Change runtime type). Otherwise running the RNNs will take forever.\n",
        "\n",
        "First we need to download the data. I created a script to download and process the Steinmetz data into the format we need. Since the processing script takes about 15 minutes, we'll skip that step, and you can just download the processed data from my Google Drive.\n",
        "\n",
        "This dataset is specifically `Cori_2016-12-18`. If you're interested in loading a different session, I've copied my downloading and preprocessing script in the bottom of this notebook and you can run it right here."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "u0Wt68jUSqTZ",
        "colab": {}
      },
      "source": [
        "!pip install googledrivedownloader\n",
        "\n",
        "from google_drive_downloader import GoogleDriveDownloader as gdd\n",
        "\n",
        "gdd.download_file_from_google_drive(file_id='1W3TwEtC0Z6Qmbfuz8_AWRiQHfuDb9FIS',\n",
        "                                    dest_path='./Binned_data.zip',\n",
        "                                    unzip=True)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "sARtnvbYSqTe",
        "colab": {}
      },
      "source": [
        "binned_spikes = np.load('binned_spikes.npy')\n",
        "choices = np.load('choices.npy')+1\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "6LQ2cxR-SqTi"
      },
      "source": [
        "### Predicting choices from neural population recordings\n",
        "\n",
        "We're going to try to predict the mouse's choices from the neuropixel recordings in the 1 second preceeding each choice. `binned_spikes.npy` is a numpy array containing the binned spike rates, and `choices.npy` contains the animal's choices. \n",
        "\n",
        "There are 228 trials, 1089 neurons, and 50 bins per trial (for a time of 20ms per bin).\n",
        "\n",
        "This is not a great situation for machine learning. As a rule of thumb, we would like more trials than datapoints per trial. (If doing this for realz, would suggest running PCA on this data and using the top components as inputs). But, it's what we got, so here goes!\n",
        "\n",
        "#### Exercise 5.0\n",
        "\n",
        "Print out the shape of `binned_spikes` and `choices`. Also print out the first 10 choices.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "korkcjUISqTi",
        "colab": {}
      },
      "source": [
        "\n",
        "print(binned_spikes.shape, choices.shape)\n",
        "print(choices[:10])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LNDeXvE_cU94",
        "colab_type": "text"
      },
      "source": [
        "You'll notice that `choices` takes values 0, 1, and 2. We're going to try to decode this."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VqEcdu4tX6oF",
        "colab_type": "text"
      },
      "source": [
        "#### Excercise 5.1\n",
        "\n",
        "Split this data into test and validation splits.\n",
        "\n",
        "(We'll skip the final testing phase in this exercise. In reality, make sure to do cross-validation and use both validation and testing data.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RuovaxSOX7Y8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# make training and validation data\n",
        "# Use an 80/20 split.|\n",
        "split = \n",
        "\n",
        "training_spikes = \n",
        "validation_spikes = \n",
        "\n",
        "training_choices = \n",
        "validation_choices ="
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H1HVdWFEZrZl",
        "colab_type": "text"
      },
      "source": [
        "##### A fitting demo.\n",
        "\n",
        "This is basically what we did above, but with actual data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "LPjqE8_OSqTs",
        "colab": {}
      },
      "source": [
        "\n",
        "my_RNN_classifier = decoders.SimpleRNNClassification(units = 100,\n",
        "                                                    dropout = 0,\n",
        "                                                    num_epochs =10,\n",
        "                                                    verbose = 1)\n",
        "\n",
        "my_RNN_classifier.fit(training_spikes, training_choices)\n",
        "\n",
        "\n",
        "predictions = my_RNN_classifier.predict(validation_spikes)\n",
        "accuracy = np.sum(predictions == validation_choices) / float(len(predictions))\n",
        "\n",
        "print(\"\\n validation accuracy: {} %\".format(100*accuracy))\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bpzpvy6PaKCv",
        "colab_type": "text"
      },
      "source": [
        "Note that the train accuracy reached about 100% in these 10 epochs, but the validation accuracy is quite low. Sounds like overfitting! We might want to try some regularization, like dropout."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Xma2jUT5SqTx"
      },
      "source": [
        "### Excercise 5.1\n",
        "\n",
        "Fit each of the following decoders:\n",
        "\n",
        "1.   A Gated Recurrent Unit (`decoders.GRUClassification`)\n",
        "2.   An LSTM (`decoders.LSTMClassification`)\n",
        "3.   Gradient boosted trees (XGBoost) (`decoders.XGBoostClassification`)\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GvvopGtKaw0k",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# GRU\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kaW868Paaw5C",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#LSTM\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jjoE3Qo3aw2n",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# XGBoost\n",
        "\n",
        "# XGBoost is powerful but does not model time dependencies.\n",
        "# Like for the logistic regression above, we have to flatten\n",
        "# the inputs into shape (n_trials, n_neurons x n_time_bins)\n",
        "\n",
        "flat_train_data = np.reshape(training_spikes, (len(training_spikes),-1))\n",
        "flat_val_data = np.reshape(validation_spikes, (len(validation_spikes),-1))\n",
        "\n",
        "\n",
        "# now train it like above\n",
        "\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mH2-UxhRLJEg",
        "colab_type": "text"
      },
      "source": [
        "### Extra credit exercise 1: reduce the dimension of data with PCA\n",
        "\n",
        "Create an instance of PCA (loading the module from scikit-learn). Then, fit it on your training data. Then transform both the validation and train data. (Note that we don't fit the PCA using train data.)\n",
        "\n",
        "You can either reduce the dimension across neurons only, preserving temporal structure, or decide to reduce across all dimensions.\n",
        "\n",
        "Does validation accuracy improve?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8dl5XbyPLdBp",
        "colab_type": "text"
      },
      "source": [
        "### Extra credit exercise 2: Set up a script to perform k-fold CV\n",
        "\n",
        "Using your favorite methods (e.g. scikit learn) or the script we wrote above, create a method to perform 5-fold cross-validation on the Neuropixels data. The function should take parameters to create a model as input, and it should output the average validation accuracy across the 5 validation sets. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rEpxVLe431kH",
        "colab_type": "text"
      },
      "source": [
        "### Extra credit exercise 3: find the best decoder\n",
        "\n",
        "Search across methods and hyperparameters for the best decoder. Try hyperopt, or random searches.\n",
        "\n",
        "If you're fancy and have lots of compute time, maybe try automated ML. (e.g. autosklearn)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ucHs_lBqSqT7"
      },
      "source": [
        "## Appendix: downloading a Neuropixels session and processing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "9jeeJvVLSqT8"
      },
      "source": [
        "This will take about 30 seconds to download the ~600M of data into your working folder, and 10 minutes to run the script."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "SI_K0MRkSqT9",
        "colab": {}
      },
      "source": [
        "session = \"Cori_2016-12-18/\"\n",
        "\n",
        "!wget -np -r -nv http://data.cortexlab.net/taskData/$session\n",
        "!mv data.cortexlab.net/taskData/ ."
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XVpyiQmWSqUB"
      },
      "source": [
        "Now we'll extract this data into Python in the form of a dictionary."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "bKqX75s8SqUB",
        "colab": {}
      },
      "source": [
        "from tqdm import tqdm as tqdm\n",
        "\n",
        "def load_data(session):\n",
        "    \"\"\"Takes a session in relative path ./taskData and loads it as a dictionary.\"\"\"\n",
        "    files = !ls taskData/$session/*.npy\n",
        "    all_files = {}\n",
        "    for file in files:\n",
        "        filename = file.split(\"/\")[1][:-4]\n",
        "        all_files[filename] = np.load(file)\n",
        "    return all_files\n",
        "  \n",
        "def count_neurons(time_interval, all_files):\n",
        "    \"\"\"In this time interval, return the neurons with nonzero spikes, and how many\n",
        "    \n",
        "    Returns (ids, counts)\n",
        "    \"\"\"\n",
        "    \n",
        "    \n",
        "    t1,t2 = time_interval\n",
        "    \n",
        "    trial_spikes = all_files['spikes.times']\n",
        "\n",
        "    interval = (trial_spikes > t1) & (trial_spikes < t2)\n",
        "\n",
        "    trial_spikes = trial_spikes[interval]\n",
        "    ids = all_files['spikes.clusters'][interval]\n",
        "    \n",
        "    # ids has all the info we need\n",
        "    return np.unique(ids, return_counts = True)\n",
        "    \n",
        "    \n",
        "\n",
        "\n",
        "def bin_into_array(all_files, time_before_response=1, n_bins = 50):\n",
        "    \n",
        "    ids = all_files['spikes.clusters']\n",
        "    idList = np.unique(ids)\n",
        "    \n",
        "    n_trials = len(all_files['trials.response_choice'])\n",
        "    n_neurons = len(idList)\n",
        "    \n",
        "    choices = np.reshape(all_files['trials.response_choice'],-1)\n",
        "    data = np.zeros((n_trials, n_neurons, n_bins))\n",
        "    \n",
        "    time_resolution = time_before_response/ float(n_bins)\n",
        "    \n",
        "    for trial in tqdm(range(n_trials)):\n",
        "        end_time = all_files['trials.response_times'][trial]\n",
        "        start_time = end_time - time_before_response\n",
        "        \n",
        "        data.trial\n",
        "        \n",
        "        for b in range(n_bins):\n",
        "        \n",
        "            which_neurons, n_spikes = count_neurons((start_time + b*time_resolution,\n",
        "                                            start_time + (b+1)*time_resolution),\n",
        "                                          all_files)\n",
        "            \n",
        "            data[trial,which_neurons,b] = n_spikes\n",
        "            \n",
        "    return data, choices\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "1kmTWMwSSqUD",
        "colab": {}
      },
      "source": [
        "session = \"Cori_2016-12-18\"\n",
        "all_files = load_data(session)\n",
        "data, choices = bin_into_array(all_files)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "HJSdc0siSqUF",
        "colab": {}
      },
      "source": [
        "#clean up the data we aren't using\n",
        "!rm -r data.cortexlab.net/"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}