{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples of all decoders (except Kalman Filter)\n",
    "\n",
    "In this example notebook, we:\n",
    "1. Import the necessary packages\n",
    "2. Load a data file (spike trains and outputs we are predicting)\n",
    "3. Preprocess the data for use in all decoders\n",
    "4. Run all decoders and print the goodness of fit\n",
    "5. Plot example decoded outputs\n",
    "\n",
    "See \"Examples_kf_decoder\" for a Kalman filter example. <br>\n",
    "Because the Kalman filter utilizes different preprocessing, we don't include an example here. to keep this notebook more understandable\n",
    "\n",
    "We also include a note on memory usage for the neural net decoders at the end of #4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Import Packages\n",
    "\n",
    "Below, we import both standard packages, and functions from the accompanying .py files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using Theano backend.\n",
      "WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n"
     ]
    }
   ],
   "source": [
    "#Import standard packages\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from scipy import io\n",
    "from scipy import stats\n",
    "import pickle\n",
    "\n",
    "# If you would prefer to load the '.h5' example file rather than the '.pickle' example file. You need the deepdish package\n",
    "# import deepdish as dd \n",
    "\n",
    "#Import function to get the covariate matrix that includes spike history from previous bins\n",
    "from Neural_Decoding.preprocessing_funcs import get_spikes_with_history\n",
    "\n",
    "#Import metrics\n",
    "from Neural_Decoding.metrics import get_R2\n",
    "from Neural_Decoding.metrics import get_rho\n",
    "\n",
    "#Import decoder functions\n",
    "from Neural_Decoding.decoders import WienerCascadeDecoder\n",
    "from Neural_Decoding.decoders import WienerFilterDecoder\n",
    "from Neural_Decoding.decoders import DenseNNDecoder\n",
    "from Neural_Decoding.decoders import SimpleRNNDecoder\n",
    "from Neural_Decoding.decoders import GRUDecoder\n",
    "from Neural_Decoding.decoders import LSTMDecoder\n",
    "from Neural_Decoding.decoders import XGBoostDecoder\n",
    "from Neural_Decoding.decoders import SVRDecoder\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Load Data\n",
    "The data for this example can be downloaded at this [link](https://www.dropbox.com/sh/n4924ipcfjqc0t6/AACPWjxDKPEzQiXKUUFriFkJa?dl=0&preview=example_data_s1.pickle). It was recorded by Raeed Chowdhury from Lee Miller's lab at Northwestern.\n",
    "\n",
    "\n",
    "The data that we load is in the format described below. We have another example notebook, \"Example_format_data\", that may be helpful towards putting the data in this format.\n",
    "\n",
    "Neural data should be a matrix of size \"number of time bins\" x \"number of neurons\", where each entry is the firing rate of a given neuron in a given time bin\n",
    "\n",
    "The output you are decoding should be a matrix of size \"number of time bins\" x \"number of features you are decoding\"\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# folder='' #ENTER THE FOLDER THAT YOUR DATA IS IN\n",
    "# folder='/home/jglaser/Data/DecData/' \n",
    "folder='/Users/jig289/Dropbox/Public/Decoding_Data/'\n",
    "\n",
    "with open(folder+'example_data_s1.pickle','rb') as f:\n",
    "    neural_data,vels_binned=pickle.load(f,encoding='latin1') #If using python 3\n",
    "#     neural_data,vels_binned=pickle.load(f) #If using python 2\n",
    "\n",
    "# #If you would prefer to load the '.h5' example file rather than the '.pickle' example file.\n",
    "# data=dd.io.load(folder+'example_data_s1.h5')\n",
    "# neural_data=data['neural_data']\n",
    "# vels_binned=data['vels_binned']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Preprocess Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3A. User Inputs\n",
    "The user can define what time period to use spikes from (with respect to the output)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins_before=6 #How many bins of neural data prior to the output are used for decoding\n",
    "bins_current=1 #Whether to use concurrent time bin of neural data\n",
    "bins_after=6 #How many bins of neural data after the output are used for decoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3B. Format Covariates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Format Input Covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Format for recurrent neural networks (SimpleRNN, GRU, LSTM)\n",
    "# Function to get the covariate matrix that includes spike history from previous bins\n",
    "X=get_spikes_with_history(neural_data,bins_before,bins_after,bins_current)\n",
    "\n",
    "# Format for Wiener Filter, Wiener Cascade, XGBoost, and Dense Neural Network\n",
    "#Put in \"flat\" format, so each \"neuron / time\" is a single feature\n",
    "X_flat=X.reshape(X.shape[0],(X.shape[1]*X.shape[2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Format Output Covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set decoding output\n",
    "y=vels_binned"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3C. Split into training / testing / validation sets\n",
    "Note that hyperparameters should be determined using a separate validation set. \n",
    "Then, the goodness of fit should be be tested on a testing set (separate from the training and validation sets)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### User Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Set what part of data should be part of the training/testing/validation sets\n",
    "training_range=[0, 0.7]\n",
    "testing_range=[0.7, 0.85]\n",
    "valid_range=[0.85,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Split Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_examples=X.shape[0]\n",
    "\n",
    "#Note that each range has a buffer of\"bins_before\" bins at the beginning, and \"bins_after\" bins at the end\n",
    "#This makes it so that the different sets don't include overlapping neural data\n",
    "training_set=np.arange(np.int(np.round(training_range[0]*num_examples))+bins_before,np.int(np.round(training_range[1]*num_examples))-bins_after)\n",
    "testing_set=np.arange(np.int(np.round(testing_range[0]*num_examples))+bins_before,np.int(np.round(testing_range[1]*num_examples))-bins_after)\n",
    "valid_set=np.arange(np.int(np.round(valid_range[0]*num_examples))+bins_before,np.int(np.round(valid_range[1]*num_examples))-bins_after)\n",
    "\n",
    "#Get training data\n",
    "X_train=X[training_set,:,:]\n",
    "X_flat_train=X_flat[training_set,:]\n",
    "y_train=y[training_set,:]\n",
    "\n",
    "#Get testing data\n",
    "X_test=X[testing_set,:,:]\n",
    "X_flat_test=X_flat[testing_set,:]\n",
    "y_test=y[testing_set,:]\n",
    "\n",
    "#Get validation data\n",
    "X_valid=X[valid_set,:,:]\n",
    "X_flat_valid=X_flat[valid_set,:]\n",
    "y_valid=y[valid_set,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3D. Process Covariates\n",
    "We normalize (z_score) the inputs and zero-center the outputs.\n",
    "Parameters for z-scoring (mean/std.) should be determined on the training set only, and then these z-scoring parameters are also used on the testing and validation sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Z-score \"X\" inputs. \n",
    "X_train_mean=np.nanmean(X_train,axis=0)\n",
    "X_train_std=np.nanstd(X_train,axis=0)\n",
    "X_train=(X_train-X_train_mean)/X_train_std\n",
    "X_test=(X_test-X_train_mean)/X_train_std\n",
    "X_valid=(X_valid-X_train_mean)/X_train_std\n",
    "\n",
    "#Z-score \"X_flat\" inputs. \n",
    "X_flat_train_mean=np.nanmean(X_flat_train,axis=0)\n",
    "X_flat_train_std=np.nanstd(X_flat_train,axis=0)\n",
    "X_flat_train=(X_flat_train-X_flat_train_mean)/X_flat_train_std\n",
    "X_flat_test=(X_flat_test-X_flat_train_mean)/X_flat_train_std\n",
    "X_flat_valid=(X_flat_valid-X_flat_train_mean)/X_flat_train_std\n",
    "\n",
    "#Zero-center outputs\n",
    "y_train_mean=np.mean(y_train,axis=0)\n",
    "y_train=y_train-y_train_mean\n",
    "y_test=y_test-y_train_mean\n",
    "y_valid=y_valid-y_train_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Run Decoders\n",
    "Note that in this example, we are evaluating the model fit on the validation set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4A. Wiener Filter (Linear Regression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.72457168 0.71731407]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_wf=WienerFilterDecoder()\n",
    "\n",
    "#Fit model\n",
    "model_wf.fit(X_flat_train,y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_wf=model_wf.predict(X_flat_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_wf=get_R2(y_valid,y_valid_predicted_wf)\n",
    "print('R2s:', R2s_wf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4B. Wiener Cascade (Linear Nonlinear Model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.73127717 0.73370796]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_wc=WienerCascadeDecoder(degree=3)\n",
    "\n",
    "#Fit model\n",
    "model_wc.fit(X_flat_train,y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_wc=model_wc.predict(X_flat_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_wc=get_R2(y_valid,y_valid_predicted_wc)\n",
    "print('R2s:', R2s_wc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4C. XGBoost (Extreme Gradient Boosting)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jig289/anaconda/envs/decode/lib/python3.5/site-packages/xgboost/core.py:614: UserWarning: Use subset (sliced data) of np.ndarray is not recommended because it will generate extra copies and increase memory consumption\n",
      "  \"because it will generate extra copies and increase memory consumption\")\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.75403802 0.76625732]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_xgb=XGBoostDecoder(max_depth=3,num_round=200,eta=0.3,gpu=-1) \n",
    "\n",
    "#Fit model\n",
    "model_xgb.fit(X_flat_train, y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_xgb=model_xgb.predict(X_flat_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_xgb=get_R2(y_valid,y_valid_predicted_xgb)\n",
    "print('R2s:', R2s_xgb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4D. SVR (Support Vector Regression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/jig289/anaconda/envs/decode/lib/python3.5/site-packages/sklearn/svm/base.py:244: ConvergenceWarning: Solver terminated early (max_iter=4000).  Consider pre-processing your data with StandardScaler or MinMaxScaler.\n",
      "  % self.max_iter, ConvergenceWarning)\n",
      "/Users/jig289/anaconda/envs/decode/lib/python3.5/site-packages/sklearn/svm/base.py:244: ConvergenceWarning: Solver terminated early (max_iter=4000).  Consider pre-processing your data with StandardScaler or MinMaxScaler.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.81684722 0.82538223]\n"
     ]
    }
   ],
   "source": [
    "#The SVR works much better when the y values are normalized, so we first z-score the y values\n",
    "#They have previously been zero-centered, so we will just divide by the stdev (of the training set)\n",
    "y_train_std=np.nanstd(y_train,axis=0)\n",
    "y_zscore_train=y_train/y_train_std\n",
    "y_zscore_test=y_test/y_train_std\n",
    "y_zscore_valid=y_valid/y_train_std\n",
    "\n",
    "#Declare model\n",
    "model_svr=SVRDecoder(C=5, max_iter=4000)\n",
    "\n",
    "#Fit model\n",
    "model_svr.fit(X_flat_train,y_zscore_train)\n",
    "\n",
    "#Get predictions\n",
    "y_zscore_valid_predicted_svr=model_svr.predict(X_flat_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_svr=get_R2(y_zscore_valid,y_zscore_valid_predicted_svr)\n",
    "print('R2s:', R2s_svr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4E. Dense Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.82578506 0.84818598]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_dnn=DenseNNDecoder(units=400,dropout=0.25,num_epochs=10)\n",
    "\n",
    "#Fit model\n",
    "model_dnn.fit(X_flat_train,y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_dnn=model_dnn.predict(X_flat_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_dnn=get_R2(y_valid,y_valid_predicted_dnn)\n",
    "print('R2s:', R2s_dnn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4F. Simple RNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.82405748 0.80346205]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_rnn=SimpleRNNDecoder(units=400,dropout=0,num_epochs=5)\n",
    "\n",
    "#Fit model\n",
    "model_rnn.fit(X_train,y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_rnn=model_rnn.predict(X_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_rnn=get_R2(y_valid,y_valid_predicted_rnn)\n",
    "print('R2s:', R2s_rnn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4G. GRU (Gated Recurrent Unit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.83770423 0.83575681]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_gru=GRUDecoder(units=400,dropout=0,num_epochs=5)\n",
    "\n",
    "#Fit model\n",
    "model_gru.fit(X_train,y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_gru=model_gru.predict(X_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_gru=get_R2(y_valid,y_valid_predicted_gru)\n",
    "print('R2s:', R2s_gru)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4H. LSTM (Long Short Term Memory)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2s: [0.84809856 0.84108359]\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_lstm=LSTMDecoder(units=400,dropout=0,num_epochs=5)\n",
    "\n",
    "#Fit model\n",
    "model_lstm.fit(X_train,y_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_lstm=model_lstm.predict(X_valid)\n",
    "\n",
    "#Get metric of fit\n",
    "R2s_lstm=get_R2(y_valid,y_valid_predicted_lstm)\n",
    "print('R2s:', R2s_lstm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4 - Side note on memory usage in TensorFlow\n",
    "When using the tensorflow backend for Keras (which is standard in newer versions), there can be issues with memory leakage, particularly when fitting many models. To avoid this problem, models can be deleted with the following code:\n",
    "\n",
    "```\n",
    "import gc\n",
    "from keras import backend as K\n",
    "\n",
    "del model_lstm\n",
    "K.clear_session()\n",
    "gc.collect()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Make Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8ea477d3d0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ArqQsHVabR00bRKEA1CJRkH0BWycIxAI5TUzWzyrRZp0Uvswh3kHhy4I7zDLB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\nlsMfKKPLPt8SECP41/NZSmxyZszvR0t8RNWRuEqn5YVUWOeD6t/rB3T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VcS6LxbiB24lS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8ea485efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#As an example, I plot an example 1000 values of the x velocity (column index 0), both true and predicted with the Wiener filter\n",
    "#Note that I add back in the mean value, so that both true and predicted values are in the original coordinates\n",
    "fig_x_wf=plt.figure()\n",
    "plt.plot(y_valid[1000:2000,0]+y_train_mean[0],'b')\n",
    "plt.plot(y_valid_predicted_wf[1000:2000,0]+y_train_mean[0],'r')\n",
    "\n",
    "#Save figure\n",
    "# fig_x_wf.savefig('x_velocity_decoding.eps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}