Examples_kf_decoder.ipynb

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    "# Example of Kalman Filter decoders\n",
    "\n",
    "This example is similar to those shown in \"Examples_all_decoders.\"\n",
    "However, there is some preprocessing is different for the Kalman, so we have made a separate notebook.\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\n",
    "4. Run the decoders and print the goodness of fit\n",
    "5. Plot example decoded outputs"
   ]
  },
  {
   "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": {
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     "text": [
      "/opt/anaconda/anaconda2/lib/python2.7/site-packages/sklearn/cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n",
      "Using Theano backend.\n",
      "WARNING (theano.sandbox.cuda): The cuda backend is deprecated and will be removed in the next release.  Please switch to the gpuarray backend. You can get more information about how to switch at this URL:\n",
      " https://github.com/Theano/Theano/wiki/Converting-to-the-new-gpu-back-end%28gpuarray%29\n",
      "\n",
      "Using gpu device 3: GeForce GTX TITAN X (CNMeM is disabled, cuDNN 5103)\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",
    "#Import metrics\n",
    "from metrics import get_R2\n",
    "from metrics import get_rho\n",
    "\n",
    "#Import decoder functions\n",
    "from decoders import KalmanFilterDecoder"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Load Data\n",
    "The data file for this example can be downloaded at https://dl.dropboxusercontent.com/u/2944301/Decoding_Data/example_data_s1.pickle. It was recorded by Raeed Chowdhury from Lee Miller's lab at Northwestern.\n",
    "\n",
    "The data that we load is in the format described below. We have another example script, \"neural_preprocessing.py\" 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\""
   ]
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  {
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   "source": [
    "folder='' #ENTER THE FOLDER THAT YOUR DATA IS IN\n",
    "# folder='/home/jglaser/Data/DecData/' \n",
    "\n",
    "with open(folder+'example_data_s1.pickle','rb') as f:\n",
    "    neural_data,vels_binned=pickle.load(f)"
   ]
  },
  {
   "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": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lag=0 #What time bin of spikes should be used relative to the output\n",
    "#(lag=-1 means use the spikes 1 bin before the output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3B. Format Covariates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Format Input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [],
   "source": [
    "#The covariate is simply the matrix of firing rates for all neurons over time\n",
    "X_kf=neural_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Format Output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "#For the Kalman filter, we use the position, velocity, and acceleration as outputs\n",
    "#Ultimately, we are only concerned with the goodness of fit of velocity (for this dataset)\n",
    "#But using them all as covariates helps performance\n",
    "\n",
    "#We will now determine position\n",
    "pos_binned=np.zeros(vels_binned.shape) #Initialize \n",
    "pos_binned[0,:]=0 #Assume starting position is at [0,0]\n",
    "#Loop through time bins and determine positions based on the velocities\n",
    "for i in range(pos_binned.shape[0]-1): \n",
    "    pos_binned[i+1,0]=pos_binned[i,0]+vels_binned[i,0]*.05 #Note that .05 is the length of the time bin\n",
    "    pos_binned[i+1,1]=pos_binned[i,1]+vels_binned[i,1]*.05\n",
    "\n",
    "#We will now determine acceleration    \n",
    "temp=np.diff(vels_binned,axis=0) #The acceleration is the difference in velocities across time bins \n",
    "acc_binned=np.concatenate((temp,temp[-1:,:]),axis=0) #Assume acceleration at last time point is same as 2nd to last\n",
    "\n",
    "#The final output covariates include position, velocity, and acceleration\n",
    "y_kf=np.concatenate((pos_binned,vels_binned,acc_binned),axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3C. Take lag into account"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_examples=X_kf.shape[0]\n",
    "\n",
    "#Re-align data to take lag into account\n",
    "if lag<0:\n",
    "    y_kf=y_kf[-lag:,:]\n",
    "    X_kf=X_kf[0:num_examples+lag,:]\n",
    "if lag>0:\n",
    "    y_kf=y_kf[0:num_examples-lag,:]\n",
    "    X_kf=X_kf[lag:num_examples,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3D. Split into training/testing/validation sets\n",
    "Note that parameters should be setting 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": 7,
   "metadata": {
    "collapsed": true
   },
   "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: For KF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "#Number of examples after taking into account bins removed for lag alignment\n",
    "num_examples_kf=X_kf.shape[0]\n",
    "        \n",
    "#Note that each range has a buffer of 1 bin at the beginning and end\n",
    "#This makes it so that the different sets don't include overlapping data\n",
    "training_set=np.arange(np.int(np.round(training_range[0]*num_examples_kf))+1,np.int(np.round(training_range[1]*num_examples_kf))-1)\n",
    "testing_set=np.arange(np.int(np.round(testing_range[0]*num_examples_kf))+1,np.int(np.round(testing_range[1]*num_examples_kf))-1)\n",
    "valid_set=np.arange(np.int(np.round(valid_range[0]*num_examples_kf))+1,np.int(np.round(valid_range[1]*num_examples_kf))-1)\n",
    "\n",
    "#Get training data\n",
    "X_kf_train=X_kf[training_set,:]\n",
    "y_kf_train=y_kf[training_set,:]\n",
    "\n",
    "#Get testing data\n",
    "X_kf_test=X_kf[testing_set,:]\n",
    "y_kf_test=y_kf[testing_set,:]\n",
    "\n",
    "#Get validation data\n",
    "X_kf_valid=X_kf[valid_set,:]\n",
    "y_kf_valid=y_kf[valid_set,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3E. Preprocessing: Normalization and zero-centering\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": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Z-score inputs \n",
    "X_kf_train_mean=np.nanmean(X_kf_train,axis=0)\n",
    "X_kf_train_std=np.nanstd(X_kf_train,axis=0)\n",
    "X_kf_train=(X_kf_train-X_kf_train_mean)/X_kf_train_std\n",
    "X_kf_test=(X_kf_test-X_kf_train_mean)/X_kf_train_std\n",
    "X_kf_valid=(X_kf_valid-X_kf_train_mean)/X_kf_train_std\n",
    "\n",
    "#Zero-center outputs\n",
    "y_kf_train_mean=np.mean(y_kf_train,axis=0)\n",
    "y_kf_train=y_kf_train-y_kf_train_mean\n",
    "y_kf_test=y_kf_test-y_kf_train_mean\n",
    "y_kf_valid=y_kf_valid-y_kf_train_mean"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Run Decoder\n",
    "Note that in this example, we are evaluating the model fit on the validation set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kalman Filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('R2:', array([ 0.68942383,  0.67256874]))\n",
      "('rho2:', array([ 0.70791634,  0.67637784]))\n"
     ]
    }
   ],
   "source": [
    "#Declare model\n",
    "model_kf=KalmanFilterDecoder()\n",
    "\n",
    "#Fit model\n",
    "model_kf.fit(X_kf_train,y_kf_train)\n",
    "\n",
    "#Get predictions\n",
    "y_valid_predicted_kf=model_kf.predict(X_kf_valid,y_kf_valid)\n",
    "\n",
    "#Get metrics of fit (see read me for more details on the differences between metrics)\n",
    "#First I'll get the R^2\n",
    "R2_kf=get_R2(y_kf_valid,y_valid_predicted_kf)\n",
    "print('R2:',R2_kf[2:4]) #I'm just printing the R^2's of the 3rd and 4th entries that correspond to the velocities\n",
    "#Next I'll get the rho^2 (the pearson correlation squared)\n",
    "rho_kf=get_rho(y_kf_valid,y_valid_predicted_kf)\n",
    "print('rho2:',rho_kf[2:4]**2) #I'm just printing the rho^2's of the 3rd and 4th entries that correspond to the velocities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Make Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1e503b1590>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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0tZryY6/HTGTio1eKfX0mUmXQSwYqpj9R1J7fKQURlqaHf5/DEATEhkVsOwNk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\nVSJx6RmdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1e5042d190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#As an example, I plot an example 1000 values of the x velocity (column index 2), both true and predicted with the Kalman 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_kf=plt.figure()\n",
    "plt.plot(y_kf_valid[1000:2000,2]+y_kf_train_mean[2],'b')\n",
    "plt.plot(y_valid_predicted_kf[1000:2000,2]+y_kf_train_mean[2],'r')\n",
    "#Save figure\n",
    "# fig_x_kf.savefig('x_velocity_decoding.eps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}