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"
   ]
  },
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   "source": [
    "## 1. Import Packages\n",
    "\n",
    "Below, we import both standard packages, and functions from the accompanying .py files"
   ]
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     "text": [
      "Using Theano backend.\n"
     ]
    }
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   "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 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 KalmanFilterDecoder"
   ]
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   "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",
    "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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   "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,encoding='latin1') #If using python 3\n",
    "    neural_data,vels_binned=pickle.load(f)\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']"
   ]
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   "source": [
    "## 3. Preprocess Data"
   ]
  },
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   "source": [
    "### 3A. User Inputs\n",
    "The user can define what time period to use spikes from (with respect to the output)."
   ]
  },
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   "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"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Format Input"
   ]
  },
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    "#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"
   ]
  },
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    "#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)"
   ]
  },
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   "source": [
    "### 3C. Take lag into account"
   ]
  },
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   "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"
   ]
  },
  {
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   "metadata": {
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   "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"
   ]
  },
  {
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   "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,:]"
   ]
  },
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   "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."
   ]
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  {
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   "execution_count": 10,
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   "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"
   ]
  },
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   "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": 11,
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   "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(C=1) #There is one optional parameter that is set to the default in this example (see ReadMe)\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"
   ]
  },
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa95a320690>]"
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     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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FFMKXx9DaBP++g0lHpA5KXq/4X3XIhm8VuYmsnugYlQpUN7LhK5YJA15vaRH2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\nOmGBKN5oiuFbTi/vH0MD22AcfmBmQQctszr7Ib+od+zJ1VojDz9tWE0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa95a322fd0>"
      ]
     },
     "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,
    "jupyter": {
     "outputs_hidden": 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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}