Reference no: EM132230399

1. Goals of the Lab

Neural Data Analysis II

This lab will address the problem of how to predict the upcoming direction of movement from a population of neuronal signals recorded from motor areas of a macaque monkey. We will implement two common decoding strategies: the population vector and maximum likelihood, and compare their performance in terms of percentage predicted correctly.

The test dataset for this lab is called "Lab6_CenterOutTest" and is found under "Modules/ Data for labs" in Canvas. Put it in your current directory and load it. This data is from the same neurons as in the Lab 5 dataset, but from different trials. This is important, as you always want to test a prediction algorithm on different data than it was originally trained on.

Otherwise, the optimal prediction would be, "the exact same thing is going to happen." Testing on novel data helps ensures that the model does not overfit the data. You will use the preferred directions for the neurons from the Lab 5 training dataset to predict which direction of movement from the neuronal firing rates around the "Go" cue.

2. Background

What is neural decoding? Simply put, it is a mathematical mapping from brain activity to the outside world. In the sensory domain, the outside world consists of the received visual, auditory, or other sensory information. In the motor domain, the outside world consists of the state of the skeletomuscular system. Historically, neuroscientists have focused on understanding neural encoding by characterizing a tuning curve. For example, cosine tuning curve specifies how a neuron modulates its firing rate depending on the upcoming direction of movement. In contrast, estimating this movement direction from one (or many) observed firing rate is an example of neural decoding. Because signals about motor intention precede movement, decoding can be thought of as "mind reading." We seek to predict an action as soon as it is intended, before it ever takes place.

Having done this, proceed as follows:

1. Assume that each neuron "votes" for its preferred movement direction. Specifically, each neuron is going to contribute a "response vector" which is aligned with its preferred direction.

2. The magnitude (or length) of each neuron's response vector is determined by the neural activity of the neuron during each trial. This is the weight given to each neuron's vote. For now, assume the weight is simply the firing rate during the hold period.

3. Sum all the response vectors from all neurons to arrive at the population vector for this trial. The direction of this population vector corresponds to the predicted direction.

3. Exercises

1. Implement a population vector decoder. Use the preferred directions determined using the firing rate computed 1 second before to 1 second after the go cue for the Lab 5 training data. Then predict the movement direction of the 80 trials whose go times are given in the Lab 6 test data. Bin the predicted direction to convert it to one of the eight discrete movement directions.

2. Implement a maximum likelihood decoder. Assume a poisson firing rate model and independent firing rates. Determine the mean firing rate for each neuron and each direction for the Lab 5 training dataset. Use the function poisspdf to determine the likelihood of each direction for the Lab 6 test data. Pick the direction which maximizes the log-likelihood of all firing rates for a given trial.

3. Compare the accuracy of these two decoding methods, using the percentage of directions correctly predicted in the 80 test trials as your metric.

4. Lab Report Requirements

1. Report the percent correct for population vector and the maximum likelihood algorithms that you implemented in the Exercises.

2. The population vector methods make assumptions about the data: that neurons were cosine tuned and that preferred directions are uniformly distributed. Are these assumptions valid? Provide evidence for your answer.

3. For the population vector method, instead of weighting the response vectors using the firing rate, weight using the change in firing rate from baseline. Specify how you determine the baseline firing rate (the easiest is to use the mean firing rate across all directions). Does this affect the decoding accuracy of the population vector method? Why might this be?

4. Use a Gaussian firing rate model for the maximum likelihood decoder (instead of Poisson). The likelihood can be determined with the function normpdf and the mean and standard deviation for each neuron and each direction. Does this affect the decoding accuracy of the maximum likelihood method? Why might this be?

Attachment:- Guide.rar