Results = glhmmfit(y,X,randn(size(ws)),T,glmopts) Īnd here’s the estimated RFs with the infered states underneath: %Update start and transition probabilities = evalGlmLikelihood(y,etas(:,jj),1,0,glmopts.family,glmopts.familyextra) %Compute the likelihood of each observation for every state
%Fit a generalized linear model with hidden Markov states Here’s a function that performs EM for this data set:įunction = glhmmfit(y,X,W0,T0,glmopts) Here are the two receptive fields it changes between: Here’s an example spike train which switches between two discrete states every 50 samples: Such an HMM with discrete emissions is standard, and you can use Matlab’s built-in HMM toolbox to analyze it. Thus there are only 2 possibly observed outputs, 0 for no spike and 1 for a spike, and what differs in each hidden state is the probability of each output being emitted. In our case, if we bin the spike data with sufficiently small bins, there will only be at most one spike per bin. Now it’s possible to outfit the HMM with any type of emission, whether discrete or continuous, and inference remains more or less the same. Thus the hidden states are discrete and have the Markov property, hence the name, Hidden Markov Model (HMM). Such a model is appropriate for the analysis of bistable neurons, which might occur with binocular rivalry data or looking at sleep-wake or on-off states.Ĭalling the hidden state that the neuron is in at time t, we can write the transition probability going from one state to the next as:
In the simplest scenario, these states will correspond to its mean firing rate. Suppose that a neuron has several discrete internal states, and that it switches slowly, at unknown times, between these states. In this post I’m going to focus on the application of HMMs to single neuron data. It’s also possible to model neurons with Hidden Markov models (HMMs), which are state-space models with discrete rather than continuous states. I posted recently about modeling neurons with continuous state-space dynamics.
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