A Parallel Gamma Sampling Implementation


I don’t have a favorite distribution, but if I had to pick one, I’d say the gamma.  Why not the Gaussian? Because everyone loves the Gaussian! But when you want a prior distribution for the mean of your Poisson, or the variance of your Normal, who’s there to pick up the mess when the Gaussian lets you down? The gamma. When you’re trying to actually sample that Dirichlet that makes such a nice prior distribution for categorical distributions over your favorite distribution (how about that tongue twister), who’s there to help you?  You guessed it, the gamma. But if you want a distribution that you can sample millions of times during each iteration of your MCMC algorithm, well, now the Gaussian is looking pretty good, but let’s not give up hope on the gamma just yet.

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Priors for Functional and Effective Connectivity

In my previous post I suggested that models of neural computation can be expressed as prior distributions over functional and effective connectivity, and with this common specification we can compare models by their posterior probability given neural recordings. I would like to explore this idea in more detail by first describing functional and effective connectivity and then considering how various models could be expressed in this framework.

Functional and effective connectivity are concepts originating in neuroimaging and spike train analysis. Functional connectivity measures the correlation between neurophysiological events (e.g. spikes on neurons or BOLD signal in fMRI voxels), whereas effective connectivity is a statement about the causal nature of a system. Effective connectivity captures the influence one neurophysiological event has upon another, either directly via a synapse, or indirectly via a polysynaptic pathway or a parallel connection. In my usage, effective connectivity may include deterministic as well as stochastic relationships. Both concepts are in contrast to structural connectivity which captures the physical synapses or fiber tracts within the brain. Of course these concepts are interrelated: functional and effective connectivity are ultimately mediated by structural connectivity, and causal effective connections imply correlational functional connections.
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The “Computation” in Computational Neuroscience

My aim in this introductory post is to provide context for future contributions by sharing my thoughts on the role of computer scientists in the study of brain, particularly in the field of computational neuroscience. For a field with “computation” in the name, it seems that computer scientists are underrepresented. I believe there are significant open questions in neuroscience which are best addressed by those who study the theory of computation, learning, and algorithms, and the systems upon which they are premised.

In my opinion “computational neuroscience” has two definitions: the first, from Marr, is the study of the computational capabilities of the brain, their algorithmic details, and their implementation in neural circuits; the second, stemming from machine learning, is the design and application of computational algorithms, either to solve problems in a biologically-inspired manner, or to aid in the processing and interpretation of neural data. Though quite different, I believe these are complementary and arguably co-dependent endeavors. The forward hypothesis generation advocated by the former seems unlikely to get the details right without the aid of computational and statistical tools for extracting patterns from neural recordings, guiding hypothesis generation, and comparing the evidence for competing models. Likewise, attempts to infer the fundamentals of neural computation from the bottom-up without strong inductive biases appear doomed to wander the vastness of the hypothesis space. How then, can computer scientists contribute to both aspects of computational neuroscience? Continue reading “The “Computation” in Computational Neuroscience”