Spike-Based Probabilistic Inference in Analog Graphical Models Using Interspike-Interval Coding

Abstract

Temporal spike codes play a crucial role in neural information processing. In particular, there is strong experimental evidence that interspike intervals (ISIs) are used for stimulus representation in neural systems. However, very few algorithmic principles exploit the benefits of such temporal codes for probabilistic inference of stimuli or decisions. Here, we describe and rigorously prove the functional properties of a spike-based processor that uses ISI distributions to perform probabilistic inference. The abstract processor architecture serves as a building block for more concrete, neural implementations of the belief-propagation (BP) algorithm in arbitrary graphical models (e.g., Bayesian networks and factor graphs). The distributed nature of graphical models matches well with the architectural and functional constraints imposed by biology. In our model, ISI distributions represent the BP messages exchanged between factor nodes, leading to the interpretation of a single spike as a random sample that follows such a distribution. We verify the abstract processor model by numerical simulation in full graphs, and demonstrate that it can be applied even in the presence of analog variables. As a particular example, we also show results of a concrete, neural implementation of the processor, although in principle our approach is more flexible and allows different neurobiological interpretations. Furthermore, electrophysiological data from area LIP during behavioral experiments are assessed in light of ISI coding, leading to concrete testable, quantitative predictions and a more accurate description of these data compared to hitherto existing models.

A Neuromorphic VLSI Circuit for Spike-Based Random Sampling

“…Using this comparison scheme, the output ISI distribution pout(t) (with t = nt ) can be written as follows: (6) where <ISI> denotes the mean ISI of the output distribution. This mean ISI is the approximate mean ISI of the user-provided input ISI distribution p(t).…”

“…Previously we have provided an answer to this question, by interpreting a spike as a random sample, whose numerical value is given by the spikes preceding ISI [6]. In this model, spike trains are assumed to follow renewal processes and hence to correspond to sequences of independent random numbers, that is, sequences of labeled spike events, where each spike's label corresponds to an ISI random number ( Fig.1).…”

“…In this model, spike trains are assumed to follow renewal processes and hence to correspond to sequences of independent random numbers, that is, sequences of labeled spike events, where each spike's label corresponds to an ISI random number ( Fig.1). Such sequences may be employed by a variety of Monte-Carlo methods [7], such as Gibbs sampling, or by message-passing algorithms using a sample-based representation of messages [8] [6].…”

Graphical Model Based Approach for Fault Diagnosis of Wind Turbines

“…Hence, we propose in this work a new avenue for wind turbines fault diagnosis using MLGMs. MLGMs are still widely used in different fields such as in bioinformatics for gene-regulatory networks inference [14], neuro-informatics [15], forensic science [16], and social networks [17].…”

Probabilistic Decision Making with Spikes: From ISI Distributions to Behaviour via Information Gain

“…Further, there is, as yet, no clear way of dealing with spike trains with arbitrary inter-spike-interval (ISI) statistics, although there has been some interest in log-ISIs as means for sampling for decision formation [ 18 ]. Almost all previous models of decision making have worked at a more abstract behavioural level, where the interpretation of evidence is less constrained.…”