Untitled - Laboratory of Neurophysics and Physiology

T4
Probabilistic inference as a neural-computing paradigm
Space Grignard, (13.30-16.50)
Dejan Pecevski, Graz University of Technology, Graz, Austria
Probabilistic inference has been proven to be a very suitable framework for explaining many of the
computations that the brain performs in face of great amount of uncertainty present in the sensory
inputs and its internal representations of the world [Rao et al., 2002; Fiser et al., 2010; Tenenbaum
et al., 2011; Kording et al., 2004]. However, it still remains an open question how these probabilistic
inference computations are implemented in the neural circuits of the brain. In this tutorial we will
present recent results that give new perspectives on how probabilistic inference and learning could be
carried out by networks of spiking neurons.
The tutorial is organized in two parts. In the first part we will briefly overview several basic topics
from probabilistic inference, including graphical models, belief propagation, Markov chain Monte
Carlo methods and Gibbs sampling. In the second part we will start by describing a recently developed
framework for probabilistic inference with stochastic networks of spiking neurons that performs
Markov chain Monte Carlo sampling, called neural sampling [Buesing et al., 2011]. We will further
show that by introducing specific network motifs or dendritic computation in the spiking neural networks,
they can be made to perform neural sampling in general graphical models that exhibit also
higher-order relations between the random variables [Pecevski et al., 2011]. We will then continue
discussing results about learning probabilistic models, in particular a study where it was shown that
STDP in a stochastic winner-take-all network structure implements the expectation-maximization algorithm,
a powerful machine learning algorithm for unsupervised learning [Nessler et al., 2009]. In
[Habenschuss et al., 2012], the model from [Nessler et al., 2009] was extended with homeostatic
plasticity of the neuronal excitabilities, which improved the performance and robustness of learning.
It was also demonstrated theoretically that this extended model can be understood as performing
expectation-maximization under posterior constraints. Finally, we will show how many winner-take-all
network motifs as in [Habenschuss et al., 2012] can be combined together in a larger recurrent spiking
neural network which is capable of solving a generic learning task: to learn a probabilistic model from
input data streams, where the dependencies in the probabilistic model can be a priori based on any
arbitrary graphical model structure.
References:
• Rao et al. (2002), Probabilistic models of the brain: Perception and neural function, Mit Press
• Fiser et al. (2010), Statistically optimal perception and learning: from behavior to neural representations,
Trends Cogn Sci 14:119–130
• Tenenbaum et al. (2011), How to Grow a Mind: Statistics, Structure, and Abstraction, Science
331:1279–1285
• Kording & Wolpert (2004), Bayesian integration in sensorimotor learning, Nature 427:244–247
• Buesing et al. (2011), Neural Dynamics as Sampling: A Model for Stochastic Computation in
Recurrent Networks of Spiking Neurons, PLoS Comput Biol 7:e1002211
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