Gregory Knoll: Inferring Hidden States and Parameters of the Kinetic Ising Model

BCCN Berlin / TU Berlin

The Ising model from statistical physics can be used as a framework to investigate problems which consist of connected, binary units. In this work, two forms of the kinetic Ising model are examined: in continuous time with all units observed and in discrete time with some obscured. In both cases, inference of the connectivity is attempted given only the states, or spins, of the units. This is achieved by means of a likelihood augmented by Pólya-Gamma variables. In the continuous, observed system, a stochastic approximation to the joint posterior of the model and latent variables is made by means of a Markov Chain Monte Carlo algorithm known as a Gibbs sampler. In the discrete, partially-obscured system, a maximum likelihood algorithm known as expectation maximization (EM) is used to estimate observed unit connectivity. Two EM implementations are developed which differ in their approach to finding the expected value of the hidden units. One uses brute, numerical force to find the exact value, while the other uses Gibbs sampling to approximate the joint posterior of the latent variables. The role of Ising models in investigating neural data is discussed and an example of using the continuous-time Ising Gibbs sampler to infer connectivity from the data set of an integrate-and-fire neural model is shown.

Additional Information

Master thesis defense in the International Master Program Computational Neuroscience.

Organized by

Manfred Opper/Robert Martin

Location

BCCN Berlin, lecture hall, Philippstr. 13 Haus 6, 10115 Berlin