Mijung Park

Title: Latent variable models (LVMs) for manifold learning and time series data

 

Abstract: 

 

Latent variables models (LVMs) are powerful tools to model complicated high dimensional data. In my talk, I will focus on two examples of LVMs applied to manifold learning and time series data. 

 

In manifold learning, most existing methods are nonpropabilistic, which provide no clear generative processes of high dimensional data and no uncertainty on manifold structure. Our model, the locally linear latent variable model (LL-LVM) provides a probabilistic framework for manifold discovery that describes a joint distribution over observations, their manifold co-ordinates and locally linear maps conditioned on a set of neighbourhood relationships.  Its probabilistic semantics make it easy to evaluate the quality of hypothesised neighbourhood relationships, and select the intrinsic dimensionality of manifold. 

 

For time series data, many existing methods fall into the category of some variants of linear dynamical systems. In neural population data particularly, linear dynamical systems coupled with the Poisson observation model are successfully used for capturing the ''fast'' latent dynamics in the population. Our model, the nonstationary Poisson linear dynamical system (NPLDS) provides a mechanism to capture "slowly" varying dynamics in firing rates across each recording session, as well as the fast latent dynamics.  

 

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LLLVM is a joint work with Wittawat Jitkrittum, Zoltan Szabo, Ahmad Qamar, Lars Buesing, Maneesh Sahani. NPLDS is a joint work with Gergo Bohner, and Jakob Macke. Both of the work are accepted at NIPS 2015.