In this thesis we develop a class of nonlinear generative models for high-dimensional time series. The first key property of these models is their distributed, or "componential" latent state, which is characterized by binary stochastic variables which interact to explain the data. The second key property is the use of an undirected graphical model to represent the relationship between latent state (features) and observations. The final key property is composability:​ the proposed class of models can form the building blocks of deep networks by successively training each model on the features extracted by the previous one.

We first propose a model based on the Restricted Boltzmann Machine (RBM) that uses an undirected model with binary latent variables and real-valued "visible" variables. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. This "conditional" RBM (CRBM) makes on-line inference efficient and allows us to use a simple approximate learning procedure. We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line filling in of data lost during motion capture. We also explore CRBMs as priors in the context of Bayesian filtering applied to multi-view and monocular 3D person tracking.

We extend the CRBM in a way that preserves its most important computational properties and introduces multiplicative three-way interactions that allow the effective interaction weight between two variables to be modulated by the dynamic state of a third variable. We introduce a factoring of the implied three-way weight tensor to permit a more compact parameterization. The resulting model can capture diverse styles of motion with a single set of parameters, and the three-way interactions greatly improve its ability to blend motion styles or to transition smoothly among them.

In separate but related work, we revisit Products of Hidden Markov Models (PoHMMs). We show how the partition function can be estimated reliably via Annealed Importance Sampling. This enables us to demonstrate that PoHMMs outperform various flavours of HMMs on a variety of tasks and metrics, including log likelihood.