Applications of Approximate Learning and Inference for Probabilistic Models

We develop approximate inference and learning methods for facilitating the use of probabilistic modeling techniques motivated by applications in two different areas. First, we consider the ill-posed inverse problem of recovering an image from an underdetermined system of linear measurements corrupted by noise. Second, we consider the problem of inferring user preferences for items from counts, pairwise comparisons and user activity logs, instances of implicit feedback. Plausible models for images and the noise, incurred when recording them, render posterior inference intractable, while the scale of the inference problem makes sampling based approximations ineffective. Therefore, we develop deterministic approximate inference algorithms for two different augmentations of a typical sparse linear model: first, for the rectified-linear Poisson likelihood, and second, for tree-structured super-Gaussian mixture models. The rectified-linear Poisson likelihood is an alternative noise model, applicable in astronomical and biomedical imaging applications, that operate in intensity regimes in which quantum effects lead to observations that are best described by counts of particles arriving at a sensor, as well as in general Poisson regression problems arising in various fields. In this context we show, that the model-specific computations for Expectation Propagation can be robustly solved by a simple dynamic program. Next, we develop a scalable approximate inference algorithm for structured mixture models, that uses a discrete graphical model to represent dependencies between the latent mixture components of a collection of mixture models. Specifically, we use tree-structured mixtures of super-Gaussians to model the persistence across scales of large coefficients of the Wavelet transform of an image for improved reconstruction. In the second part on models of user preference, we consider two settings: the global static and the contextual dynamic setting. In the global static setting, we represent user-item preferences by a latent low-rank matrix. Instead of using numeric ratings we develop methods to infer this latent representation for two types of implicit feedback: aggregate counts of users interacting with a service and the binary outcomes of pairwise comparisons. We model count data using a latent Gaussian bilinear model with Poisson likelihoods. For this model, we show that the Variational Gaussian approximation can be further relaxed to be available in closed-form by adding additional constraints, leading to an efficient inference algorithm. In the second implicit feedback scenario, we infer the latent preference matrix from pairwise preference statements. We combine a low-rank bilinear model with non-parameteric item- feature regression and develop a novel approximate variational Expectation Maximization algorithm that mitigates the computational challenges due to latent couplings induced by the pairwise comparisons. Finally, in the contextual dynamic setting, we model sequences of user activity at the granularity of single interaction events instead of aggregate counts. Routinely gathered in the background at a large scale in many applications, such sequences can reveal temporal and contextual aspects of user behavior through recurrent patterns. To describe such data, we propose a generic collaborative sequence model based on recurrent neural networks, that combines ideas from collaborative filtering and language modeling.