Bayesian Learning with Dependency Structures via Latent Factors, Mixtures, and Copulas

Bayesian methods offer a flexible and convenient probabilistic learning framework to extract interpretable knowledge from complex and structured data. Such methods can characterize dependencies among multiple levels of hidden variables and share statistical strength across heterogeneous sources. In the first part of this dissertation, we develop two dependent variational inference methods for full posterior approximation in non-conjugate Bayesian models through hierarchical mixture- and copula-based variational proposals, respectively. The proposed methods move beyond the widely used factorized approximation to the posterior and provide generic applicability to a broad class of probabilistic models with minimal model-specific derivations. In the second part of this dissertation, we design probabilistic graphical models to accommodate multimodal data, describe dynamical behaviors and account for task heterogeneity. In particular, the sparse latent factor model is able to reveal common low-dimensional structures from high-dimensional data. We demonstrate the effectiveness of the proposed statistical learning methods on both synthetic and real-world data.

Cumulon: Simplified Matrix-Based Data Analytics in the Cloud

Cumulon is a system aimed at simplifying the development and deployment of statistical analysis of big data in public clouds. Cumulon allows users to program in their familiar language of matrices and linear algebra, without worrying about how to map data and computation to specific hardware and cloud software platforms. Given user-specified requirements in terms of time, monetary cost, and risk tolerance, Cumulon automatically makes intelligent decisions on implementation alternatives, execution parameters, as well as hardware provisioning and configuration settings -- such as what type of machines and how many of them to acquire. Cumulon also supports clouds with auction-based markets: it effectively utilizes computing resources whose availability varies according to market conditions, and suggests best bidding strategies for them. Cumulon explores two alternative approaches toward supporting such markets, with different trade-offs between system and optimization complexity. Experimental study is conducted to show the efficiency of Cumulon's execution engine, as well as the optimizer's effectiveness in finding the optimal plan in the vast plan space.