The Infinite Hierarchical Factor Regression Model

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis

Doctor of Philosophy

dissertationLatent structures play a vital role in many data analysis tasks. By providing compact yet expressive representations, such structures can offer useful insights into the complex and high-dimensional datasets encountered in domains such as computational biology, computer vision, natural language processing, etc. Specifying the right complexity of these latent structures for a given problem is an important modeling decision. Instead of using models with an a priori fixed complexity, it is desirable to have models that can adapt their complexity as the data warrant. Nonparametric Bayesian models are motivated precisely based on this desideratum by offering a flexible modeling paradigm for data without limiting the model-complexity a priori. The flexibility comes from the model's ability to adjust its complexity adaptively with data. This dissertation is about nonparametric Bayesian learning of two specific types of latent structures: (1) low-dimensional latent features underlying high-dimensional observed data where the latent features could exhibit interdependencies, and (2) latent task structures that capture how a set of learning tasks relate with each other, a notion critical in the paradigm of Multitask Learning where the goal is to solve multiple learning tasks jointly in order to borrow information across similar tasks. Another focus of this dissertation is on designing efficient approximate inference algorithms for nonparametric Bayesian models. Specifically, for the nonparametric Bayesian latent feature model where the goal is to infer the binary-valued latent feature assignment matrix for a given set of observations, the dissertation proposes two approximate inference methods. The first one is a search-based algorithm to find the maximum-a-posteriori (MAP) solution for the latent feature assignment matrix. The second one is a sequential Monte-Carlo-based approximate inference algorithm that allows processing the data oneexample- at-a-time while being space-efficient in terms of the storage required to represent the posterior distribution of the latent feature assignment matrix

A comparative investigation of inter-row delay timing vis-à-vis some rock properties on high sandstone benches

112-119The inter-row delay timing plays a pivotal role in any blast round as it not only influences the mechanism of fragmentation, but also offers a vast potential in improving the overall results of fragmentation. It is in this perspective that the current study presents a comparative investigation of the influence of inter-row delay timing on fragmentation in two different strength sandstone formation in large-scale, multi-row blast rounds of a two surface coal mines in India. The investigations are based on full-scale field blasts. The study highlights the role of p-wave velocity and brittleness vis-à-vis impedance to shock wave propagation during the initial as well as final stages of rock breakage. Given this, the role of shattering effect (in stronger sandstone formations) and heaving effect in weaker strength sandstone has been clearly established in the rock breakage mechanism. Furthermore, the study also suggests that for weaker sandstone, longer inter-row delay timing (15-25 ms/m of effective burden) yields the best fragment size results. Similarly, for stronger sandstone formation, shorter inter-row delay timing (10-17.85 ms/m of effective burden) yields the best fragment size results

Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors

We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale up in the number of \emph{ones} in the tensor, which is especially appealing for massive but sparse binary tensors; (2) side-information in form of binary pairwise relationships (e.g., an adjacency network) between objects in any tensor mode can also be leveraged, which can be especially useful in "cold-start" settings; and (3) the model admits simple Bayesian inference via batch, as well as \emph{online} MCMC; the latter allows scaling up even for \emph{dense} binary data (i.e., when the number of ones in the tensor/network is also massive). In addition, non-negative factor matrices in our model provide easy interpretability, and the tensor rank can be inferred from the data. We evaluate our model on several large-scale real-world binary tensors, achieving excellent computational scalability, and also demonstrate its usefulness in leveraging side-information provided in form of mode-network(s).Comment: UAI (Uncertainty in Artificial Intelligence) 201