Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.Comment: 49 pages including appendi

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 matrix factorization framework for jointly analyzing multiple nonnegative data

Nonnegative matrix factorization based methods provide one of the simplest and most effective approaches to text mining. However, their applicability is mainly limited to analyzing a single data source. In this paper, we propose a novel joint matrix factorization framework which can jointly analyze multiple data sources by exploiting their shared and individual structures. The proposed framework is flexible to handle any arbitrary sharing configurations encountered in real world data. We derive an efficient algorithm for learning the factorization and show that its convergence is theoretically guaranteed. We demonstrate the utility and effectiveness of the proposed framework in two real-world applications–improving social media retrieval using auxiliary sources and cross-social media retrieval. Representing each social media source using their textual tags, for both applications, we show that retrieval performance exceeds the existing state-of-the-art techniques. The proposed solution provides a generic framework and can be applicable to a wider context in data mining wherever one needs to exploit mutual and individual knowledge present across multiple data sources

Probabilistic analysis of the human transcriptome with side information

Understanding functional organization of genetic information is a major challenge in modern biology. Following the initial publication of the human genome sequence in 2001, advances in high-throughput measurement technologies and efficient sharing of research material through community databases have opened up new views to the study of living organisms and the structure of life. In this thesis, novel computational strategies have been developed to investigate a key functional layer of genetic information, the human transcriptome, which regulates the function of living cells through protein synthesis. The key contributions of the thesis are general exploratory tools for high-throughput data analysis that have provided new insights to cell-biological networks, cancer mechanisms and other aspects of genome function. A central challenge in functional genomics is that high-dimensional genomic observations are associated with high levels of complex and largely unknown sources of variation. By combining statistical evidence across multiple measurement sources and the wealth of background information in genomic data repositories it has been possible to solve some the uncertainties associated with individual observations and to identify functional mechanisms that could not be detected based on individual measurement sources. Statistical learning and probabilistic models provide a natural framework for such modeling tasks. Open source implementations of the key methodological contributions have been released to facilitate further adoption of the developed methods by the research community.Comment: Doctoral thesis. 103 pages, 11 figure

A review of domain adaptation without target labels

Domain adaptation has become a prominent problem setting in machine learning and related fields. This review asks the question: how can a classifier learn from a source domain and generalize to a target domain? We present a categorization of approaches, divided into, what we refer to as, sample-based, feature-based and inference-based methods. Sample-based methods focus on weighting individual observations during training based on their importance to the target domain. Feature-based methods revolve around on mapping, projecting and representing features such that a source classifier performs well on the target domain and inference-based methods incorporate adaptation into the parameter estimation procedure, for instance through constraints on the optimization procedure. Additionally, we review a number of conditions that allow for formulating bounds on the cross-domain generalization error. Our categorization highlights recurring ideas and raises questions important to further research.Comment: 20 pages, 5 figure

A survey on Bayesian nonparametric learning

© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. Bayesian (machine) learning has been playing a significant role in machine learning for a long time due to its particular ability to embrace uncertainty, encode prior knowledge, and endow interpretability. On the back of Bayesian learning's great success, Bayesian nonparametric learning (BNL) has emerged as a force for further advances in this field due to its greater modelling flexibility and representation power. Instead of playing with the fixed-dimensional probabilistic distributions of Bayesian learning, BNL creates a new “game” with infinite-dimensional stochastic processes. BNL has long been recognised as a research subject in statistics, and, to date, several state-of-the-art pilot studies have demonstrated that BNL has a great deal of potential to solve real-world machine-learning tasks. However, despite these promising results, BNL has not created a huge wave in the machine-learning community. Esotericism may account for this. The books and surveys on BNL written by statisticians are overcomplicated and filled with tedious theories and proofs. Each is certainly meaningful but may scare away new researchers, especially those with computer science backgrounds. Hence, the aim of this article is to provide a plain-spoken, yet comprehensive, theoretical survey of BNL in terms that researchers in the machine-learning community can understand. It is hoped this survey will serve as a starting point for understanding and exploiting the benefits of BNL in our current scholarly endeavours. To achieve this goal, we have collated the extant studies in this field and aligned them with the steps of a standard BNL procedure-from selecting the appropriate stochastic processes through manipulation to executing the model inference algorithms. At each step, past efforts have been thoroughly summarised and discussed. In addition, we have reviewed the common methods for implementing BNL in various machine-learning tasks along with its diverse applications in the real world as examples to motivate future studies