Healing Products of Gaussian Process Experts

Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification

Healing Products of Gaussian Processes

Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification.Comment: ICML 202

A Bayesian Perspective of Statistical Machine Learning for Big Data

Statistical Machine Learning (SML) refers to a body of algorithms and methods by which computers are allowed to discover important features of input data sets which are often very large in size. The very task of feature discovery from data is essentially the meaning of the keyword `learning' in SML. Theoretical justifications for the effectiveness of the SML algorithms are underpinned by sound principles from different disciplines, such as Computer Science and Statistics. The theoretical underpinnings particularly justified by statistical inference methods are together termed as statistical learning theory. This paper provides a review of SML from a Bayesian decision theoretic point of view -- where we argue that many SML techniques are closely connected to making inference by using the so called Bayesian paradigm. We discuss many important SML techniques such as supervised and unsupervised learning, deep learning, online learning and Gaussian processes especially in the context of very large data sets where these are often employed. We present a dictionary which maps the key concepts of SML from Computer Science and Statistics. We illustrate the SML techniques with three moderately large data sets where we also discuss many practical implementation issues. Thus the review is especially targeted at statisticians and computer scientists who are aspiring to understand and apply SML for moderately large to big data sets.Comment: 26 pages, 3 figures, Review pape

Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach

Recently there has been an increasing interest in the multivariate Gaussian process (MGP) which extends the Gaussian process (GP) to deal with multiple outputs. One approach to construct the MGP and account for non-trivial commonalities amongst outputs employs a convolution process (CP). The CP is based on the idea of sharing latent functions across several convolutions. Despite the elegance of the CP construction, it provides new challenges that need yet to be tackled. First, even with a moderate number of outputs, model building is extremely prohibitive due to the huge increase in computational demands and number of parameters to be estimated. Second, the negative transfer of knowledge may occur when some outputs do not share commonalities. In this paper we address these issues. We propose a regularized pairwise modeling approach for the MGP established using CP. The key feature of our approach is to distribute the estimation of the full multivariate model into a group of bivariate GPs which are individually built. Interestingly pairwise modeling turns out to possess unique characteristics, which allows us to tackle the challenge of negative transfer through penalizing the latent function that facilitates information sharing in each bivariate model. Predictions are then made through combining predictions from the bivariate models within a Bayesian framework. The proposed method has excellent scalability when the number of outputs is large and minimizes the negative transfer of knowledge between uncorrelated outputs. Statistical guarantees for the proposed method are studied and its advantageous features are demonstrated through numerical studies

Synergizing human-machine intelligence: Visualizing, labeling, and mining the electronic health record

We live in a world where data surround us in every aspect of our lives. The key challenge for humans and machines is how we can make better use of such data. Imagine what would happen if you were to have intelligent machines that could give you insight into the data. Insight that will enable you to better 1) reason about, 2) learn, and 3) understand the underlying phenomena that produced the data. The possibilities of combined human-machine intelligence are endless and will impact our lives in ways we can not even imagine today. Synergistic human-machine intelligence aims to facilitate the analytical reasoning and inference process of humans by creating machines that maximize a human's ability to 1) reason about, 2) learn, and 3) understand large, complex, and heterogeneous data. Combined human-machine intelligence is a powerful symbiosis of mutual benefit, in which we depend on the computational capabilities of the machine for the tasks we are not good at, and the machine requires human intervention for the tasks it performs poorly on. This relationship provides a compelling alternative to either approach in isolation for solving today's and tomorrow's arising data challenges. In his regard, this dissertation proposes a diverse analytical framework that leverages synergistic human-machine intelligence to maximize a human's ability to better 1) reason about, 2) learn, and 3) understand different biomedical imaging and healthcare data present in the patient's electronic health record (EHR). Correspondingly, we approach the data analyses problem from the 1) visualization, 2) labeling, and 3) mining perspective and demonstrate the efficacy of our analytics on specific application scenarios and various data domains. In the first part of this dissertation we explore the question how we can build intelligent imaging analytics that are commensurate with human capabilities and constraints, specifically for optimizing data visualization and automated labeling workflows. Our journey starts with heuristic rule-based analytical models that are derived from task-specific human knowledge. From this experience, we move on to data-driven analytics, where we adapt and combine the intelligence of the model based on prior information provided by the human and synthetic knowledge learned from partial data observations. Within this realm, we propose a novel Bayesian transductive Markov random field model that requires minimal human intervention and is able to cope with scarce label information to learn and infer object shapes in complex spatial, multimodal, spatio-temporal, and longitudinal data. We then study the question how machines can learn discriminative object representations from dense human provided label information by investigating learning and inference mechanisms that make use of deep learning architectures. The developed analytics can aid visualization and labeling tasks, which enables the interpretation and quantification of clinically relevant image information. The second part explores the question how we can build data-driven analytics for exploratory analysis in longitudinal event data that are commensurate with human capabilities and constraints. We propose human-intuitive analytics that enable the representation and discovery of interpretable event patterns to ease knowledge absorption and comprehension of the employed analytics model and the underlying data. We propose a novel doubly-constrained convolutional sparse-coding framework that learns interpretable and shift-invariant latent temporal event patterns. We apply the model to mine complex event data in EHRs. By mapping the event space to heterogeneous patient encounters in the EHR we explore the linkage between healthcare resource utilization (HRU) in relation to disease severity. This linkage may help to better understand how disease specific co-morbidities and their clinical attributes incur different HRU patterns. Such insight helps to characterize the patient's care history, which then enables the comparison against clinical practice guidelines, the discovery of prevailing practices based on common HRU group patterns, and the identification of outliers that might indicate poor patient management

Joint learning from multiple information sources for biological problems

Thanks to technological advancements, more and more biological data havebeen generated in recent years. Data availability offers unprecedented opportunities to look at the same problem from multiple aspects. It also unveils a more global view of the problem that takes into account the intricated inter-play between the involved molecules/entities. Nevertheless, biological datasets are biased, limited in quantity, and contain many false-positive samples. Such challenges often drastically downgrade the performance of a predictive model on unseen data and, thus, limit its applicability in real biological studies. Human learning is a multi-stage process in which we usually start with simple things. Through the accumulated knowledge over time, our cognition ability extends to more complex concepts. Children learn to speak simple words before being able to formulate sentences. Similarly, being able to speak correct sentences supports our learning to speak correct and meaningful paragraphs, etc. Generally, knowledge acquired from related learning tasks would help boost our learning capability in the current task. Motivated by such a phenomenon, in this thesis, we study supervised machine learning models for bioinformatics problems that can improve their performance through exploiting multiple related knowledge sources. More specifically, we concern with ways to enrich the supervised models’ knowledge base with publicly available related data to enhance the computational models’ prediction performance. Our work shares commonality with existing works in multimodal learning, multi-task learning, and transfer learning. Nevertheless, there are certain differences in some cases. Besides the proposed architectures, we present large-scale experiment setups with consensus evaluation metrics along with the creation and release of large datasets to showcase our approaches’ superiority. Moreover, we add case studies with detailed analyses in which we place no simplified assumptions to demonstrate the systems’ utilities in realistic application scenarios. Finally, we develop and make available an easy-to-use website for non-expert users to query the model’s generated prediction results to facilitate field experts’ assessments and adaptation. We believe that our work serves as one of the first steps in bridging the gap between “Computer Science” and “Biology” that will open a new era of fruitful collaboration between computer scientists and biological field experts

Constraint based approaches to interpretable and semi-supervised machine learning

Interpretability and Explainability of machine learning algorithms are becoming increasingly important as Machine Learning (ML) systems get widely applied to domains like clinical healthcare, social media and governance. A related major challenge in deploying ML systems pertains to reliable learning when expert annotation is severely limited. This dissertation prescribes a common framework to address these challenges, based on the use of constraints that can make an ML model more interpretable, lead to novel methods for explaining ML models, or help to learn reliably with limited supervision. In particular, we focus on the class of latent variable models and develop a general learning framework by constraining realizations of latent variables and/or model parameters. We propose specific constraints that can be used to develop identifiable latent variable models, that in turn learn interpretable outcomes. The proposed framework is first used in Non–negative Matrix Factorization and Probabilistic Graphical Models. For both models, algorithms are proposed to incorporate such constraints with seamless and tractable augmentation of the associated learning and inference procedures. The utility of the proposed methods is demonstrated for our working application domain – identifiable phenotyping using Electronic Health Records (EHRs). Evaluation by domain experts reveals that the proposed models are indeed more clinically relevant (and hence more interpretable) than existing counterparts. The work also demonstrates that while there may be inherent trade–offs between constraining models to encourage interpretability, the quantitative performance of downstream tasks remains competitive. We then focus on constraint based mechanisms to explain decisions or outcomes of supervised black-box models. We propose an explanation model based on generating examples where the nature of the examples is constrained i.e. they have to be sampled from the underlying data domain. To do so, we train a generative model to characterize the data manifold in a high dimensional ambient space. Constrained sampling then allows us to generate naturalistic examples that lie along the data manifold. We propose ways to summarize model behavior using such constrained examples. In the last part of the contributions, we argue that heterogeneity of data sources is useful in situations where very little to no supervision is available. This thesis leverages such heterogeneity (via constraints) for two critical but widely different machine learning algorithms. In each case, a novel algorithm in the sub-class of co–regularization is developed to combine information from heterogeneous sources. Co–regularization is a framework of constraining latent variables and/or latent distributions in order to leverage heterogeneity. The proposed algorithms are utilized for clustering, where the intent is to generate a partition or grouping of observed samples, and for Learning to Rank algorithms – used to rank a set of observed samples in order of preference with respect to a specific search query. The proposed methods are evaluated on clustering web documents, social network users, and information retrieval applications for ranking search queries.Electrical and Computer Engineerin