Bayesian Learning of Noisy Markov Decision Processes

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the structure of a Markov decision process. Adopting a Bayesian approach to inference, we show how latent variables of the model can be estimated, and how predictions about actions can be made, in a unified framework. A new Markov chain Monte Carlo (MCMC) sampler is devised for simulation from the posterior distribution. This step includes a parameter expansion step, which is shown to be essential for good convergence properties of the MCMC sampler. As an illustration, the method is applied to learning a human controller.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Essays in Empirical Operations Management: Bayesian Learning of Service Quality and Structural Estimation of Complementary Product Pricing and Inventory Management

This dissertation contributes to the rapidly growing empirical research area in the field of operations management. It contains two essays, tackling two different sets of operations management questions which are motivated by and built on field data sets from two very different industries --- air cargo logistics and retailing.

The first essay, based on the data set obtained from a world leading third-party logistics company, develops a novel and general Bayesian hierarchical learning framework for estimating customers' spillover learning, that is, customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. We then apply our model to the data set to study how customers' experiences from shipping on a particular route affect their future decisions about shipping not only on that route, but also on other routes serviced by the same logistics company. We find that customers indeed borrow experiences from similar but different services to update their quality beliefs that determine future purchase decisions. Also, service quality beliefs have a significant impact on their future purchasing decisions. Moreover, customers are risk averse; they are averse to not only experience variability but also belief uncertainty (i.e., customer's uncertainty about their beliefs). Finally, belief uncertainty affects customers' utilities more compared to experience variability.

The second essay is based on a data set obtained from a large Chinese supermarket chain, which contains sales as well as both wholesale and retail prices of un-packaged perishable vegetables. Recognizing the special characteristics of this particularly product category, we develop a structural estimation model in a discrete-continuous choice model framework. Building on this framework, we then study an optimization model for joint pricing and inventory management strategies of multiple products, which aims at improving the company's profit from direct sales and at the same time reducing food waste and thus improving social welfare.

Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, insights, and guidance for firms to utilize vast sales and operations data to devise more effective business strategies.

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.

A Bayesian Model for Learning Using Flashcards

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A Bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots. The framework proposed combines nonlinear dimensionality reduction, nonlinear regression under noise, and variational Bayesian learning to create consistent probabilistic representations of places from images. These generative models are learnt from a few images and used for multi-class place recognition where classification is computed from a set of feature-vectors. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions and blurring. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

A bayesian approach for place recognition

This paper presents a robust place recognition algorithm for mobile robots that can be used for planning and navigation tasks. The proposed framework combines nonlinear dimensionality reduction, nonlinear regression under noise, and Bayesian learning to create consistent probabilistic representations of places from images. These generative models are incrementally learnt from very small training sets and used for multi-class place recognition. Recognition can be performed in near real-time and accounts for complexity such as changes in illumination, occlusions, blurring and moving objects. The algorithm was tested with a mobile robot in indoor and outdoor environments with sequences of 1579 and 3820 images, respectively. This framework has several potential applications such as map building, autonomous navigation, search-rescue tasks and context recognition.

Bayesian framework and message passing for joint support and signal recovery of approximately sparse signals

In this paper, we develop a low-complexity message passing algorithm for joint support and signal recovery of approximately sparse signals. The problem of recovery of strictly sparse signals from noisy measurements can be viewed as a problem of recovery of approximately sparse signals from noiseless measurements, making the approach applicable to strictly sparse signal recovery from noisy measurements. The support recovery embedded in the approach makes it suitable for recovery of signals with same sparsity profiles, as in the problem of multiple measurement vectors (MMV). Simulation results show that the proposed algorithm, termed as JSSR-MP (joint support and signal recovery via message passing) algorithm, achieves performance comparable to that of sparse Bayesian learning (M-SBL) algorithm in the literature, at one order less complexity compared to the M-SBL algorithm.

Locally regularised two-stage learning algorithm for RBF network centre selection

Nonlinear models constructed from radial basis function (RBF) networks can easily be over-fitted due to the noise on the data. While information criteria, such as the final prediction error (FPE), can provide a trade-off between training error and network complexity, the tunable parameters that penalise a large size of network model are hard to determine and are usually network dependent. This article introduces a new locally regularised, two-stage stepwise construction algorithm for RBF networks. The main objective is to produce a parsomous network that generalises well over unseen data. This is achieved by utilising Bayesian learning within a two-stage stepwise construction procedure to penalise centres that are mainly interpreted by the noise.

Nonparametric discovery of learning patterns and autism subgroups from therapeutic data

Autism Spectrum Disorder (ASD) is growing at a staggering rate, but, little is known about the cause of this condition. Inferring learning patterns from therapeutic performance data, and subsequently clustering ASD children into subgroups, is important to understand this domain, and more importantly to inform evidence-based intervention. However, this data-driven task was difficult in the past due to insufficiency of data to perform reliable analysis. For the first time, using data from a recent application for early intervention in autism (TOBY Play pad), whose download count is now exceeding 4500, we present in this paper the automatic discovery of learning patterns across 32 skills in sensory, imitation and language. We use unsupervised learning methods for this task, but a notorious problem with existing methods is the correct specification of number of patterns in advance, which in our case is even more difficult due to complexity of the data. To this end, we appeal to recent Bayesian nonparametric methods, in particular the use of Bayesian Nonparametric Factor Analysis. This model uses Indian Buffet Process (IBP) as prior on a binary matrix of infinite columns to allocate groups of intervention skills to children. The optimal number of learning patterns as well as subgroup assignments are inferred automatically from data. Our experimental results follow an exploratory approach, present different newly discovered learning patterns. To provide quantitative results, we also report the clustering evaluation against K-means and Nonnegative matrix factorization (NMF). In addition to the novelty of this new problem, we were able to demonstrate the suitability of Bayesian nonparametric models over parametric rivals.

Recognition on Finite Set of Events: Bayesian Analysis of Generalization Ability and Classification Tree Pruning

The problem of recognition on finite set of events is considered. The generalization ability of classifiers for this problem is studied within the Bayesian approach. The method for non-uniform prior distribution specification on recognition tasks is suggested. It takes into account the assumed degree of intersection between classes. The results of the analysis are applied for pruning of classification trees.

Bayesian Emulation for Sequential Modeling, Inference and Decision Analysis

The advances in three related areas of state-space modeling, sequential Bayesian learning, and decision analysis are addressed, with the statistical challenges of scalability and associated dynamic sparsity. The key theme that ties the three areas is Bayesian model emulation: solving challenging analysis/computational problems using creative model emulators. This idea defines theoretical and applied advances in non-linear, non-Gaussian state-space modeling, dynamic sparsity, decision analysis and statistical computation, across linked contexts of multivariate time series and dynamic networks studies. Examples and applications in financial time series and portfolio analysis, macroeconomics and internet studies from computational advertising demonstrate the utility of the core methodological innovations.

Chapter 1 summarizes the three areas/problems and the key idea of emulating in those areas. Chapter 2 discusses the sequential analysis of latent threshold models with use of emulating models that allows for analytical filtering to enhance the efficiency of posterior sampling. Chapter 3 examines the emulator model in decision analysis, or the synthetic model, that is equivalent to the loss function in the original minimization problem, and shows its performance in the context of sequential portfolio optimization. Chapter 4 describes the method for modeling the steaming data of counts observed on a large network that relies on emulating the whole, dependent network model by independent, conjugate sub-models customized to each set of flow. Chapter 5 reviews those advances and makes the concluding remarks.