This thesis presents new Bayesian nonparametric models and approaches for their development, for the problems of name disambiguation and supervised learning. Bayesian nonparametric methods form an increasingly popular approach for solving problems that demand a high amount of model flexibility. However, this field is relatively new, and there are many areas that need further investigation. Previous work on Bayesian nonparametrics has neither fully explored the problems of entity disambiguation and supervised learning nor the advantages of nested hierarchical models. Entity disambiguation is a widely encountered problem where different references need to be linked to a real underlying entity. This problem is often unsupervised as there is no previously known information about the entities. Further to this, effective use of Bayesian nonparametrics offer a new approach to tackling supervised problems, which are frequently encountered. The main original contribution of this thesis is a set of new structured Dirichlet process mixture models for name disambiguation and supervised learning that can also have a wide range of applications. These models use techniques from Bayesian statistics, including hierarchical and nested Dirichlet processes, generalised linear models, Markov chain Monte Carlo methods and optimisation techniques such as BFGS. The new models have tangible advantages over existing methods in the field as shown with experiments on real-world datasets including citation databases and classification and regression datasets. I develop the unsupervised author-topic space model for author disambiguation that uses free-text to perform disambiguation unlike traditional author disambiguation approaches. The model incorporates a name variant model that is based on a nonparametric Dirichlet language model. The model handles both novel unseen name variants and can model the unknown authors of the text of the documents. Through this, the model can disambiguate authors with no prior knowledge of the number of true authors in the dataset. In addition, it can do this when the authors have identical names. I use a model for nesting Dirichlet processes named the hybrid NDP-HDP. This model allows Dirichlet processes to be clustered together and adds an additional level of structure to the hierarchical Dirichlet process. I also develop a new hierarchical extension to the hybrid NDP-HDP. I develop this model into the grouped author-topic model for the entity disambiguation task. The grouped author-topic model uses clusters to model the co-occurrence of entities in documents, which can be interpreted as research groups. Since this model does not require entities to be linked to specific words in a document, it overcomes the problems of some existing author-topic models. The model incorporates a new method for modelling name variants, so that domain-specific name variant models can be used. Lastly, I develop extensions to supervised latent Dirichlet allocation, a type of supervised topic model. The keyword-supervised LDA model predicts document responses more accurately by modelling the effect of individual words and their contexts directly. The supervised HDP model has more model flexibility by using Bayesian nonparametrics for supervised learning. These models are evaluated on a number of classification and regression problems, and the results show that they outperform existing supervised topic modelling approaches. The models can also be extended to use similar information to the previous models, incorporating additional information such as entities and document titles to improve prediction.

<p>Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns. </p><p>Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.</p><p>Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with</p><p>little or no prior knowledge</p> / Dissertation

The main goal of this thesis is to investigate the frequentist asymptotic properties of nonparametric Bayesian procedures in inverse problems and the Gaussian white noise model. In the first part, we study the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. This rate provides a quantitative measure of the quality of statistical estimation of the procedure. A theorem is proved in a general Hilbert space setting under approximation-theoretic assumptions on the prior. The result is applied to non-conjugate priors, notably sieve and wavelet series priors, as well as in the conjugate setting. In the mildly ill-posed setting, minimax optimal rates are obtained, with sieve priors being rate adaptive over Sobolev classes. In the severely ill-posed setting, oversmoothing the prior yields minimax rates. Previously established results in the conjugate setting are obtained using this method. Examples of applications include deconvolution, recovering the initial condition in the heat equation and the Radon transform. In the second part of this thesis, we investigate Bernstein--von Mises type results for adaptive nonparametric Bayesian procedures in both the Gaussian white noise model and the mildly ill-posed inverse setting. The Bernstein--von Mises theorem details the asymptotic behaviour of the posterior distribution and provides a frequentist justification for the Bayesian approach to uncertainty quantification. We establish weak Bernstein--von Mises theorems in both a Hilbert space and multiscale setting, which have applications in $L^2$ and $L^\infty$ respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets using a Bayesian approach. We also provide simulations to numerically illustrate our approach and obtain a visual representation of the different geometries involved.

<p>In this thesis, we develop some Bayesian mixture density estimation for univariate and multivariate data. We start proposing a repulsive process favoring mixture components further apart. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too close together to be scientifically meaningful. Current Bayesian practice generates component-specific parameters independently from a common prior, which tends to favor similar components and often leads to substantial probability assigned to redundant components that are not needed to fit the data. As an alternative, we propose to generate components from a repulsive process, which leads to fewer, better separated and more interpretable clusters. </p><p>In the second part of the thesis, we face the problem of modeling the conditional distribution of a response variable given a high dimensional vector of predictors potentially concentrated near a lower dimensional subspace or manifold. In many settings it is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiresolution model that scales efficiently to massive numbers of features, and can be implemented efficiently with slice sampling.</p><p> In the third part of the thesis, we deal with the problem of characterizing the conditional density of a multivariate vector of response given a potentially high dimensional vector of predictors. The proposed model flexibly characterizes the density of the response variable by hierarchically coupling a collection of factor models, each one defined on a different scale of resolution. As it is illustrated in Chapter 4, our proposed method achieves good predictive performance compared to competitive models while efficiently scaling to high dimensional predictors.</p> / Dissertation

There is significant interest in using gene expression measurements to aid in the personalization of medical treatment. The presence of significant normal tissue contamination in tumor samples makes it difficult to use tumor expression measurements to predict clinical variables and treatment response. I present a probabilistic method, TMMpure, to infer the expression profile of the cancerous tissue using a modified topic model that contains a hierarchical Dirichlet process prior on the cancer profiles. I demonstrate that TMMpure is able to infer the expression profile of cancerous tissue and improves the power of predictive models for clinical variables using expression profiles.

There is significant interest in using gene expression measurements to aid in the personalization of medical treatment. The presence of significant normal tissue contamination in tumor samples makes it difficult to use tumor expression measurements to predict clinical variables and treatment response. I present a probabilistic method, TMMpure, to infer the expression profile of the cancerous tissue using a modified topic model that contains a hierarchical Dirichlet process prior on the cancer profiles. I demonstrate that TMMpure is able to infer the expression profile of cancerous tissue and improves the power of predictive models for clinical variables using expression profiles.

abstract: The cell is a dense environment composes of proteins, nucleic acids, as well as other small molecules, which are constantly bombarding each other and interacting. These interactions and the diffusive motions are driven by internal thermal fluctuations. Upon collision, molecules can interact and form complexes. It is of interest to learn kinetic parameters such as reaction rates of one molecule converting to different species or two molecules colliding and form a new species as well as to learn diffusion coefficients. Several experimental measurements can probe diffusion coefficients at the single-molecule and bulk level. The target of this thesis is on single-molecule methods, which can assess diffusion coefficients at the individual molecular level. For instance, super resolution methods like stochastic optical reconstruction microscopy (STORM) and photo activated localization microscopy (PALM), have a high spatial resolution with the cost of lower temporal resolution. Also, there is a different group of methods, such as MINFLUX, multi-detector tracking, which can track a single molecule with high spatio-temporal resolution. The problem with these methods is that they are only applicable to very diluted samples since they need to ensure existence of a single molecule in the region of interest (ROI). In this thesis, the goal is to have the best of both worlds by achieving high spatio-temporal resolutions without being limited to a few molecules. To do so, one needs to refocus on fluorescence correlation spectroscopy (FCS) as a method that applies to both in vivo and in vitro systems with a high temporal resolution and relies on multiple molecules traversing a confocal volume for an extended period of time. The difficulty here is that the interpretation of the signal leads to different estimates for the kinetic parameters such as diffusion coefficients based on a different number of molecules we consider in the model. It is for this reason that the focus of this thesis is now on using Bayesian nonparametrics (BNPs) as a way to solve this model selection problem and extract kinetic parameters such as diffusion coefficients at the single-molecule level from a few photons, and thus with the highest temporal resolution as possible. / Dissertation/Thesis / Source code related to chapter 3 / Source code related to chapter 4 / Doctoral Dissertation Physics 2020

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<div>Mixture modeling is a classical unsupervised learning method with applications to clustering and density estimation. This dissertation studies two challenges in modeling data with mixture models. The first part addresses problems that arise when modeling observations lying on constrained spaces, such as the boundaries of a city or a landmass. It is often desirable to model such data through the use of mixture models, especially nonparametric mixture models. Specifying the component distributions and evaluating normalization constants raise modeling and computational challenges. In particular, the likelihood forms an intractable quantity, and Bayesian inference over the parameters of these models results in posterior distributions that are doubly-intractable. We address this problem via a model based on rejection sampling and an algorithm based on data augmentation. Our approach is to specify such models as restrictions of standard, unconstrained distributions to the constraint set, with measurements from the model simulated by a rejection sampling algorithm. Posterior inference proceeds by Markov chain Monte Carlo, first imputing the rejected samples given mixture parameters and then resampling parameters given all samples. We study two modeling approaches: mixtures of truncated Gaussians and truncated mixtures of Gaussians, along with Markov chain Monte Carlo sampling algorithms for both. We also discuss variations of the models, as well as approximations to improve mixing, reduce computational cost, and lower variance.</div><div><br></div><div>The second part of this dissertation explores the application of mixture models to estimate contamination rates in matched tumor and normal samples. Bulk sequencing of tumor samples are prone to contaminations from normal cells, which lead to difficulties and inaccuracies in determining the mutational landscape of the cancer genome. In such instances, a matched normal sample from the same patient can be used to act as a control for germline mutations. Probabilistic models are popularly used in this context due to their flexibility. We propose a hierarchical Bayesian model to denoise the contamination in such data and detect somatic mutations in tumor cell populations. We explore the use of a Dirichlet prior on the contamination level and extend this to a framework of Dirichlet processes. We discuss MCMC schemes to sample from the joint posterior distribution and evaluate its performance on both synthetic experiments and publicly available data.</div>

In longitudinal studies, outcomes are measured repeatedly over time, but in reality clinical studies are full of missing data points of monotone and non-monotone nature. Often this missingness is related to the unobserved data so that it is non-ignorable. In such context, pattern-mixture model (PMM) is one popular tool to analyze the joint distribution of outcome and missingness patterns. Then the unobserved outcomes are imputed using the distribution of observed outcomes, conditioned on missing patterns. However, the existing methods suffer from model identification issues if data is sparse in specific missing patterns, which is very likely to happen with a small sample size or a large number of repetitions. We extend the existing methods using latent class analysis (LCA) and a shared-parameter PMM. The LCA groups patterns of missingness with similar features and the shared-parameter PMM allows a subset of parameters to be different among latent classes when fitting a model, thus restoring model identifiability. A novel imputation method is also developed using the distribution of observed data conditioned on latent classes. We develop this model for continuous response data and extend it to handle ordinal rating scale data. Our model performs better than existing methods for data with small sample size. The method is applied to two datasets from a phase II clinical trial that studies the quality of life for patients with prostate cancer receiving radiation therapy, and another to study the relationship between the perceived neighborhood condition in adolescence and the drinking habit in adulthood.