Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed data of interest. These posterior model probabilities (PMPs) are measures of uncertainty, but -- when derived from a finite number of observations -- are also uncertain themselves. In this paper, we conceptualize distinct levels of uncertainty which arise in BMC. We explore a fully probabilistic framework for quantifying meta-uncertainty, resulting in an applied method to enhance any BMC workflow. Drawing on both Bayesian and frequentist techniques, we represent the uncertainty over the uncertain PMPs via meta-models which combine simulated and observed data into a predictive distribution for PMPs on new data. We demonstrate the utility of the proposed method in the context of conjugate Bayesian regression, likelihood-based inference with Markov chain Monte Carlo, and simulation-based inference with neural networks.

Density Ratio Estimation (DRE) is an important machine learning technique with many downstream applications. We consider the challenge of DRE with missing not at random (MNAR) data. In this setting, we show that using standard DRE methods leads to biased results while our proposal (M-KLIEP), an adaptation of the popular DRE procedure KLIEP, restores consistency. Moreover, we provide finite sample estimation error bounds for M-KLIEP, which demonstrate minimax optimality with respect to both sample size and worst-case missingness. We then adapt an important downstream application of DRE, Neyman-Pearson (NP) classification, to this MNAR setting. Our procedure both controls Type I error and achieves high power, with high probability. Finally, we demonstrate promising empirical performance both synthetic data and real-world data with simulated missingness.

Developing new drugs for target diseases is a time-consuming and expensive task, drug repurposing has become a popular topic in the drug development field. As much health claim data become available, many studies have been conducted on the data. The real-world data is noisy, sparse, and has many confounding factors. In addition, many studies have shown that drugs effects are heterogeneous among the population. Lots of advanced machine learning models about estimating heterogeneous treatment effects (HTE) have emerged in recent years, and have been applied to in econometrics and machine learning communities. These studies acknowledge medicine and drug development as the main application area, but there has been limited translational research from the HTE methodology to drug development. We aim to introduce the HTE methodology to the healthcare area and provide feasibility consideration when translating the methodology with benchmark experiments on healthcare administrative claim data. Also, we want to use benchmark experiments to show how to interpret and evaluate the model when it is applied to healthcare research. By introducing the recent HTE techniques to a broad readership in biomedical informatics communities, we expect to promote the wide adoption of causal inference using machine learning. We also expect to provide the feasibility of HTE for personalized drug effectiveness.

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the models typically used in statistical modelling, the majority of neural network research has been conducted outside of the field of statistics. This has resulted in a lack of statistically-based methodology, and, in particular, there has been little emphasis on model parsimony. Determining the input layer structure is analogous to variable selection, while the structure for the hidden layer relates to model complexity. In practice, neural network model selection is often carried out by comparing models using out-of-sample performance. However, in contrast, the construction of an associated likelihood function opens the door to information-criteria-based variable and architecture selection. A novel model selection method, which performs both input- and hidden-node selection, is proposed using the Bayesian information criterion (BIC) for FNNs. The choice of BIC over out-of-sample performance as the model selection objective function leads to an increased probability of recovering the true model, while parsimoniously achieving favourable out-of-sample performance. Simulation studies are used to evaluate and justify the proposed method, and applications on real data are investigated.

Speaker diarization is a crucial task in many real-world applications, such as meeting transcription, call center monitoring, and broadcast news processing. The goal of speaker diarization is to partition an audio or video stream into homogeneous segments, each corresponding to a single speaker, without any prior knowledge of the speakers' identities [1, 2]. This task has traditionally been addressed using unsupervised clustering methods [3, 4, 5], but recent advances in deep learning have led to the development of more powerful embedding-based approaches [6, 7, 5]. Despite the recent progress, speaker diarization remains a challenging problem, particularly in real-time and online scenarios where new speakers may enter or leave the conversation at any time. In such cases, pre-trained models may not be sufficient, and the system must be able to adapt to new speakers on the fly [8, 9, 10]. As in the successful applications to other speech and language tasks [11], the reinforcement learning (RL) has emerged as a promising approach for developing next-generation speaker diarization systems that can learn online and adapt to changing circumstances. In this paper, we propose a novel RL framework for online speaker diarization that does not require prior registration or pretraining. Our approach combines embedding extraction, clustering, and resegmentation into a single online decision-making problem, where the agent receives feedback in the form of rewards or penalties for each segmentation decision. We demonstrate the effectiveness of our approach using a Q-learning-based diarization agent on a desktop app, and discuss practical considerations for implementing and deploying RL-based speaker diarization systems.

Graph Neural Networks (GNNs) have been applied to many problems in computer sciences. Capturing higher-order relationships between nodes is crucial to increase the expressive power of GNNs. However, existing methods to capture these relationships could be infeasible for large-scale graphs. In this work, we introduce a new higher-order sparse convolution based on the Sobolev norm of graph signals. Our Sparse Sobolev GNN (S-SobGNN) computes a cascade of filters on each layer with increasing Hadamard powers to get a more diverse set of functions, and then a linear combination layer weights the embeddings of each filter. We evaluate S-SobGNN in several applications of semi-supervised learning. S-SobGNN shows competitive performance in all applications as compared to several state-of-the-art methods.

This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian optimization have enabled the convenient recovery of solutions by adapting unconstrained optimization algorithms over manifolds. However, it remains challenging to scale up and meanwhile maintain stable convergence rates and handle saddle points. We propose a new second-order Riemannian optimization algorithm, aiming at improving convergence rate and reducing computational cost. It enhances the Riemannian trust-region algorithm that explores curvature information to escape saddle points through a mixture of subsampling and cubic regularization techniques. We conduct rigorous analysis to study the convergence behavior of the proposed algorithm. We also perform extensive experiments to evaluate it based on two general machine learning tasks using multiple datasets. The proposed algorithm exhibits improved computational speed and convergence behavior compared to a large set of state-of-the-art Riemannian optimization algorithms.

Vehicle insurance claims size prediction needs methods to efficiently handle these claims. Machine learning (ML) is one of the methods that solve this problem. Tree-based ensemble learning algorithms are highly effective and widely used ML methods. This study considers how vehicle insurance providers incorporate ML methods in their companies and explores how the models can be applied to insurance big data. We utilize various tree-based ML methods, such as bagging, random forest, and gradient boosting, to determine the relative importance of predictors in predicting claims size and to explore the relationships between claims size and predictors. Furthermore, we evaluate and compare these models' performances. The results show that tree-based ensemble methods are better than the classical least square method. Keywords: claims size prediction; machine learning; tree-based ensemble methods; vehicle insurance.

Language contact is a pervasive phenomenon reflected in the borrowing of words from donor to recipient languages. Most computational approaches to borrowing detection treat all languages under study as equally important, even though dominant languages have a stronger impact on heritage languages than vice versa. We test new methods for lexical borrowing detection in contact situations where dominant languages play an important role, applying two classical sequence comparison methods and one machine learning method to a sample of seven Latin American languages which have all borrowed extensively from Spanish. All methods perform well, with the supervised machine learning system outperforming the classical systems. A review of detection errors shows that borrowing detection could be substantially improved by taking into account donor words with divergent meanings from recipient words.

Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of interest. While such technique, coined transfer learning, is very effective in domains such as computer vision or natural langage processing, it does not yet solve common problems of deep learning such as model interpretability or the overall need for data. This thesis explores a different answer to the problem of learning expressive models in data constrained settings: instead of relying on big datasets to learn neural networks, we will replace some modules by known functions reflecting the structure of the data. Very often, these functions will be drawn from the rich literature of kernel methods. Indeed, many kernels can reflect the underlying structure of the data, thus sparing learning parameters to some extent. Our approach falls under the hood of "inductive biases", which can be defined as hypothesis on the data at hand restricting the space of models to explore during learning. We demonstrate the effectiveness of this approach in the context of sequences, such as sentences in natural language or protein sequences, and graphs, such as molecules. We also highlight the relationship between our work and recent advances in deep learning. Additionally, we study convex machine learning models. Here, rather than proposing new models, we wonder which proportion of the samples in a dataset is really needed to learn a "good" model. More precisely, we study the problem of safe sample screening, i.e, executing simple tests to discard uninformative samples from a dataset even before fitting a machine learning model, without affecting the optimal model. Such techniques can be used to prune datasets or mine for rare samples.