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The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…

The problem of model selection is inevitable in an increasingly large number of applications involving partial theoretical knowledge and vast amounts of information, like in medicine, biology or economics. The associated techniques are…

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…

Discriminative linear models are a popular tool in machine learning. These can be generally divided into two types: The first is linear classifiers, such as support vector machines, which are well studied and provide state-of-the-art…

In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as A-, D-, and E-optimal…

The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…

We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…

A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in…

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with…

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…

In this paper we study the relationship between the optimal value of a homogeneous quadratic optimization problem and that of its Semidefinite Programming (SDP) relaxation. We consider two quadratic optimization models: (1) $\min \{x^* C x…

In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…

We investigate model based classification with partially labelled training data. In many biostatistical applications, labels are manually assigned by experts, who may leave some observations unlabelled due to class uncertainty. We analyse…

This work studies the general principles of improving the learning of language models (LMs), which aims at reducing the necessary training steps for achieving superior performance. Specifically, we present a theory for the optimal learning…

Designing efficient experiments under practical constraints is critical in both scientific research and industrial practice. Focusing on minimizing the average variance of the parameter estimates, A-optimal designs show advantages in…

Multi-class classification methods based on both labeled and unlabeled functional data sets are discussed. We present a semi-supervised logistic model for classification in the context of functional data analysis. Unknown parameters in our…

This paper considers a half-duplex scenario where an interferer behaves according to a parametric model but the values of the model parameters are unknown. We explore the necessary number of sensing steps to gather sufficient knowledge…

Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate…