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Out-of-distribution (OOD) generalisation is challenging because it involves not only learning from empirical data, but also deciding among various notions of generalisation, e.g., optimising the average-case risk, worst-case risk, or…

The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…

Data-driven machine learning models are being increasingly employed in several important inference problems in biology, chemistry, and physics which require learning over combinatorial spaces. Recent empirical evidence (see, e.g., [1], [2],…

The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction error or the so-called Area Under the Curve (AUC) for a particular data distribution. However, when the models are…

Measurement-constrained datasets, often encountered in semi-supervised learning, arise when data labeling is costly, time-intensive, or hindered by confidentiality or ethical concerns, resulting in a scarcity of labeled data. In certain…

We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…

In recent years, machine learning models have achieved success based on the independently and identically distributed assumption. However, this assumption can be easily violated in real-world applications, leading to the Out-of-Distribution…

To address the uncertainty in function types, recent progress in online convex optimization (OCO) has spurred the development of universal algorithms that simultaneously attain minimax rates for multiple types of convex functions. However,…

Bayesian optimization (BO) with Gaussian process (GP) surrogate models is a powerful black-box optimization method. Acquisition functions are a critical part of a BO algorithm as they determine how the new samples are selected. Some of the…

Modern regression problems often involve high-dimensional data and a careful tuning of the regularization hyperparameters is crucial to avoid overly complex models that may overfit the training data while guaranteeing desirable properties…

We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…

Substitution resolution supports the computational character of $\beta$-reduction, complementing its execution with a capture-avoiding exchange of terms for bound variables. Alas, the meta-level definition of substitution, masking a…

We study the generalization error of statistical learning algorithms in a non-i.i.d. setting, where the training data is sampled from a stationary mixing process. We develop an analytic framework for this scenario based on a reduction to…

A typical goal of research in combinatorial optimization is to come up with fast algorithms that find optimal solutions to a computational problem. The process that takes a real-world problem and extracts a clean mathematical abstraction of…

It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…

In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…

Uncertainty quantification is essential in safety-critical settings--from autonomous driving to aviation, finance, and health--where decisions must rely on conservative bounds rather than point estimates. Predictor-level intervals (e.g.,…

Optimizing expensive black-box objectives over mixed search spaces is a common challenge across the natural sciences. Bayesian optimization (BO) offers sample-efficient strategies through probabilistic surrogate models and acquisition…

An increasingly popular method for solving a constrained combinatorial optimisation problem is to first convert it into a quadratic unconstrained binary optimisation (QUBO) problem, and solve it using a standard QUBO solver. However, this…

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…