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This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…

Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…

Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference…

The robustness of fault detection algorithms against uncertainty is crucial in the real-world industrial environment. Recently, a new probabilistic design scheme called distributionally robust fault detection (DRFD) has emerged and received…

For the model of constrained multi-armed bandit, we show that by construction there exists an index-based deterministic asymptotically optimal algorithm. The optimality is achieved by the convergence of the probability of choosing an…

In distributed machine learning, data is dispatched to multiple machines for processing. Motivated by the fact that similar data points often belong to the same or similar classes, and more generally, classification rules of high accuracy…

Extreme value theory provides rigorous theory and statistical tools for extrapolation in machine learning, particularly in settings where traditional methods struggle due to data scarcity in the tails. A broad range of tasks benefit from…

Feature-based transfer is one of the most effective methodologies for transfer learning. Existing studies usually assume that the learned new feature representation is \emph{domain-invariant}, and thus train a transfer model $\mathcal{M}$…

Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…

Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly,…

The stochastic multi-arm bandit problem has been extensively studied under standard assumptions on the arm's distribution (e.g bounded with known support, exponential family, etc). These assumptions are suitable for many real-world problems…

Diffusion models (DMs) have demonstrated exceptional generative capabilities across various domains, including image, video, and so on. A key factor contributing to their effectiveness is the high quantity and quality of data used during…

This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…

We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…

Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…

Offline reinforcement learning aims to learn from pre-collected datasets without active exploration. This problem faces significant challenges, including limited data availability and distributional shifts. Existing approaches adopt a…

The problem of selecting a handful of truly relevant variables in supervised machine learning algorithms is a challenging problem in terms of untestable assumptions that must hold and unavailability of theoretical assurances that selection…

Generative models have proven to be an outstanding tool for representing high-dimensional probability distributions and generating realistic-looking images. An essential characteristic of generative models is their ability to produce…

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could…