机器学习

As probabilistic models continue to permeate various facets of our society and contribute to scientific advancements, it becomes a necessity to go beyond traditional metrics such as predictive accuracy and error rates and assess their…

Neal (1996) proved that infinitely wide shallow Bayesian neural networks (BNN) converge to Gaussian processes (GP), when the network weights have bounded prior variance. Cho & Saul (2009) provided a useful recursive formula for deep kernel…

Multivariate density estimation is of great interest in various scientific and engineering disciplines. In this work, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariate…

This paper addresses the challenge of offline policy learning in reinforcement learning with continuous action spaces when unmeasured confounders are present. While most existing research focuses on policy evaluation within partially…

Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then,…

We show that deep Heaviside networks (DHNs) have limited expressiveness but that this can be overcome by including either skip connections or neurons with linear activation. We provide lower and upper bounds for the Vapnik-Chervonenkis (VC)…

Rapid developments in advanced sensing and imaging have significantly enhanced information visibility, opening opportunities for predictive modeling of complex dynamic systems. However, sensing signals acquired from such complex systems are…

Estimates of heterogeneous treatment effects such as conditional average treatment effects (CATEs) and conditional quantile treatment effects (CQTEs) play an important role in real-world decision making. Given this importance, one should…

The objective of canonical multi-armed bandits is to identify and repeatedly select an arm with the largest reward, often in the form of the expected value of the arm's probability distribution. Such a utilitarian perspective and focus on…

The effect of relative entropy asymmetry is analyzed in the context of empirical risk minimization (ERM) with relative entropy regularization (ERM-RER). Two regularizations are considered: $(a)$ the relative entropy of the measure to be…

We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…

In many, if not most, machine learning applications the training data is naturally heterogeneous (e.g. federated learning, adversarial attacks and domain adaptation in neural net training). Data heterogeneity is identified as one of the…

Consider an edge computing setting in which a user submits queries for the solution of a linear system to an edge processor, which is subject to time-varying computing availability. The edge processor applies a probabilistic linear solver…

We study the problem of estimating the \emph{value} of the largest mean among K distributions via samples from them (rather than estimating \emph{which} distribution has the largest mean), which arises from various machine learning tasks…

Many practical applications of online reinforcement learning require the satisfaction of safety constraints while learning about the unknown environment. In this work, we establish theoretical foundations for reinforcement learning with…

The description of the dynamics of complex systems, in particular the capture of the interaction structure and causal relationships between elements of the system, is one of the central questions of interdisciplinary research. While the…

This paper introduces a new regularized version of the robust $\tau$-regression estimator for analyzing high-dimensional datasets subject to gross contamination in the response variables and covariates. The resulting estimator, termed…

The plug-in estimator of the squared Euclidean 2-Wasserstein distance is conservative, however due to its large positive bias it is often uninformative. We eliminate most of this bias using a simple centering procedure based on linear…

We consider an online model for recommendation systems, with each user being recommended an item at each time-step and providing 'like' or 'dislike' feedback. A latent variable model specifies the user preferences: both users and items are…

When implementing prediction models for high-stakes real-world applications such as medicine, finance, and autonomous systems, quantifying prediction uncertainty is critical for effective risk management. Traditional approaches to…