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Distributed learning is the problem of inferring a function in the case where training data is distributed among multiple geographically separated sources. Particularly, the focus is on designing learning strategies with low computational…

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck.…

A procedure for unfolding the true distribution from experimental data is presented. Machine learning methods are applied for simultaneous identification of an apparatus function and solving of an inverse problem. A priori information about…

In reinforcement learning an agent interacts with the environment by taking actions and observing the next state and reward. When sampled probabilistically, these state transitions, rewards, and actions can all induce randomness in the…

Transfer learning refers to the promising idea of initializing model fits based on pre-training on other data. We particularly consider regression modeling settings where parameter estimates from previous data can be used as anchoring…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

The effectiveness of reinforcement learning (RL) agents in continuous control robotics tasks is mainly dependent on the design of the underlying reward function, which is highly prone to reward hacking. A misalignment between the reward…

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings…

We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…

Limiting failures of machine learning systems is of paramount importance for safety-critical applications. In order to improve the robustness of machine learning systems, Distributionally Robust Optimization (DRO) has been proposed as a…

The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…

Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…

In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

In this paper I propose a generative model of supervised learning that unifies two approaches to supervised learning, using a concept of a correct loss function. Addressing two measurability problems, which have been ignored in statistical…

The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models.…

We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…

In this paper, we study the optimal dividend problem under the continuous time diffusion model with the bounded dividend rate from the Reinforcement Learning (RL) perspective. Unlike the standard literature, our main focus will be on…