Related papers: Mathematical Analysis on Out-of-Sample Extensions

Distributionally Robust Reinforcement Learning (DR-RL) aims to derive a policy optimizing the worst-case performance within a predefined uncertainty set. Despite extensive research, previous DR-RL algorithms have predominantly favored…

Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…

Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states. However, most analysis of such algorithms gives…

Reinforcement-learning (RL) agents often struggle when deployed from simulation to the real-world. A dominant strategy for reducing the sim-to-real gap is domain randomization (DR) which trains the policy across many simulators produced by…

The proper handling of out-of-distribution (OOD) samples in deep classifiers is a critical concern for ensuring the suitability of deep neural networks in safety-critical systems. Existing approaches developed for robust OOD detection in…

Deep Reinforcement Learning (DRL) algorithms have achieved great success in solving many challenging tasks while their black-box nature hinders interpretability and real-world applicability, making it difficult for human experts to…

Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on…

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…

Reinforcement Learning (RL) based solutions are being adopted in a variety of domains including robotics, health care and industrial automation. Most focus is given to when these solutions work well, but they fail when presented with out of…

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…

Learning with Reproducing Kernel Hilbert Spaces (RKHS) has been widely used in many scientific disciplines. Because a RKHS can be very flexible, it is common to impose a regularization term in the optimization to prevent overfitting.…

In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…

When machine learning (ML) models are supplied with data outside their training distribution, they are more likely to make inaccurate predictions; in a cyber-physical system (CPS), this could lead to catastrophic system failure. To mitigate…

As breakthroughs in deep learning transform key industries, models are increasingly required to extrapolate on datapoints found outside the range of the training set, a challenge we coin as out-of-support (OoS) generalisation. However,…

Out-of-Distribution (OOD) detection, i.e., identifying whether an input is sampled from a novel distribution other than the training distribution, is a critical task for safely deploying machine learning systems in the open world. Recently,…

Deep learning (DL) has driven broad advances across scientific and engineering domains. Despite its success, DL models often exhibit limited interpretability and generalization, which can undermine trust, especially in safety-critical…

Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying…

Detecting out-of-distribution (OOD) samples is vital for developing machine learning based models for critical safety systems. Common approaches for OOD detection assume access to some OOD samples during training which may not be available…

Despite their remarkable success in approximating a wide range of operators defined by PDEs, existing neural operators (NOs) do not necessarily perform well for all physics problems. We focus here on high-frequency waves to highlight…

Out-of-distribution (OOD) detection aims to detect test samples outside the training category space, which is an essential component in building reliable machine learning systems. Existing reviews on OOD detection primarily focus on method…