机器学习

Physics phenomena are often described by ordinary and/or partial differential equations (ODEs/PDEs), and solved analytically or numerically. Unfortunately, many real-world systems are described only approximately with missing or unknown…

Machine learning (ML) models always make a prediction, even when they are likely to be wrong. This causes problems in practical applications, as we do not know if we should trust a prediction. ML with reject option addresses this issue by…

Authors Yi-Cheng Chen, Ping-En Lu, Cheng-Shang Chang, and Tzu-Hsuan Liu use the Finite Impulse Response (FIR) linear system filtering method to track and predict the number of people infected and recovered from COVID-19, in a pandemic…

We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral…

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and…

Short-term forecasting models typically assume the availability of input data (features) when they are deployed and in use. However, equipment failures, disruptions, cyberattacks, may lead to missing features when such models are used…

In artificial intelligence (AI), the complexity of many models and processes surpasses human understanding, making it challenging to determine why a specific prediction is made. This lack of transparency is particularly problematic in…

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by…

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based…

Reinforcement learning is a general technique that allows an agent to learn an optimal policy and interact with an environment in sequential decision making problems. The goodness of a policy is measured by its value function starting from…

We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…

This paper introduces a new approach for approximating the learning dynamics of multiple reinforcement learning (RL) agents interacting in a finite-state Markov game. The idea is to rescale the learning process by simultaneously reducing…

Forecasting geopolitical conflict from data sources like the Global Database of Events, Language, and Tone (GDELT) is a critical challenge for national security. The inherent sparsity, burstiness, and overdispersion of such data cause…

We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincar\'{e} and log-Sobolev inequalities for the…

The Latent Stochastic Differential Equation (SDE) is a powerful tool for time series and sequence modeling. However, training Latent SDEs typically relies on adjoint sensitivity methods, which depend on simulation and backpropagation…

In this research, we investigate the high-dimensional linear contextual bandit problem where the number of features $p$ is greater than the budget $T$, or it may even be infinite. Differing from the majority of previous works in this field,…

Conformal prediction offers a distribution-free framework for constructing prediction sets with coverage guarantees. In practice, multiple valid conformal prediction sets may be available, arising from different models or methodologies.…

In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image classification tasks that encounter various input perturbations. While data augmentation techniques…

The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…

We study methods for identifying heterogeneous parameter components in distributed M-estimation with minimal data transmission. One is based on a re-normalized Wald test, which is shown to be consistent as long as the number of distributed…