The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by computational costs ...

A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change is ...

Estimating the ratio of two probability densities from finitely many observations of the densities is a central problem in machine learning and statistics with applications in two-sample testing, divergence estimation, generative modeling, covariate ...

Recent work has focused on the very common practice of prediction-based inference: that is, (i) using a pre-trained machine learning model to predict an unobserved response variable, and then (ii) conducting inference on the association between that ...

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how optimization ...

Reinforcement learning algorithms are known to exhibit a variety of convergence rates depending on the problem structure. Recent years have witnessed considerable progress in developing theory that is instance-dependent, along with algorithms that ...

Kernel methods are built upon the mathematical theory of reproducing kernels and reproducing kernel Hilbert spaces. They enjoy good interpretability thanks to the solid mathematical foundation. Recently, motivated by deep neural networks in deep learning,...

Differential replication through copying refers to the process of replicating the decision behavior of a machine learning model using another model that possesses enhanced features and attributes. This process is relevant when external constraints limit ...

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, ...

Meta-Learning aims to speed up the learning process on new tasks by acquiring useful inductive biases from datasets of related learning tasks. While, in practice, the number of related tasks available is often small, most of the existing approaches ...

We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most n components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence with regularization ...

In this paper, we provide statistical guarantees for over-parameterized deep nonparametric regression in the presence of dependent data. By decomposing the error, we establish nonasymptotic error bounds for deep estimation, which is achieved by ...

In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion, and tensor PCA/...

Understanding the iterative behavior of stochastic optimization algorithms for minimizing nonconvex functions remains a crucial challenge in demystifying deep learning. In particular, it is not yet understood why certain simple techniques are remarkably ...

We study the problem of out-of-distribution (OOD) detection, that is, detecting whether a machine learning (ML) model's output can be trusted at inference time. While a number of tests for OOD detection have been proposed in prior work, a formal ...

Scaling up training datasets and model parameters have benefited neural network-based language models, but also present challenges like distributed compute, input data bottlenecks and reproducibility of results. We introduce two simple and scalable ...

Recent works have studied implicit biases in deep learning, especially the behavior of last-layer features and classifier weights. However, they usually need to simplify the intermediate dynamics under gradient ow or gradient descent due to the ...

Set-valued classification, a new classification paradigm that aims to identify all the plausible classes that an observation belongs to, improves over the traditional classification paradigms in multiple aspects. Existing set-valued classification ...

The dynamic Schrödinger bridge problem seeks a stochastic process that defines a transport between two target probability measures, while optimally satisfying the criteria of being closest, in terms of Kullback-Leibler divergence, to a reference process. ...

We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An in-depth theoretical ...