相关论文: Learning High-Dimensional Distributions with Laten…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…

This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a weak formulation of the FPE where the adjoint operator of…

We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…

Generative adversarial networks (GANs) are emerging machine learning models for generating synthesized data similar to real data by jointly training a generator and a discriminator. In many applications, data and computational resources are…

Deep Reinforcement Learning has shown its ability in solving complicated problems directly from high-dimensional observations. However, in end-to-end settings, Reinforcement Learning algorithms are not sample-efficient and requires long…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Generative adversarial networks have proven to be a powerful tool for learning complex and high-dimensional data distributions, but issues such as mode collapse have been shown to make it difficult to train them. This is an even harder…

Gaussian processes (GPs) stand as crucial tools in machine learning and signal processing, with their effectiveness hinging on kernel design and hyper-parameter optimization. This paper presents a novel GP linear multiple kernel (LMK) and a…

A generative adversarial network (GAN) has been a representative backbone model in generative artificial intelligence (AI) because of its powerful performance in capturing intricate data-generating processes. However, the GAN training is…

Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

The deep neural network suffers from many fundamental issues in machine learning. For example, it often gets trapped into a local minimum in training, and its prediction uncertainty is hard to be assessed. To address these issues, we…

In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This…

Grokking, the phenomenon of delayed generalization, is often attributed to the depth and compositional structure of deep neural networks. We study grokking in one of the simplest possible settings: the learning of a linear model with…

Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close…

Though generative adversarial networks (GANs) areprominent models to generate realistic and crisp images,they often encounter the mode collapse problems and arehard to train, which comes from approximating the intrinsicdiscontinuous…