Related papers: Learning High-Dimensional Distributions with Laten…

Our world is ambiguous and this is reflected in the data we use to train our algorithms. This is particularly true when we try to model natural processes where collected data is affected by noisy measurements and differences in measurement…

Deep neural networks suffer from over-fitting and catastrophic forgetting when trained with small data. One natural remedy for this problem is data augmentation, which has been recently shown to be effective. However, previous works either…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…

We propose a distributed computing framework, based on a divide and conquer strategy and hierarchical modeling, to accelerate posterior inference for high-dimensional Bayesian factor models. Our approach distributes the task of…

Recent advancement in generative models have demonstrated remarkable performance across various data modalities. Beyond their typical use in data synthesis, these models play a crucial role in distribution matching tasks such as latent…

Large deep learning models have shown great potential for delivering exceptional results in various applications. However, the training process can be incredibly challenging due to the models' vast parameter sizes, often consisting of…

Auto-encoding generative adversarial networks (GANs) combine the standard GAN algorithm, which discriminates between real and model-generated data, with a reconstruction loss given by an auto-encoder. Such models aim to prevent mode…

Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

In this work, we introduce Adapt & Align, a method for continual learning of neural networks by aligning latent representations in generative models. Neural Networks suffer from abrupt loss in performance when retrained with additional…

We present a deep learning model for data-driven simulations of random dynamical systems without a distributional assumption. The deep learning model consists of a recurrent neural network, which aims to learn the time marching structure,…

Generative adversarial networks (GANs), a class of distribution-learning methods based on a two-player game between a generator and a discriminator, can generally be formulated as a minmax problem based on the variational representation of…

At the interface of machine learning and quantum computing, an important question is what distributions can be learned provably with optimal sample complexities and with quantum-accelerated time complexities. In the classical case, Klivans…

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep…

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

Sampling invariant distributions from an It\^o diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential equations require both a fine step size and a lengthy…

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…

Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate…

Diffusion models have achieved remarkable success in image and video generation. In this work, we demonstrate that diffusion models can also \textit{generate high-performing neural network parameters}. Our approach is simple, utilizing an…

We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…