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Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides…
We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear…
Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…
Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detection and root finding procedure to learn the high dimensional…
Unsupervised domain adaptation (UDA) is an approach to minimizing domain gap. Generative methods are common approaches to minimizing the domain gap of aerial images which improves the performance of the downstream tasks, e.g., cross-domain…
With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…
Generative Retrieval (GR), autoregressively decoding relevant document identifiers given a query, has been shown to perform well under the setting of small-scale corpora. By memorizing the document corpus with model parameters, GR…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured…
Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…
Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…
Spatial Transcriptomics (ST) offers spatially resolved gene expression but remains costly. Predicting expression directly from widely available Hematoxylin and Eosin (H&E) stained images presents a cost-effective alternative. However, most…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. In this work, we analyze a new data-driven regularized stochastic gradient descent…
Although recent research applying text-to-image (T2I) diffusion models to real-world super-resolution (SR) has achieved remarkable progress, the misalignment of their targets leads to a suboptimal trade-off between inference speed and…
Multimodal Emotion Recognition in Conversations (MERC) aims to classify utterance emotions using textual, auditory, and visual modal features. Most existing MERC methods assume each utterance has complete modalities, overlooking the common…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that…
A low-resolution digital surface model (DSM) features distinctive attributes impacted by noise, sensor limitations and data acquisition conditions, which failed to be replicated using simple interpolation methods like bicubic. This causes…
Remote sensing images captured by different platforms exhibit significant disparities in spatial resolution. Large scale factor super-resolution (SR) algorithms are vital for maximizing the utilization of low-resolution (LR) satellite data…
Deep generative modeling has led to new and state of the art approaches for enforcing structural priors in a variety of inverse problems. In contrast to priors given by sparsity, deep models can provide direct low-dimensional…
Disentangled representation is a powerful technique to tackle domain shift problem in medical image analysis in unsupervised domain adaptation setting.However, previous methods only focus on exacting domain-invariant feature and ignore…