Related papers: Probing the Latent Hierarchical Structure of Data …

Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…

Deep neural networks have been shown to be very successful at learning feature hierarchies in supervised learning tasks. Generative models, on the other hand, have benefited less from hierarchical models with multiple layers of latent…

Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a linear latent feature model with additive noise constructed from probabilistic…

While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images…

Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting…

Identifying subtle phenotypic variations in cellular images is critical for advancing biological research and accelerating drug discovery. These variations are often masked by the inherent cellular heterogeneity, making it challenging to…

Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Recent work on diffusion models proposed that they operate in two regimes: memorization, in which models reproduce their training data, and generalization, in which they generate novel samples. While this has been tested in high-noise…

We present an architecture which lets us train deep, directed generative models with many layers of latent variables. We include deterministic paths between all latent variables and the generated output, and provide a richer set of…

The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Learning controllable and generalizable representation of multivariate data with desired structural properties remains a fundamental problem in machine learning. In this paper, we present a novel framework for learning generative models…

Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…

We study a parametric family of latent variable models, namely topic models, equipped with a hierarchical structure among the topic variables. Such models may be viewed as a finite mixture of the latent Dirichlet allocation (LDA) induced…

A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…