相关论文: On Latent Distributions Without Finite Mean in Gen…
Diffusion models have achieved unprecedented performance in generative modeling. The commonly-adopted formulation of the latent code of diffusion models is a sequence of gradually denoised samples, as opposed to the simpler (e.g., Gaussian)…
The use of Cauchy Markov random field priors in statistical inverse problems can potentially lead to posterior distributions which are non-Gaussian, high-dimensional, multimodal and heavy-tailed. In order to use such priors successfully,…
This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…
This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a…
The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…
The tabular form constitutes the standard way of representing data in relational database systems and spreadsheets. But, similarly to other forms, tabular data suffers from class imbalance, a problem that causes serious performance…
In latent Dirichlet allocation (LDA), topics are multinomial distributions over the entire vocabulary. However, the vocabulary usually contains many words that are not relevant in forming the topics. We adopt a variable selection method…
High-dimensional sample correlation matrices are a crucial class of random matrices in multivariate statistical analysis. The central limit theorem (CLT) provides a theoretical foundation for statistical inference. In this paper, assuming…
Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and non-vanishing noise. A generalized least squares estimator is used to estimate the…
The purpose of unconditional text generation is to train a model with real sentences, then generate novel sentences of the same quality and diversity as the training data. However, when different metrics are used for comparing the methods…
We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…
Diffusion models have become a standard approach for generative modeling in continuous domains, yet their application to discrete data remains challenging. We investigate why Gaussian diffusion models with the DDPM solver struggle to sample…
Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their…
The problem of inverse scattering proposed by Angles and Mallat in 2018, concerns training a deep neural network to invert the scattering transform applied to an image. After such a network is trained, it can be used as a generative model…
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
Advances in generative models increase the need for sample quality assessment. To do so, previous methods rely on a pre-trained feature extractor to embed the generated samples and real samples into a common space for comparison. However,…
We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the…
We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant $n$. Under mild assumptions on the non-linearity, we obtain…