Related papers: Estimating Distributions with Low-dimensional Stru…
The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Variational Autoencoder (VAE) and its variations are classic generative models by learning a low-dimensional latent representation to satisfy some prior distribution (e.g., Gaussian distribution). Their advantages over GAN are that they can…
We propose a novel approach to learning the generative neural fields represented by linear combinations of implicit basis networks. Our algorithm learns basis networks in the form of implicit neural representations and their coefficients in…
What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous…
The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…
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…
Machine learning enables unbinned, highly-differential cross section measurements. A recent idea uses generative models to morph a starting simulation into the unfolded data. We show how to extend two morphing techniques, Schr\"odinger…
Popular generative model learning methods such as Generative Adversarial Networks (GANs), and Variational Autoencoders (VAE) enforce the latent representation to follow simple distributions such as isotropic Gaussian. In this paper, we…
Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimension of data can be much lower than the ambient dimension. We argue that this discrepancy may contribute to the…
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
How do score-based generative models (SBMs) learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…
In recent years, numerous graph generative models (GGMs) have been proposed. However, evaluating these models remains a considerable challenge, primarily due to the difficulty in extracting meaningful graph features that accurately…
Mapping data from and/or onto a known family of distributions has become an important topic in machine learning and data analysis. Deep generative models (e.g., generative adversarial networks ) have been used effectively to match known and…
Correcting measured detector-level distributions to particle-level is essential to make data usable outside the experimental collaborations. The term unfolding is used to describe this procedure. A new method of unfolding data using a…