Related papers: Relative Entropy Gradient Sampler for Unnormalized…
Our universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work we develop Translation and Rotation Equivariant Normalizing Flow (TRENF), a generative Normalizing Flow (NF) model which…
Variational inference is a technique that approximates a target distribution by optimizing within the parameter space of variational families. On the other hand, Wasserstein gradient flows describe optimization within the space of…
The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods…
The vertex-random graphs called proximity catch digraphs (PCDs) have been introduced recently and have applications in pattern recognition and spatial pattern analysis. A PCD is a random directed graph (i.e., digraph) which is constructed…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to…
A random balanced sample (RBS) is a multivariate distribution with n components X_1,...,X_n, each uniformly distributed on [-1, 1], such that the sum of these components is precisely 0. The corresponding vectors X lie in an…
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…
Sampling from constrained distributions has a wide range of applications, including in Bayesian optimization and robotics. Prior work establishes convergence and feasibility guarantees for constrained sampling, but assumes that the feasible…
Random splitting of datasets in image segmentation often leads to unrepresentative test sets, resulting in biased evaluations and poor model generalization. While stratified sampling has proven effective for addressing label distribution…
Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a…
We show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs…
Various machine learning tasks, from generative modeling to domain adaptation, revolve around the concept of dataset transformation and manipulation. While various methods exist for transforming unlabeled datasets, principled methods to do…
In this paper, we developed a novel method of nonparametric relative entropy (RlEn) for modelling loss of complexity in intermittent time series. The method consists of two steps. We first fit a nonlinear autoregressive model to each…
We present the Liouville Flow Importance Sampler (LFIS), an innovative flow-based model for generating samples from unnormalized density functions. LFIS learns a time-dependent velocity field that deterministically transports samples from a…
The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence of big data and machine learning methodology. Discovering governing equations and quantifying dynamical properties of…
We introduce a (de)-regularization of the Maximum Mean Discrepancy (DrMMD) and its Wasserstein gradient flow. Existing gradient flows that transport samples from source distribution to target distribution with only target samples, either…
Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…