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Data discretization, also known as binning, is a frequently used technique in computer science, statistics, and their applications to biological data analysis. We present a new method for the discretization of real-valued data into a finite…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Time series in real-world applications often have missing observations, making typical analytical methods unsuitable. One method for dealing with missing data is the concept of amplitude modulation. While this principle works with any data,…
With the growing volume of data in society, the need for privacy protection in data analysis also rises. In particular, private selection tasks, wherein the most important information is retrieved under differential privacy are emphasized…
The incorporation of unlabeled data in regression and classification analysis is an increasing focus of the applied statistics and machine learning literatures, with a number of recent examples demonstrating the potential for unlabeled data…
Skewness is a common occurrence in statistical applications. In recent years, various distribution families have been proposed to model skewed data by introducing unequal scales based on the median or mode. However, we argue that the point…
In physics, density $\rho(\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process. Modeling $\rho(\cdot)$ typically scales poorly…
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the…
Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…
Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…
This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S^d. Our methodology and theory are based on harmonic analysis on general S^d. We establish novel nonparametric density…
Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural…
The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…
Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…
Data noising is an effective technique for regularizing neural network models. While noising is widely adopted in application domains such as vision and speech, commonly used noising primitives have not been developed for discrete…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…