Related papers: Fast multivariate empirical cumulative distributio…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
Dust properties, such as mass and porosity, impact planet formation directly. Understanding the time evolution of dust distribution across multiple properties requires numerical computation. However, available ways to calculate the…
Despite their success, kernel methods suffer from a massive computational cost in practice. In this paper, in lieu of commonly used kernel expansion with respect to $N$ inputs, we develop a novel optimal design maximizing the entropy among…
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk…
This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
We present an algorithm that computes the multipole coefficients of the galaxy three-point correlation function (3PCF) without explicitly considering triplets of galaxies. Rather, centering on each galaxy in the survey, it expands the…
We address one of the important problems in Big Data, namely how to combine estimators from different subsamples by robust fusion procedures, when we are unable to deal with the whole sample. We propose a general framework based on the…
We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…
Density Estimation Trees (DETs) are decision trees trained on a multivariate dataset to estimate its probability density function. While not competitive with kernel techniques in terms of accuracy, they are incredibly fast, embarrassingly…
In distributed learning, the goal is to perform a learning task over data distributed across multiple nodes with minimal (expensive) communication. Prior work (Daume III et al., 2012) proposes a general model that bounds the communication…
The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two…
Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…
In this paper, we address the challenge of performing counterfactual inference with observational data via Bayesian nonparametric regression adjustment, with a focus on high-dimensional settings featuring multiple actions and multiple…
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so…
Estimating the distribution of outcomes under counterfactual policies is critical for decision-making in domains such as recommendation, advertising, and healthcare. We propose and analyze a novel framework-Counterfactual Policy Mean…
To generate data from trained diffusion models, most inference algorithms, such as DDPM, DDIM, and other variants, rely on discretizing the reverse SDEs or their equivalent ODEs. In this paper, we view such approaches as decomposing the…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
Estimating causal quantities (CQs) typically requires large datasets, which can be expensive to obtain, especially when measuring individual outcomes is costly. This challenge highlights the importance of sample-efficient active learning…
Crowd counting is a fundamental problem in crowd analysis which is typically accomplished by estimating a crowd density map and summing over the density values. However, this approach suffers from background noise accumulation and loss of…