Related papers: Deterministic Sampling of Multivariate Densities b…
We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…
Recent methods in quantile regression have adopted a classification perspective to handle challenges posed by heteroscedastic, multimodal, or skewed data by quantizing outputs into fixed bins. Although these regression-as-classification…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
In this work we study the topic of high-resolution adaptive sampling of a given deterministic signal and establish a connection with classic approaches to high-rate quantization. Specifically, we formulate solutions for the task of optimal…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
In this paper, we present a generic methodology for the efficient numerical approximation of the density function of the McKean-Vlasov SDEs. The weak error analysis for the projected process motivates us to combine the iterative Multilevel…
Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
Probability metrics have become an indispensable part of modern statistics and machine learning, and they play a quintessential role in various applications, including statistical hypothesis testing and generative modeling. However, in a…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
This work studies distributed (probability) density estimation of large-scale systems. Such problems are motivated by many density-based distributed control tasks in which the real-time density of the swarm is used as feedback information,…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon. Using this result, we obtain the closed-form probability…
We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response…