Related papers: Direct Density-Derivative Estimation and Its Appli…

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot…

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…

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. However, SIC requires additional hyper-parameter tunning, and no algorithms for computing higher order derivative…

We study the problem of nonparametric estimation of density functions with a product form on the domain $\triangle=\{( x_1, \ldots, x_d)\in \mathbb{R}^d, 0\leq x_1\leq \dots \leq x_d \leq 1\}$. Such densities appear in the random truncation…

We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…

Synthetic data generation is a promising technique to facilitate the use of sensitive data while mitigating the risk of privacy breaches. However, for synthetic data to be useful in downstream analysis tasks, it needs to be of sufficient…

This paper addresses the problem of approximating an unknown probability distribution with density $f$ -- which can only be evaluated up to an unknown scaling factor -- with the help of a sequential algorithm that produces at each iteration…

Many machine learning solutions are framed as optimization problems which rely on good hyperparameters. Algorithms for tuning these hyperparameters usually assume access to exact solutions to the underlying learning problem, which is…

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…

The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…

The goal of this paper is to provide theorems on convergence rates of posterior distributions that can be applied to obtain good convergence rates in the context of density estimation as well as regression. We show how to choose priors so…

The main contribution of this paper is the formulation of a diffuse approximation method(DAM), for two-dimensional channel flows. The proposed method is based on the vorticity-streamfunction formulation. The DAM which estimates derivates of…

Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…

In this study, we propose a high-performance disparity (depth) estimation method using dual-pixel (DP) images with few parameters. Conventional end-to-end deep-learning methods have many parameters but do not fully exploit disparity…

A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…

How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one…

Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in…