Related papers: Nonparametric Density Estimation for High-Dimensio…
Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis,…
Deep learning models frequently make incorrect predictions with high confidence when presented with test examples that are not well represented in their training dataset. We propose a novel and straightforward approach to estimate…
We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
Anomaly and similarity detection in multidimensional series have a long history and have found practical usage in many different fields such as medicine, networks, and finance. Anomaly detection is of great appeal for many different…
We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
Clustering aims to divide a set of points into groups. The current paradigm assumes that the grouping is well-defined (unique) given the probability model from which the data is drawn. Yet, recent experiments have uncovered several…
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.…
Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…
In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
We study non-parametric estimation of an unknown density with support in R (respectively R+). The proposed estimation procedure is based on the projection on finite dimensional subspaces spanned by the Hermite (respectively the Laguerre)…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…
There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the…
High-throughput data analyses are becoming common in biology, communications, economics and sociology. The vast amounts of data are usually represented in the form of matrices and can be considered as knowledge networks. Spectra-based…