Related papers: Estimating multidimensional probability fields usi…
We derive an adaptive hierarchical method of estimating high dimensional probability density functions. We call this method of density estimation the "adaptive cluster expansion" or ACE for short. We present an application of this approach,…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Photometric redshift estimation is an indispensable tool of precision cosmology. One problem that plagues the use of this tool in the era of large-scale sky surveys is that the bright galaxies that are selected for spectroscopic observation…
We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies…
Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…
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…
This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…
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…
Given a sample $\{X_i\}_{i=1}^n$ from $f_X$, we construct kernel density estimators for $f_Y$, the convolution of $f_X$ with a known error density $f_{\epsilon}$. This problem is known as density estimation with Berkson error and has…
We construct a kernel density estimator on symmetric spaces of non-compact type and establish an upper bound for its convergence rate, analogous to the minimax rate for classical kernel density estimators on Euclidean space. Symmetric…
The machine learning community has recently put effort into quantized or low-precision arithmetics to scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…
Modern surveys have provided the astronomical community with a flood of high-dimensional data, but analyses of these data often occur after their projection to lower-dimensional spaces. In this work, we introduce a local two-sample…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
We present a new subspace-based method to construct probabilistic models for high-dimensional data and highlight its use in anomaly detection. The approach is based on a statistical estimation of probability density using densities of…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
Reliable wall-to-wall biomass density estimation from NASA's GEDI mission requires interpolating sparse LIDAR observations across heterogeneous landscapes. While machine learning approaches like Random Forest and XGBoost are widely used,…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…