Related papers: Mixture Proportion Estimation via Kernel Embedding…
The determination of chemical mixture components is vital to a multitude of scientific fields. Oftentimes spectroscopic methods are employed to decipher the composition of these mixtures. However, the sheer density of spectral features…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Families of mixtures of multivariate power exponential (MPE) distributions have been previously introduced and shown to be competitive for cluster analysis in comparison to other elliptical mixtures including mixtures of Gaussian…
In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…
Density ratio estimation (DRE) is a paramount task in machine learning, for its broad applications across multiple domains, such as covariate shift adaptation, causal inference, independence tests and beyond. Parametric methods for…
The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…
Estimating parameters of mixture model has wide applications ranging from classification problems to estimating of complex distributions. Most of the current literature on estimating the parameters of the mixture densities are based on…
Machine learning for molecular property prediction has focused largely on pure compounds, even though many practical applications depend on mixtures with intermolecular interactions. Recent work has expanded the availability of mixture…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
In mixtures-of-experts (ME) model, where a number of submodels (experts) are combined, there have been two longstanding problems: (i) how many experts should be chosen, given the size of the training data? (ii) given the total number of…
We consider a discriminative learning (regression) problem, whereby the regression function is a convex combination of k linear classifiers. Existing approaches are based on the EM algorithm, or similar techniques, without provable…
Understanding model's sensitivity to its training data is crucial but can also be challenging and costly, especially during training. To simplify such issues, we present the Memory-Perturbation Equation (MPE) which relates model's…
An exact, closed form, and easy to compute expression for the mean integrated squared error (MISE) of a kernel estimator of a normal mixture cumulative distribution function is derived for the class of arbitrary order Gaussian-based…
The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
Maximum likelihood estimation of mixture proportions has a long history, and continues to play an important role in modern statistics, including in development of nonparametric empirical Bayes methods. Maximum likelihood of mixture…