Related papers: An Operator Theoretic Approach to Nonparametric Mi…
Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors…
In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional…
Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
We present a framework for generating multiple imputations for continuous data when the missing data mechanism is unknown. Imputations are generated from more than one imputation model in order to incorporate uncertainty regarding the…
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…
Unsupervised mixture learning (UML) aims at identifying linearly or nonlinearly mixed latent components in a blind manner. UML is known to be challenging: Even learning linear mixtures requires highly nontrivial analytical tools, e.g.,…
The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many…
The infinite-dimensional information operator for the nuisance parameter plays a key role in semiparametric inference, as it is closely related to the regular estimability of the target parameter. Calculation of information operators has…
We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate…
Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
Abundance estimates from animal point-count surveys require accurate estimates of detection probabilities. The standard model for estimating detection from removal-sampled point-count surveys assumes that organisms at a survey site are…
A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…
We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
In this work we consider the task of relaxing the i.i.d assumption in pattern recognition (or classification), aiming to make existing learning algorithms applicable to a wider range of tasks. Pattern recognition is guessing a discrete…