Related papers: Discrete Component Analysis

Independent component analysis is intended to recover the mutually independent components from their linear mixtures. This technique has been widely used in many fields, such as data analysis, signal processing, and machine learning. To…

A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact…

In this paper, we propose an alternative method to the disjoint principal component analysis. The method consists of a principal component analysis with constraints, which allows us to determine disjoint components that are linear…

We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible…

The purpose of this paper is to develop a mathematical analysis theory to solve differential privacy problems. The heart of our approaches is to use analytic tools to characterize the correlations among the outputs of different datasets,…

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…

In signal processing, the data collected from sensing devices is often a noisy linear superposition of multiple components, and the estimation of components of interest constitutes a crucial pre-processing step. In this work, we develop a…

Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

This paper considers the private release of statistics of disjoint subsets of a dataset, in the setting of data heterogeneity, where users could contribute more than one sample, with different users contributing potentially different…

These notes are dedicated to whom may be interested in algorithms, Markov chain, coupling, and graph theory etc. I present some preliminaries on coupling and explanations of the important formulas or phrases, which may be helpful for us to…

Distributed multi-party learning provides an effective approach for training a joint model with scattered data under legal and practical constraints. However, due to the quagmire of a skewed distribution of data labels across participants…

We consider the problem of jointly estimating a collection of graphical models for discrete data, corresponding to several categories that share some common structure. An example for such a setting is voting records of legislators on…

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…

Posterior computation in hierarchical Dirichlet process (HDP) mixture models is an active area of research in nonparametric Bayes inference of grouped data. Existing literature almost exclusively focuses on the Chinese restaurant franchise…

Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…

We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these…

The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space…

We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…