Related papers: Density Estimation using Entropy Maximization for …
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
We are concerned in clustering continuous data sets subject to non-ignorable missingness. We perform clustering with a specific semi-parametric mixture, under the assumption of conditional independence given the component. The mixture model…
Compression of documents, images, audios and videos have been traditionally practiced to increase the efficiency of data storage and transfer. However, in order to process or carry out any analytical computations, decompression has become…
Analysis of a probabilistic system often requires to learn the joint probability distribution of its random variables. The computation of the exact distribution is usually an exhaustive precise analysis on all executions of the system. To…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
Motivated by learning dynamical structures from static snapshot data, this paper presents a distribution-on-scalar regression approach for estimating the density evolution of a stochastic process from its noisy temporal point clouds. We…
The method of maximum entropy is quite a powerful tool to solve the generalized moment problem, which consists of determining the probability density of a random variable X from the knowledge of the expected values of a few functions of the…
In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood…
Entropy estimation plays a crucial role in various fields, such as information theory, statistical data science, and machine learning. However, traditional entropy estimation methods often struggle with complex data distributions.…
In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…
The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…