Related papers: Estimating Joint Probability Distribution With Low…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
Word sense disambiguation (WSD) improves many Natural Language Processing (NLP) applications such as Information Retrieval, Machine Translation or Lexical Simplification. WSD is the ability of determining a word sense among different ones…
Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however,…
Performing likelihood ratio based detection with high dimensional multimodal data is a challenging problem since the computation of the joint probability density functions (pdfs) in the presence of inter-modal dependence is difficult. While…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Based on the manifold hypothesis, real-world data often lie on a low-dimensional manifold, while normalizing flows as a likelihood-based generative model are incapable of finding this manifold due to their structural constraints. So, one…
Through viewing out the literature, many generated distributions took a new special form of probability density function (PDF) in which it is written as a linear combination of n other distributions. Therefore, we define in this paper a new…
Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further…
We present a new predictor combination algorithm that improves a given task predictor based on potentially relevant reference predictors. Existing approaches are limited in that, to discover the underlying task dependence, they either…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
We introduce Probabilistic FastText, a new model for word embeddings that can capture multiple word senses, sub-word structure, and uncertainty information. In particular, we represent each word with a Gaussian mixture density, where the…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
We propose a new geometric method for measuring the quality of representations obtained from deep learning. Our approach, called Random Polytope Descriptor, provides an efficient description of data points based on the construction of…
In many supervised learning applications, the response consists of both continuous and binary outcomes. Studies have shown that jointly modeling such mixed-type responses can substantially improve predictive performance compared to separate…
Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (pdf) and/or by the…
In this paper we study a probabilistic framework for Radon partitions, where our points are chosen independently from the $d$-dimensional normal distribution. For every point set we define a corresponding Radon polytope, which encodes all…
We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…
In Divide & Recombine (D&R), big data are divided into subsets, each analytic method is applied to subsets, and the outputs are recombined. This enables deep analysis and practical computational performance. An innovate D\&R procedure is…