Related papers: Comments on the estimate for Pareto Distribution
We characterize conditions under which collections of distributions on $\{0,1\}^\mathbb{N}$ admit uniform estimation of their mean. Prior work from Vapnik and Chervonenkis (1971) has focused on uniform convergence using the empirical mean…
This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a…
Density ratio estimation (DRE) is a fundamental machine learning technique for comparing two probability distributions. However, existing methods struggle in high-dimensional settings, as it is difficult to accurately compare probability…
This paper explores Maximum Likelihood in parametric models in the context of Sanov type Large Deviation Probabilities. MLE in parametric models under weighted sampling is shown to be associated with the minimization of a specific…
The estimation of cumulative distribution functions (CDF) and probability density functions (PDF) is a fundamental practice in applied statistics. However, challenges often arise when dealing with data arranged in grouped intervals. In this…
The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new…
Positive--unlabeled (PU) learning considers two samples, a positive set P with observations from only one class and an unlabeled set U with observations from two classes. The goal is to classify observations in U. Class mixture proportion…
The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and…
Weather forecasting is usually solved through numerical weather prediction (NWP), which can sometimes lead to unsatisfactory performance due to inappropriate setting of the initial states. In this paper, we design a data-driven method…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
In this paper, we propose a probabilistic representation of MultiLayer Perceptrons (MLPs) to improve the information-theoretic interpretability. Above all, we demonstrate that the activations being i.i.d. is not valid for all the hidden…
A selection of the latest and most frequently used parton distribution functions (PDFs) is incorporated in Pythia8, including the Monte Carlo-adapted PDFs from the MSTW and CTEQ collaborations. This article examines the differences in PDFs…
In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a theoretical argument explaining the experimental…
We present marginal cumulative distribution functions (CDF) for density matrices $\rho$ of fixed purity $\tfrac{1}{N}\le\mu_N(\rho)=\textrm{Tr}[\rho^2]\le 1$ for arbitrary dimension $N$. We give closed form analytic formulas for the cases…
We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework…
When aggregating preferences of agents via voting, two desirable goals are to incentivize agents to participate in the voting process and then identify outcomes that are Pareto efficient. We consider participation as formalized by Brandl,…
A preference order or ranking aggregated from pairwise comparison data is commonly understood as a strict total order. However, in real-world scenarios, some items are intrinsically ambiguous in comparisons, which may very well be an…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…
Modularity is one of the most widely used measures for evaluating communities in networks. In probabilistic networks, where the existence of edges is uncertain and uncertainty is represented by probabilities, the expected value of…