Related papers: Comments on the estimate for Pareto Distribution
An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue…
We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…
The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution that best explain the observed data. In the context of text generation, MLE is often used to train generative language…
Transmutation is a technique for extending classical probability distributions in order to give them more flexibility. In this paper, we are interested in cubic transmutations of the Pareto distribution. We establish a general formula that…
Product models of low dimensional experts are a powerful way to avoid the curse of dimensionality. We present the ``under-complete product of experts' (UPoE), where each expert models a one dimensional projection of the data. The UPoE is…
We study integer-valued multiplicative dynamics driven by i.i.d. prime multipliers and connect their macroscopic statistics to universal codelengths. We introduce the Multiplicative Turing Ensemble (MTE) and show how it arises naturally -…
We consider estimating the Shannon entropy of a discrete distribution $P$ from $n$ i.i.d. samples. Recently, Jiao, Venkat, Han, and Weissman, and Wu and Yang constructed approximation theoretic estimators that achieve the minimax $L_2$…
We discover a theoretical connection between explanation estimation and distribution compression that significantly improves the approximation of feature attributions, importance, and effects. While the exact computation of various machine…
This paper is a sequel of the 2019 paper [5]. It demonstrates the following: a) the Poisson multi-Bernoulli mixture (PMBM) approach to detected vs. undetected (U/D) targets cannot be rigorously formulated using either the two-step or…
In mixtures-of-experts (ME) model, where a number of submodels (experts) are combined, there have been two longstanding problems: (i) how many experts should be chosen, given the size of the training data? (ii) given the total number of…
We review various methods used to estimate uncertainties in quantum correlation functions, such as parton distribution functions (PDFs). Using a toy model of a PDF, we compare the uncertainty estimates yielded by the traditional Hessian and…
In this paper, we study the probability density function, $\mathbb{P}(c,\alpha,\beta, n)\,dc$, of the center of mass of the finite $n$ Jacobi unitary ensembles with parameters $\alpha\,>-1$ and $\beta >-1$; that is the probability that…
According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires…
Under the condition of Karush-Kuhn-Tucker, the Pareto Set (PS) in the decision area of an m-objective optimization problem is a piecewise continuous (m-1)-D manifold. For illustrate the degree of convergence of the population, we employed…
We present recent results of the NNPDF collaboration on a full DIS analysis of Parton Distribution Functions (PDFs). Our method is based on the idea of combining a Monte Carlo sampling of the probability measure in the space of PDFs with…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
When working with decomposition-based algorithms, an appropriate set of weights might improve quality of the final solution. A set of uniformly distributed weights usually leads to well-distributed solutions on a Pareto front. However,…
Suppose we are given observations, where each observation is drawn independently from one of $k$ known distributions. The goal is to match each observation to the distribution from which it was drawn. We observe that the maximum likelihood…
Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…