相关论文: Maximum likelihood degree of the two-dimensional l…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based…
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…
An open problem in graphical Gaussian models is to determine the smallest number of observations needed to guarantee the existence of the maximum likelihood estimator of the covariance matrix with probability one. In this paper we formalize…
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data,…
Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article, we describe the special locus of data for which the…
The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling…
Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…
The field of extreme value statistics is concerned with modeling and predicting rare events. In a H\"usler-Reiss graphical model, a graph represents extremal conditional independence (CI) relations between random variables. These models are…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bi-directed graph into a maximal ancestral graph that (i)…
The asymptotic results pertaining to the distribution of the log likelihood ratio allow for the creation of a confidence region, which is a general extension of the confidence interval. Two and three dimensional regions can be displayed…
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
We prove that the maximum degree $\Delta_n$ of a random series-parallel graph with $n$ vertices satisfies $\Delta_n/\log n \to c$ in probability, and $\mathbb{E}\, \Delta_n \sim c \log n$ for a computable constant $c>0$. The same result…