相关论文: Note on the bias and variance of variational infer…

We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior…

Consider the Gaussian sequence model under the additional assumption that a fixed fraction of the means is known. We study the problem of variance estimation from a frequentist Bayesian perspective. The maximum likelihood estimator (MLE)…

Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the table. While classical results show that…

The traditional measurement theory interprets the variance as the dispersion of a measured value, which is actually contrary to a general mathematical concept that the variance of a constant is 0. This paper will fully demonstrate that the…

We give an upper bound on the total variation distance between the linear eigenvalue statistic, properly scaled and centred, of a random matrix with a variance profile and the standard Gaussian random variable. The second order Poincar\'e…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…

Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how…

The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the…

Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…

Variational inference has been widely used in machine learning literature to fit various Bayesian models. In network analysis, this method has been successfully applied to solve the community detection problems. Although these results are…

I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than $L_2$ regularized…

This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…

We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…

The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard…

We highlight the different uses of the word 'likelihood' that have arisen in statistics and meteorology, and make the recommendation that one of these uses should be dropped to prevent confusion and misunderstanding.

High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…

Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…

A regression method for proportional, or fractional, data with mixed effects is outlined, designed for analysis of datasets in which the outcomes have substantial weight at the bounds. In such cases a normal approximation is particularly…

The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…