相关论文: Integration by parts and representation of informa…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
In Data Science, entities are typically represented by single valued measurements. Symbolic Data Analysis extends this framework to more complex structures, such as intervals and histograms, that express internal variability. We propose an…
We provide a novel characterization of semiparametric efficiency in a generic supervised learning setting where the outcome mean function -- defined as the conditional expectation of the outcome of interest given the other observed…
In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…
A generalized information formula related to logical probability and fuzzy set is deduced from the classical information formula. The new information measure accords with to Popper's criterion for knowledge evolution very much. In…
Based on the canonical correlation analysis we derive series representations of the probability density function (PDF) and the cumulative distribution function (CDF) of the information density of arbitrary Gaussian random vectors as well as…
Information functionals allow to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the…
Suppose we have individual data from an internal study and various summary statistics from relevant external studies. External summary statistics have the potential to improve statistical inference for the internal population; however, it…
We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric.…
New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…
Using a representation of the score function by means of the divergence operator we exhibit a sufficient condition, in terms of the negative moments of the norm of the Malliavin derivative, under which convergence in Fisher information to…
With the development of biomedical science, researchers have increasing access to an abundance of studies focusing on similar research questions. There is a growing interest in the integration of summary information from those studies to…
This paper will focus on the process of 'fusing' several observations or models of uncertainty into a single resultant model. Many existing approaches to fusion use subjective quantities such as 'strengths of belief' and process these…
In the partially-observed outcome setting, a recent set of proposals known as "prediction-powered inference" (PPI) involve (i) applying a pre-trained machine learning model to predict the response, and then (ii) using these predictions to…
We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincare inequalities, to provide a better understanding of the…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
We introduce a notion of integration defined from filters over families of finite sets. This procedure corresponds to determining the average value of functions whose range lies in any algebraic structure in which finite averages make…
New asymptotic approximations of the non-central $t$ distribution are given, a generalization of the Student's $t$ distribution. Using new integral representations, we give new asymptotic expansions for large values of the noncentrality…