相关论文: Unification of field theory and maximum entropy me…

We study the continuity property of the generalized entropy as a function of the underlying probability distribution, defined with an action space and a loss function, and use this property to answer the basic questions in statistical…

Bayesian inference is applied directly to the problem of unfolding. The outcome is a posterior probability density for the spectrum before smearing, defined in the multi-dimensional space of all possible spectra. Regularization consists in…

This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…

We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…

This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies…

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…

A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…

Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…

As machine learning becomes more prominent there is a growing demand to perform several inference tasks in parallel. Running a dedicated model for each task is computationally expensive and therefore there is a great interest in multi-task…

In this paper, we aim to design and analyze distributed Bayesian estimation algorithms for sensor networks. The challenges we address are to (i) derive a distributed provably-correct algorithm in the functional space of probability…

I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…

This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…

It is shown that a consistent application of Bayesian updating from a prior probability density to a posterior using evidence in the form of expectation constraints leads to exactly the same results as the application of the maximum entropy…

It is shown that if the Euclidean path integral measure of a minimally coupled free quantum scalar field on a classical metric background is interpreted as probability of observing the field configuration given the background metric then…

Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…