Related papers: Generalized Bayesian predictive density operators

We present a parametric deterministic formulation of Bayesian inverse problems with input parameter from infinite dimensional, separable Banach spaces. In this formulation, the forward problems are parametric, deterministic elliptic partial…

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…

As commonly understood, the noise spectroscopy problem---characterizing the statistical properties of a noise process affecting a quantum system by measuring its response---is ill-posed. Ad-hoc solutions assume implicit structure which is…

We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter…

Variational Bayes (VB) inference is one of the most important algorithms in machine learning and widely used in engineering and industry. However, VB is known to suffer from the problem of local optima. In this Letter, we generalize VB by…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

We formulate and study, in general terms, the problem of quantum system identification, i.e., the determination (or estimation) of unknown quantum channels through their action on suitably chosen input density operators. We also present a…

Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to…

A Bayesian net (BN) is more than a succinct way to encode a probabilistic distribution; it also corresponds to a function used to answer queries. A BN can therefore be evaluated by the accuracy of the answers it returns. Many algorithms for…

Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…