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The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
In order to improve forecasts, a decisionmaker often combines probabilities given by various sources, such as human experts and machine learning classifiers. When few training data are available, aggregation can be improved by incorporating…
Consider the problem of estimating a random variable $X$ from noisy observations $Y = X+ Z$, where $Z$ is standard normal, under the $L^1$ fidelity criterion. It is well known that the optimal Bayesian estimator in this setting is the…
Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
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…
A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics.
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
The quantum many-electron problem is not just at the heart of condensed matter phenomena, but also essential for first-principles simulation of chemical phenomena. Strong correlation in chemical systems are prevalent and present a…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in…
Nowadays, g-mode detection is based upon a priori theoretical knowledge. By doing so, detection becomes more restricted to what we can imagine. De facto, the universe of possibilities is made narrower. Such an approach is pertinent for…
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…
Quantification, or prevalence estimation, is the task of predicting the prevalence of each class within an unknown bag of examples. Most existing quantification methods in the literature rely on prior probability shift assumptions to create…
A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…