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Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
Evidential reasoning in expert systems has often used ad-hoc uncertainty calculi. Although it is generally accepted that probability theory provides a firm theoretical foundation, researchers have found some problems with its use as a…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
Robust Bayesian inference is the calculation of posterior probability bounds given perturbations in a probabilistic model. This paper focuses on perturbations that can be expressed locally in Bayesian networks through convex sets of…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…
Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…
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 paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…