Related papers: Guaranteed Bounds for Posterior Inference in Unive…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Probabilistic programs are a powerful and convenient approach to formalise distributions over system executions. A classical verification problem for probabilistic programs is temporal inference: to compute the likelihood that the execution…
In many real-world problems, there is a limited set of training data, but an abundance of unlabeled data. We propose a new method, Generative Posterior Networks (GPNs), that uses unlabeled data to estimate epistemic uncertainty in…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
We introduce a framework for robust uncertainty quantification in situations where labeled training data are corrupted, through noisy or missing labels. We build on conformal prediction, a statistical tool for generating prediction sets…
We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…
In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…
We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…