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We study upper and lower bounds on the sample-complexity of learning near-optimal behaviour in finite-state discounted Markov Decision Processes (MDPs). For the upper bound we make the assumption that each action leads to at most two…
Monte Carlo algorithms, such as Markov chain Monte Carlo (MCMC) and Hamiltonian Monte Carlo (HMC), are routinely used for Bayesian inference in generalized linear models; however, these algorithms are prohibitively slow in massive data…
Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
Deep neural network(DNN) based classifiers do extremely well in discriminating between observations, resulting in higher ROC AUC and accuracy metrics, but their outputs are often miscalibrated with respect to true event likelihoods.…
The algorithm for Monte Carlo simulation of parton-level events based on an Artificial Neural Network (ANN) proposed in arXiv:1810.11509 is used to perform a simulation of $H\to 4\ell$ decay. Improvements in the training algorithm have been…
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…
A novel procedure is described for accelerating the convergence of Markov chain Monte Carlo computations. The algorithm uses an adaptive bootstrap technique to generate candidate steps in the Markov Chain. It is efficient for symmetric,…
In recent years, deep neural networks (DNNs) have shown competitive results in many fields. Despite this success, they often suffer from poor calibration, especially in safety-critical scenarios such as autonomous driving and healthcare,…
Optimal Power Flow (OPF) is a fundamental problem in power systems. It is computationally challenging and a recent line of research has proposed the use of Deep Neural Networks (DNNs) to find OPF approximations at vastly reduced runtimes…
We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach…
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…
As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst…
Bayesian neural networks (BNNs) provide a formalism to quantify and calibrate uncertainty in deep learning. Current inference approaches for BNNs often resort to few-sample estimation for scalability, which can harm predictive performance,…
We propose Differentiable Satisfiability and Differentiable Answer Set Programming (Differentiable SAT/ASP) for multi-model optimization. Models (answer sets or satisfying truth assignments) are sampled using a novel SAT/ASP solving…
Calibrating deep learning models to yield uncertainty-aware predictions is crucial as deep neural networks get increasingly deployed in safety-critical applications. While existing post-hoc calibration methods achieve impressive results on…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
Methods based on Deep Learning have recently been applied on astrophysical parameter recovery thanks to their ability to capture information from complex data. One of these methods is the approximate Bayesian Neural Networks (BNNs) which…
Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing…