Related papers: Black Box Probabilistic Numerics
In science and medicine, model interpretations may be reported as discoveries of natural phenomena or used to guide patient treatments. In such high-stakes tasks, false discoveries may lead investigators astray. These applications would…
In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties of optimal solutions. In this work we…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…
In the last years many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The…
Causal inference and the estimation of causal effects plays a central role in decision-making across many areas, including healthcare and economics. Estimating causal effects typically requires an estimator that is tailored to each problem…
Backward Stochastic Differential Equations (BSDEs) have been widely employed in various areas of social and natural sciences, such as the pricing and hedging of financial derivatives, stochastic optimal control problems, optimal stopping…
We present a probabilistic modeling framework and adaptive sampling algorithm wherein unsupervised generative models are combined with black box predictive models to tackle the problem of input design. In input design, one is given one or…
We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences scheme without appealing to the theory of…
Modern deep learning methods constitute incredibly powerful tools to tackle a myriad of challenging problems. However, since deep learning methods operate as black boxes, the uncertainty associated with their predictions is often…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
In theory, the probabilistic linkage method provides two distinct advantages over non-probabilistic methods, including minimal rates of linkage error and accurate measures of these rates for data users. However, implementations can fall…
The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between of two real $n$-vectors. We derive probabilistic perturbation bounds, as well as probabilistic…
We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum…
Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization…