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Interpretable Machine Learning faces a recurring challenge of explaining the predictions made by opaque classifiers such as ensemble models, kernel methods, or neural networks in terms that are understandable to humans. When the model is…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…

Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

We build on abduction-based explanations for ma-chine learning and develop a method for computing local explanations for neural network models in natural language processing (NLP). Our explanations comprise a subset of the words of the…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of…

Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in…

Decomposition methods have been proposed to approximate solutions to large sequential decision making problems. In contexts where an agent interacts with multiple entities, utility decomposition can be used to separate the global objective…

We propose a new point-based method for approximate planning in Dec-POMDP which outperforms the state-of-the-art approaches in terms of solution quality. It uses a heuristic estimation of the prior probability of beliefs to choose a bounded…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* solves many NP-hard minimum-cost path problems in time polynomial in the branching…

We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…