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Finding robust solutions of an optimization problem is an important issue in practice, and various concepts on how to define the robustness of a solution have been suggested. The idea of recoverable robustness requires that a solution can…

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…

Multi-objective evaluation is a necessary aspect when managing complex systems, as the intrinsic complexity of a system is generally closely linked to the potential number of optimization objectives. However, an evaluation makes no sense…

Robustness verification that aims to formally certify the prediction behavior of neural networks has become an important tool for understanding model behavior and obtaining safety guarantees. However, previous methods can usually only…

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…

When training automated systems, it has been shown to be beneficial to adapt the representation of data by learning a problem-specific metric. This metric is global. We extend this idea and, for the widely used family of k nearest neighbors…

The robustness of properties of a statistical physics model to slight perturbations in the exact local interactions of the model is a very relevant philosophical question, considering real-life measurements on which we base some models can…

While the traditional formulation of machine learning tasks is in terms of performance on average, in practice we are often interested in how well a trained model performs on rare or difficult data points at test time. To achieve more…

Making classifiers robust to adversarial examples is hard. Thus, many defenses tackle the seemingly easier task of detecting perturbed inputs. We show a barrier towards this goal. We prove a general hardness reduction between detection and…

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

This paper proposes minimum distance inference for a structural parameter of interest, which is robust to the lack of identification of other structural nuisance parameters. Some choices of the weighting matrix lead to asymptotic…

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to…

We investigate how ideas from covariance localization in numerical weather prediction can be used in Markov chain Monte Carlo (MCMC) sampling of high-dimensional posterior distributions arising in Bayesian inverse problems. To localize an…

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges…

We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency…

Since its inception the Metropolis-Hastings kernel has been applied in sophisticated ways to address ever more challenging and diverse sampling problems. Its success stems from the flexibility brought by the fact that its verification and…

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…