Related papers: Chance constrained sets approximation: A probabili…
Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian…
This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…
Computing optimal control policies for complex dynamical systems requires approximation methods to remain computationally tractable. Several approximation methods have been developed to tackle this problem. However, these methods do not…
Scenario decision making offers a flexible way of making decision in an uncertain environment while obtaining probabilistic guarantees on the risk of failure of the decision. The idea of this approach is to draw samples of the uncertainty…
In recent years, advanced model-based and data-driven control methods are unlocking the potential of complex robotics systems, and we can expect this trend to continue at an exponential rate in the near future. However, ensuring safety with…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…
We study the scenario approach for solving chance-constrained optimization in time-coupled dynamic environments. Scenario generation methods approximate the true feasible region from scenarios generated independently and identically from…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…
We study quasi-convex optimization problems, where only a subset of the constraints can be sampled, and yet one would like a probabilistic guarantee on the obtained solution with respect to the initial (unknown) optimization problem. Even…
Almost every software system provides configuration options to tailor the system to the target platform and application scenario. Often, this configurability renders the analysis of every individual system configuration infeasible. To…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…
A specific family of point processes are introduced that allow to select samples for the purpose of estimating the mean or the integral of a function of a real variable. These processes, called quasi-systematic processes, depend on a tuning…