Related papers: Inferring Loop Invariants using Postconditions
This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
The functional properties of a program are often specified by providing a contract for each of its functions. A contract of a function consists of a pair of formulas, called a precondition and a postcondition, which, respectively, should…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
Algorithms for computing equilibria, optima, and fixed points in nonconvex problems often depend sensitively on practitioner-chosen initial conditions. When uniqueness of a solution is of interest, a common heuristic is to run such…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…
The performance of machine learning models can be impacted by changes in data over time. A promising approach to address this challenge is invariant learning, with a particular focus on a method known as invariant risk minimization (IRM).…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
The main question is: why and how can we ever predict based on a finite sample? The question is not answered by statistical learning theory. Here, I suggest that prediction requires belief in "predictability" of the underlying dependence,…
It is crucial for robots to be aware of the presence of constraints in order to acquire safe policies. However, explicitly specifying all constraints in an environment can be a challenging task. State-of-the-art constraint inference…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
Deep neural networks often produce miscalibrated probability estimates, leading to overconfident predictions. A common approach for calibration is fitting a post-hoc calibration map on unseen validation data that transforms predicted…
Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…
In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…