Related papers: Synthesizing Probabilistic Invariants via Doob's D…
The main goal of the paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate a decomposition procedure for the…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
In this paper we study the path-regularity and martingale properties of the set-valued stochastic integrals defined in our previous work Ararat et al. (2023). Such integrals have some fundamental differences from the well-known…
Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…
In Bayesian probabilistic programming, a central problem is to estimate the normalised posterior distribution (NPD) of a probabilistic program with conditioning via score (a.k.a. observe) statements. Most previous approaches address this…
One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected…
We present a novel algorithm that synthesizes imperative programs for introductory programming courses. Given a set of input-output examples and a partial program, our algorithm generates a complete program that is consistent with every…
This paper presents a new method for automatically generating numerical invariants for imperative programs. Given a program, our procedure computes a binary input/output relation on program states which over-approximates the behaviour of…
Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…
This article provides an introductory tutorial on structural results in partially observed Markov decision processes (POMDPs). Typically, computing the optimal policy of a POMDP is computationally intractable. We use lattice program- ming…
A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…
In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous…
Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an…
In this article, we develop a semigroup-theoretic framework for the analytic characterisation of martingales with path-dependent terminal conditions. Our main result establishes that a measurable adapted process of the form \[ V(t) -…
Probabilistic inference is fundamentally hard, yet many tasks require optimization on top of inference, which is even harder. We present a new optimization-via-compilation strategy to scalably solve a certain class of such problems. In…
We formulate and solve the martingale problem in a nonlinear expectation space. Unlike the classical work of Stroock and Varadhan (1969) where the linear operator in the associated PDE is naturally defined from the corresponding diffusion…
In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: 1. qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii)…
In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…
Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a…
Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…