Related papers: Sound Value Iteration
Despite the possibility to quickly compute reachable sets of large-scale linear systems, current methods are not yet widely applied by practitioners. The main reason for this is probably that current approaches are not push-button-capable…
When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…
We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval Valued Probability Measure (IVPM), we present IVPM's interval expected values whose…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…
We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…
Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…
We address the reachability problem for continuous-time stochastic dynamic systems. Our objective is to present a unified framework that characterizes the reachable set of a dynamic system in the presence of both stochastic disturbances and…
The reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying…
We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…
Partially observable Markov decision processes (POMDPs) form an attractive and principled framework for agent planning under uncertainty. Point-based approximate techniques for POMDPs compute a policy based on a finite set of points…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to…
This paper addresses the issue of estimating the expectation of a real-valued random variable of the form $X = g(\mathbf{U})$ where $g$ is a deterministic function and $\mathbf{U}$ can be a random finite- or infinite-dimensional vector.…
Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…
Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on…
Statistical model checking (SMC) is a technique for analysis of probabilistic systems that may be (partially) unknown. We present an SMC algorithm for (unbounded) reachability yielding probably approximately correct (PAC) guarantees on the…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
Simple stochastic games can be solved by value iteration (VI), which yields a sequence of under-approximations of the value of the game. This sequence is guaranteed to converge to the value only in the limit. Since no stopping criterion is…