Related papers: Lower Bounds for Possibly Divergent Probabilistic …
We derive upper bounds on the tail conditional expectation of binomial and Poisson random variables. Those upper bounds are subsequently employed to the problem of obtaining non-asymptotic lower bounds on the probability that the…
Anytime approximation algorithms that compute the probabilities of queries over probabilistic databases can be of great use to statistical learning tasks. Those approaches have been based so far on either (i) sampling or (ii)…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally.…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
Existing complexity bounds for point-based POMDP value iteration algorithms focus either on the curse of dimensionality or the curse of history. We derive a new bound that relies on both and uses the concept of discounted reachability; our…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…
We show that universal positive almost sure termination (UPAST) is decidable for a class of simple randomized programs, i.e., it is decidable whether the expected runtime of such a program is finite for all inputs. Our class contains all…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…
We consider a Branching Random Walk on $\R$ whose step size decreases by a fixed factor, $0<b<1$, with each turn. This process generates a random probability measure on $\R$, that is, the limit of uniform distribution among the $2^n$…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Bounded model checking of pointer programs is a debugging technique for programs that manipulate dynamically allocated pointer structures on the heap. It is based on the following four observations. First, error conditions like dereference…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…