Related papers: A Weakest Pre-Expectation Semantics for Mixed-Sign…
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…
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…
Time-to-event forecasts are essential when decisions depend on event timing. This article develops a framework for evaluating such forecasts when the event has not yet occurred or is not predicted within the forecast horizon. We introduce a…
We describe an extension of Earley's parser for stochastic context-free grammars that computes the following quantities given a stochastic context-free grammar and an input string: a) probabilities of successive prefixes being generated by…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
Probabilistic Hoare logic (PHL) is an extension of Hoare logic and is specifically useful in verifying randomized programs. It allows researchers to formally reason about the behavior of programs with stochastic elements, ensuring the…
We consider a multi-step algorithm for the computation of the historical expected shortfall such as defined by the Basel Minimum Capital Requirements for Market Risk. At each step of the algorithm, we use Monte Carlo simulations to reduce…
We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a…
We present a probabilistic modeling and inference framework for discriminative analysis dictionary learning under a weak supervision setting. Dictionary learning approaches have been widely used for tasks such as low-level signal denoising…
A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it,…
This paper presents a non-interleaving denotational semantics for the ?-calculus. The basic idea is to define a notion of test where the outcome is not only whether a given process passes a given test, but also in how many different ways it…
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of…
In this paper, we propose a novel Mixed-Integer Non-Linear Optimization formulation to construct a risk score, where we optimize the logistic loss with sparsity constraints. Previous approaches are typically designed to handle binary…
Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to…
Three versions of the Weak Law of Large Numbers are proposed for weakly dependent and generally speaking non-equally distributed random variables, with finite or possibly infinite expectations.
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
We present an exact approach to analyze and quantify the sensitivity of higher moments of probabilistic loops with symbolic parameters, polynomial arithmetic and potentially uncountable state spaces. Our approach integrates methods from…
In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose denominator is the inner product of a corresponding pair of…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…