In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these ...

Large knowledge bases such as YAGO [SKW07] or DBpedia [BLK+09] can be used to answer queries in various domains. However, as they are automatically harvested from Web sources, they may be incomplete: important facts may be missing because they were not materialized in the original sources, or could not be extracted correctly. To mitigate this problem, approaches such as association rule mining ...

Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to explicitly model such uncertainty through probabilistic constraints over the parameter space. In contrast to hard parameter constraints, our approach is effective als...

1. Abstract This paper proposes a methodology for sampling-based design optimization in the presence of interval variables. Assuming that an accurate surrogate model is available, the proposed method first searches the worst combination of interval variables for constraints when only interval variables are present or for probabilistic constraints when both interval and random variables are pres...

During the last decades, several methodologies have been proposed for the harmonization of a given melody with algorithmic means. Among the most successful are methodologies that incorporate probabilistic mechanisms and statistical learning, since they have the ability to generate harmonies that statistically adhere to the harmonic characteristics of the idiom that the training pieces belong to...

We consider stochastic programming problems with probabilistic constraints in volving integer valued random variables The concept of p e cient points of a prob ability distribution is used to derive various equivalent problem formulations Next we modify the concept of r concave discrete probability distributions and analyse its relevance for problems under consideration These notions are used t...

The problem of clustering with constraints is receiving increasing attention. Many existing algorithms assume the specified constraints are correct and consistent. We take a new approach and model the uncertainty of constraints in a principled manner by treating the constraints as random variables. The effect of specified constraints on a subset of points is propagated to other data points by b...

* Corresponding author ABSTRACT In this work, we propose an integrated framework for probabilistic optimization that can bring both the design objective robustness and the probabilistic constraints into account. The fundamental development of this work is the employment of an inverse reliability strategy that uses percentile performance for assessing both the objective robustness and probabilis...

In this paper we aim at output analysis with respect to changes of the probability distribution for problems with probabilistic (chance) constraints. The perturbations are modeled via contamination of the initial probability distribution. Dependence of the set of solutions on the probability distribution rules out the straightforward construction of the convexity-based global contamination boun...