14,767 research outputs found
Confidence-based Reasoning in Stochastic Constraint Programming
In this work we introduce a novel approach, based on sampling, for finding
assignments that are likely to be solutions to stochastic constraint
satisfaction problems and constraint optimisation problems. Our approach
reduces the size of the original problem being analysed; by solving this
reduced problem, with a given confidence probability, we obtain assignments
that satisfy the chance constraints in the original model within prescribed
error tolerance thresholds. To achieve this, we blend concepts from stochastic
constraint programming and statistics. We discuss both exact and approximate
variants of our method. The framework we introduce can be immediately employed
in concert with existing approaches for solving stochastic constraint programs.
A thorough computational study on a number of stochastic combinatorial
optimisation problems demonstrates the effectiveness of our approach.Comment: 53 pages, working draf
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
Distribution matching for transduction
Many transductive inference algorithms assume that distributions over training and test estimates should be related, e.g. by providing a large margin of separation on both sets. We use this idea to design a transduction algorithm which can be used without modification for classification, regression, and structured estimation. At its heart we exploit the fact that for a good learner the distributions over the outputs on training and test sets should match. This is a classical two-sample problem which can be solved efficiently in its most general form by using distance measures in Hilbert Space. It turns out that a number of existing heuristics can be viewed as special cases of our approach.
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