387,504 research outputs found
From average case complexity to improper learning complexity
The basic problem in the PAC model of computational learning theory is to
determine which hypothesis classes are efficiently learnable. There is
presently a dearth of results showing hardness of learning problems. Moreover,
the existing lower bounds fall short of the best known algorithms.
The biggest challenge in proving complexity results is to establish hardness
of {\em improper learning} (a.k.a. representation independent learning).The
difficulty in proving lower bounds for improper learning is that the standard
reductions from -hard problems do not seem to apply in this
context. There is essentially only one known approach to proving lower bounds
on improper learning. It was initiated in (Kearns and Valiant 89) and relies on
cryptographic assumptions.
We introduce a new technique for proving hardness of improper learning, based
on reductions from problems that are hard on average. We put forward a (fairly
strong) generalization of Feige's assumption (Feige 02) about the complexity of
refuting random constraint satisfaction problems. Combining this assumption
with our new technique yields far reaching implications. In particular,
1. Learning 's is hard.
2. Agnostically learning halfspaces with a constant approximation ratio is
hard.
3. Learning an intersection of halfspaces is hard.Comment: 34 page
Learning Max-CSPs via Active Constraint Acquisition
Constraint acquisition can assist non-expert users to model their problems as constraint networks. In active constraint acquisition, this is achieved through an interaction between the learner, who posts examples, and the user who classifies them as solutions or not. Although there has been recent progress in active constraint acquisition, the focus has only been on learning satisfaction problems with hard constraints. In this paper, we deal with the problem of learning soft constraints in optimization problems via active constraint acquisition, specifically in the context of the Max-CSP. Towards this, we first introduce a new type of queries in the context of constraint acquisition, namely partial preference queries, and then we present a novel algorithm for learning soft constraints in Max-CSPs, using such queries. We also give some experimental results
Bayesian Network Structure Learning with Permutation Tests
In literature there are several studies on the performance of Bayesian
network structure learning algorithms. The focus of these studies is almost
always the heuristics the learning algorithms are based on, i.e. the
maximisation algorithms (in score-based algorithms) or the techniques for
learning the dependencies of each variable (in constraint-based algorithms). In
this paper we investigate how the use of permutation tests instead of
parametric ones affects the performance of Bayesian network structure learning
from discrete data. Shrinkage tests are also covered to provide a broad
overview of the techniques developed in current literature.Comment: 13 pages, 4 figures. Presented at the Conference 'Statistics for
Complex Problems', Padova, June 15, 201
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