159 research outputs found
PAC-Bayes and Domain Adaptation
We provide two main contributions in PAC-Bayesian theory for domain
adaptation where the objective is to learn, from a source distribution, a
well-performing majority vote on a different, but related, target distribution.
Firstly, we propose an improvement of the previous approach we proposed in
Germain et al. (2013), which relies on a novel distribution pseudodistance
based on a disagreement averaging, allowing us to derive a new tighter domain
adaptation bound for the target risk. While this bound stands in the spirit of
common domain adaptation works, we derive a second bound (introduced in Germain
et al., 2016) that brings a new perspective on domain adaptation by deriving an
upper bound on the target risk where the distributions' divergence-expressed as
a ratio-controls the trade-off between a source error measure and the target
voters' disagreement. We discuss and compare both results, from which we obtain
PAC-Bayesian generalization bounds. Furthermore, from the PAC-Bayesian
specialization to linear classifiers, we infer two learning algorithms, and we
evaluate them on real data.Comment: Neurocomputing, Elsevier, 2019. arXiv admin note: substantial text
overlap with arXiv:1503.0694
A New PAC-Bayesian Perspective on Domain Adaptation
We study the issue of PAC-Bayesian domain adaptation: We want to learn, from
a source domain, a majority vote model dedicated to a target one. Our
theoretical contribution brings a new perspective by deriving an upper-bound on
the target risk where the distributions' divergence---expressed as a
ratio---controls the trade-off between a source error measure and the target
voters' disagreement. Our bound suggests that one has to focus on regions where
the source data is informative.From this result, we derive a PAC-Bayesian
generalization bound, and specialize it to linear classifiers. Then, we infer a
learning algorithmand perform experiments on real data.Comment: Published at ICML 201
PAC-Bayesian Learning and Domain Adaptation
In machine learning, Domain Adaptation (DA) arises when the distribution gen-
erating the test (target) data differs from the one generating the learning
(source) data. It is well known that DA is an hard task even under strong
assumptions, among which the covariate-shift where the source and target
distributions diverge only in their marginals, i.e. they have the same labeling
function. Another popular approach is to consider an hypothesis class that
moves closer the two distributions while implying a low-error for both tasks.
This is a VC-dim approach that restricts the complexity of an hypothesis class
in order to get good generalization. Instead, we propose a PAC-Bayesian
approach that seeks for suitable weights to be given to each hypothesis in
order to build a majority vote. We prove a new DA bound in the PAC-Bayesian
context. This leads us to design the first DA-PAC-Bayesian algorithm based on
the minimization of the proposed bound. Doing so, we seek for a \rho-weighted
majority vote that takes into account a trade-off between three quantities. The
first two quantities being, as usual in the PAC-Bayesian approach, (a) the
complexity of the majority vote (measured by a Kullback-Leibler divergence) and
(b) its empirical risk (measured by the \rho-average errors on the source
sample). The third quantity is (c) the capacity of the majority vote to
distinguish some structural difference between the source and target samples.Comment: https://sites.google.com/site/multitradeoffs2012
PAC-Bayesian Analysis of Martingales and Multiarmed Bandits
We present two alternative ways to apply PAC-Bayesian analysis to sequences
of dependent random variables. The first is based on a new lemma that enables
to bound expectations of convex functions of certain dependent random variables
by expectations of the same functions of independent Bernoulli random
variables. This lemma provides an alternative tool to Hoeffding-Azuma
inequality to bound concentration of martingale values. Our second approach is
based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis.
We also introduce a way to apply PAC-Bayesian analysis in situation of limited
feedback. We combine the new tools to derive PAC-Bayesian generalization and
regret bounds for the multiarmed bandit problem. Although our regret bound is
not yet as tight as state-of-the-art regret bounds based on other
well-established techniques, our results significantly expand the range of
potential applications of PAC-Bayesian analysis and introduce a new analysis
tool to reinforcement learning and many other fields, where martingales and
limited feedback are encountered
- …