2,639 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
Patterns of Scalable Bayesian Inference
Datasets are growing not just in size but in complexity, creating a demand
for rich models and quantification of uncertainty. Bayesian methods are an
excellent fit for this demand, but scaling Bayesian inference is a challenge.
In response to this challenge, there has been considerable recent work based on
varying assumptions about model structure, underlying computational resources,
and the importance of asymptotic correctness. As a result, there is a zoo of
ideas with few clear overarching principles.
In this paper, we seek to identify unifying principles, patterns, and
intuitions for scaling Bayesian inference. We review existing work on utilizing
modern computing resources with both MCMC and variational approximation
techniques. From this taxonomy of ideas, we characterize the general principles
that have proven successful for designing scalable inference procedures and
comment on the path forward
A review of domain adaptation without target labels
Domain adaptation has become a prominent problem setting in machine learning
and related fields. This review asks the question: how can a classifier learn
from a source domain and generalize to a target domain? We present a
categorization of approaches, divided into, what we refer to as, sample-based,
feature-based and inference-based methods. Sample-based methods focus on
weighting individual observations during training based on their importance to
the target domain. Feature-based methods revolve around on mapping, projecting
and representing features such that a source classifier performs well on the
target domain and inference-based methods incorporate adaptation into the
parameter estimation procedure, for instance through constraints on the
optimization procedure. Additionally, we review a number of conditions that
allow for formulating bounds on the cross-domain generalization error. Our
categorization highlights recurring ideas and raises questions important to
further research.Comment: 20 pages, 5 figure
Domain adaptation of weighted majority votes via perturbed variation-based self-labeling
In machine learning, the domain adaptation problem arrives when the test
(target) and the train (source) data are generated from different
distributions. A key applied issue is thus the design of algorithms able to
generalize on a new distribution, for which we have no label information. We
focus on learning classification models defined as a weighted majority vote
over a set of real-val ued functions. In this context, Germain et al. (2013)
have shown that a measure of disagreement between these functions is crucial to
control. The core of this measure is a theoretical bound--the C-bound (Lacasse
et al., 2007)--which involves the disagreement and leads to a well performing
majority vote learning algorithm in usual non-adaptative supervised setting:
MinCq. In this work, we propose a framework to extend MinCq to a domain
adaptation scenario. This procedure takes advantage of the recent perturbed
variation divergence between distributions proposed by Harel and Mannor (2012).
Justified by a theoretical bound on the target risk of the vote, we provide to
MinCq a target sample labeled thanks to a perturbed variation-based
self-labeling focused on the regions where the source and target marginals
appear similar. We also study the influence of our self-labeling, from which we
deduce an original process for tuning the hyperparameters. Finally, our
framework called PV-MinCq shows very promising results on a rotation and
translation synthetic problem
Gamma Processes, Stick-Breaking, and Variational Inference
While most Bayesian nonparametric models in machine learning have focused on
the Dirichlet process, the beta process, or their variants, the gamma process
has recently emerged as a useful nonparametric prior in its own right. Current
inference schemes for models involving the gamma process are restricted to
MCMC-based methods, which limits their scalability. In this paper, we present a
variational inference framework for models involving gamma process priors. Our
approach is based on a novel stick-breaking constructive definition of the
gamma process. We prove correctness of this stick-breaking process by using the
characterization of the gamma process as a completely random measure (CRM), and
we explicitly derive the rate measure of our construction using Poisson process
machinery. We also derive error bounds on the truncation of the infinite
process required for variational inference, similar to the truncation analyses
for other nonparametric models based on the Dirichlet and beta processes. Our
representation is then used to derive a variational inference algorithm for a
particular Bayesian nonparametric latent structure formulation known as the
infinite Gamma-Poisson model, where the latent variables are drawn from a gamma
process prior with Poisson likelihoods. Finally, we present results for our
algorithms on nonnegative matrix factorization tasks on document corpora, and
show that we compare favorably to both sampling-based techniques and
variational approaches based on beta-Bernoulli priors
An Exact Characterization of the Generalization Error for the Gibbs Algorithm
Various approaches have been developed to upper bound the generalization error of a supervised learning algorithm. However, existing bounds are often loose and lack of guarantees. As a result, they may fail to characterize the exact generalization ability of a learning algorithm.Our main contribution is an exact characterization of the expected generalization error of the well-known Gibbs algorithm (a.k.a. Gibbs posterior) using symmetrized KL information between the input training samples and the output hypothesis. Our result can be applied to tighten existing expected generalization error and PAC-Bayesian bounds. Our approach is versatile, as it also characterizes the generalization error of the Gibbs algorithm with data-dependent regularizer and that of the Gibbs algorithm in the asymptotic regime, where it converges to the empirical risk minimization algorithm. Of particular relevance, our results highlight the role the symmetrized KL information plays in controlling the generalization error of the Gibbs algorithm
Topic Models Conditioned on Arbitrary Features with Dirichlet-multinomial Regression
Although fully generative models have been successfully used to model the
contents of text documents, they are often awkward to apply to combinations of
text data and document metadata. In this paper we propose a
Dirichlet-multinomial regression (DMR) topic model that includes a log-linear
prior on document-topic distributions that is a function of observed features
of the document, such as author, publication venue, references, and dates. We
show that by selecting appropriate features, DMR topic models can meet or
exceed the performance of several previously published topic models designed
for specific data.Comment: Appears in Proceedings of the Twenty-Fourth Conference on Uncertainty
in Artificial Intelligence (UAI2008
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