2,639 research outputs found

    PAC-Bayes and Domain Adaptation

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    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

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    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

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    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

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    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

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    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

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    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

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    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

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    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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