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  • Journal article
    Zhang Q, Filippi S, Gretton A, Sejdinovic Det al., 2017,

    Large-Scale Kernel Methods for Independence Testing

    , Statistics and Computing, Vol: 28, Pages: 113-130, ISSN: 1573-1375

    Representations of probability measures in reproducing kernel Hilbert spacesprovide a flexible framework for fully nonparametric hypothesis tests ofindependence, which can capture any type of departure from independence,including nonlinear associations and multivariate interactions. However, theseapproaches come with an at least quadratic computational cost in the number ofobservations, which can be prohibitive in many applications. Arguably, it isexactly in such large-scale datasets that capturing any type of dependence isof interest, so striking a favourable tradeoff between computational efficiencyand test performance for kernel independence tests would have a direct impacton their applicability in practice. In this contribution, we provide anextensive study of the use of large-scale kernel approximations in the contextof independence testing, contrasting block-based, Nystrom and random Fourierfeature approaches. Through a variety of synthetic data experiments, it isdemonstrated that our novel large scale methods give comparable performancewith existing methods whilst using significantly less computation time andmemory.

  • Conference paper
    Chamberlain BP, Humby C, Deisenroth MP, 2017,

    Probabilistic Inference of Twitter Users' Age Based on What They Follow.

    , Publisher: Springer, Pages: 191-203
  • Conference paper
    Eleftheriadis S, Rudovic O, Deisenroth MP, Pantic Met al., 2016,

    Variational Gaussian Process Auto-Encoder for Ordinal Prediction of Facial Action Units

    , 13th Asian Conference on Computer Vision (ACCV’16), Publisher: Springer, Pages: 154-170, ISSN: 0302-9743

    We address the task of simultaneous feature fusion and modelingof discrete ordinal outputs. We propose a novel Gaussian process(GP) auto-encoder modeling approach. In particular, we introduce GPencoders to project multiple observed features onto a latent space, whileGP decoders are responsible for reconstructing the original features. Inferenceis performed in a novel variational framework, where the recoveredlatent representations are further constrained by the ordinal outputlabels. In this way, we seamlessly integrate the ordinal structure in thelearned manifold, while attaining robust fusion of the input features.We demonstrate the representation abilities of our model on benchmarkdatasets from machine learning and affect analysis. We further evaluatethe model on the tasks of feature fusion and joint ordinal predictionof facial action units. Our experiments demonstrate the benefits of theproposed approach compared to the state of the art.

  • Conference paper
    Joulani P, Gyorgy A, Szepesvari C, 2016,

    A unified modular analysis of online and stochastic optimization: adaptivity, optimism, non-convexity

    , 9th NIPS Workshop on Optimization for Machine Learning

    We present a simple unified analysis of adaptive Mirror Descent (MD) and Follow-the-Regularized-Leader (FTRL) algorithms for online and stochastic optimizationin (possibly infinite-dimensional) Hilbert spaces. The analysis is modular inthe sense that it completely decouples the effect of possible assumptions on theloss functions (such as smoothness, strong convexity, and non-convexity) andon the optimization regularizers (such as strong convexity, non-smooth penaltiesin composite-objective learning, and non-monotone step-size sequences). Wedemonstrate the power of this decoupling by obtaining generalized algorithms andimproved regret bounds for the so-called “adaptive optimistic online learning” set-ting. In addition, we simplify and extend a large body of previous work, includingseveral various AdaGrad formulations, composite-objective and implicit-updatealgorithms. In all cases, the results follow as simple corollaries within few linesof algebra. Finally, the decomposition enables us to obtain preliminary globalguarantees for limited classes of non-convex problems.

  • Conference paper
    Huang R, Lattimore T, Gyorgy A, Szepesvari Cet al., 2016,

    Following the Leader and Fast Rates in Linear Prediction: Curved Constraint Sets and Other Regularities

    , Advances in Neural Information Processing Systems 29 (NIPS 2016), Publisher: Neutral Information Processing Systems Foundation, Inc.

    The follow the leader (FTL) algorithm, perhaps the simplest of all online learningalgorithms, is known to perform well when the loss functions it is used on are positivelycurved. In this paper we ask whether there are other “lucky” settings whenFTL achieves sublinear, “small” regret. In particular, we study the fundamentalproblem of linear prediction over a non-empty convex, compact domain. Amongstother results, we prove that the curvature of the boundary of the domain can act asif the losses were curved: In this case, we prove that as long as the mean of the lossvectors have positive lengths bounded away from zero, FTL enjoys a logarithmicgrowth rate of regret, while, e.g., for polyhedral domains and stochastic data itenjoys finite expected regret. Building on a previously known meta-algorithm, wealso get an algorithm that simultaneously enjoys the worst-case guarantees and thebound available for FTL.

  • Conference paper
    Shaloudegi K, Gyorgy A, Szepesvari C, Xu Wet al., 2016,

    SDP relaxation with randomized rounding for energy disaggregation

    , The Thirtieth Annual Conference on Neural Information Processing Systems (NIPS), Publisher: Neutral Information Processing Systems Foundation, Inc.

    We develop a scalable, computationally efficient method for the task of energydisaggregation for home appliance monitoring. In this problem the goal is toestimate the energy consumption of each appliance over time based on the totalenergy-consumption signal of a household. The current state of the art is to modelthe problem as inference in factorial HMMs, and use quadratic programming tofind an approximate solution to the resulting quadratic integer program. Here wetake a more principled approach, better suited to integer programming problems,and find an approximate optimum by combining convex semidefinite relaxationsrandomized rounding, as well as a scalable ADMM method that exploits the specialstructure of the resulting semidefinite program. Simulation results both in syntheticand real-world datasets demonstrate the superiority of our method.

  • Journal article
    Filippi S, Holmes CC, Nieto-Barajas LE, 2016,

    Scalable Bayesian nonparametric measures for exploring pairwise dependence via Dirichlet Process Mixtures

    , Electronic Journal of Statistics, Vol: 10, Pages: 3338-3354, ISSN: 1935-7524

    In this article we propose novel Bayesian nonparametric methods using Dirichlet Process Mixture (DPM) models for detecting pairwise dependence between random variables while accounting for uncertainty in the form of the underlying distributions. A key criteria is that the procedures should scale to large data sets. In this regard we find that the formal calculation of the Bayes factor for a dependent-vs.-independent DPM joint probability measure is not feasible computationally. To address this we present Bayesian diagnostic measures for characterising evidence against a “null model” of pairwise independence. In simulation studies, as well as for a real data analysis, we show that our approach provides a useful tool for the exploratory nonparametric Bayesian analysis of large multivariate data sets.

  • Conference paper
    Kern T, Gyorgy A, 2016,

    SVRG++ with non-uniform sampling

    , 9th NIPS Workshop on Optimization for Machine Learning, Publisher: Neural Information Processing Systems Foundation, Inc.

    SVRG++ is a recent randomized optimization algorithm designed to solve non-strongly convex smooth composite optimization problems in the large data regime.In this paper we combine SVRG++ with non-uniform sampling of the data points(already present in the original SVRG algorithm), leading to an algorithm with thebest sample complexity to date and state-of-the art empirical performance. Whilethe combination and the analysis of the algorithm is admittedly straightforward,our experimental results show significant improvement over the original SVRG++method with the new method outperforming all competitors on datasets where thesmoothness of the components varies. This demonstrates that, despite its simplicityand limited novelty, this extension is important in practice.

  • Conference paper
    Calandra R, Peters J, Rasmussen CE, Deisenroth MPet al., 2016,

    Manifold Gaussian Processes for Regression

    , International Joint Conference on Neural Networks, Publisher: IEEE, ISSN: 2161-4407

    Off-the-shelf Gaussian Process (GP) covariancefunctions encode smoothness assumptions on the structureof the function to be modeled. To model complex and nondifferentiablefunctions, these smoothness assumptions are oftentoo restrictive. One way to alleviate this limitation is to finda different representation of the data by introducing a featurespace. This feature space is often learned in an unsupervisedway, which might lead to data representations that are notuseful for the overall regression task. In this paper, we proposeManifold Gaussian Processes, a novel supervised method thatjointly learns a transformation of the data into a featurespace and a GP regression from the feature space to observedspace. The Manifold GP is a full GP and allows to learn datarepresentations, which are useful for the overall regressiontask. As a proof-of-concept, we evaluate our approach oncomplex non-smooth functions where standard GPs performpoorly, such as step functions and robotics tasks with contacts.

  • Journal article
    de Montjoye YKJV, Rocher L, Pentland AS, 2016,

    bandicoot: an open-source Python toolbox to analyze mobile phone metadata

    , Journal of Machine Learning Research, Vol: 17, ISSN: 1532-4435

    bandicoot is an open-source Python toolbox to extract more than 1442 features from standard mobile phone metadata. bandicoot makes it easy for machine learning researchers and practitioners to load mobile phone data, to analyze and visualize them, and to extract robust features which can be used for various classification and clustering tasks. Emphasis is put on ease of use, consistency, and documentation. bandicoot has no dependencies and is distributed under MIT license

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