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    Battey HS, 2019,

    On sparsity scales and covariance matrix transformations

    , Biometrika, ISSN: 0006-3444

    We develop a theory of covariance and concentration matrix estimation on any given or es-timated sparsity scale when the matrix dimension is larger than the sample size. Non-standardsparsity scales are justified when such matrices are nuisance parameters, distinct from interest pa-rameters which should always have a direct subject-matter interpretation. The matrix logarithmicand inverse scales are studied as special cases, with the corollary that a constrained optimization-10based approach is unnecessary for estimating a sparse concentration matrix. It is shown throughsimulations that, for large unstructured covariance matrices, there can be appreciable advantagesto estimating a sparse approximation to the log-transformed covariance matrix and convertingthe conclusions back to the scale of interest.

    Battey HS, Cox DR, 2018,

    Large numbers of explanatory variables: a probabilistic assessment

    Battey H, Fan J, Liu H, Lu J, Zhu Zet al., 2018,


    , ANNALS OF STATISTICS, Vol: 46, Pages: 1352-1382, ISSN: 0090-5364
    Avella-Medina M, Battey HS, Fan J, Li Qet al., 2018,

    Robust estimation of high-dimensional covariance and precision matrices

    , Biometrika, Vol: 105, Pages: 271-284, ISSN: 0006-3444
    Battey H, 2017,

    Eigen structure of a new class of covariance and inverse covariance matrices

    , Bernoulli, Vol: 23, Pages: 3166-3177, ISSN: 1350-7265
    Bodenham DA, Adams NM, 2017,

    Continuous monitoring for changepoints in data streams using adaptive estimation

    , STATISTICS AND COMPUTING, Vol: 27, Pages: 1257-1270, ISSN: 0960-3174
    Cox DR, Battey HS, 2017,

    Large numbers of explanatory variables, a semi-descriptive analysis

    , Proceedings of the National Academy of Sciences, Vol: 114, Pages: 8592-8595, ISSN: 0027-8424
    Bennedsen M, Lunde A, Pakkanen MS, 2017,

    Hybrid scheme for Brownian semistationary processes

    , Finance and Stochastics, Vol: 21, Pages: 931-965, ISSN: 1432-1122

    We introduce a simulation scheme for Brownian semistationary processes, whichis based on discretizing the stochastic integral representation of the processin the time domain. We assume that the kernel function of the process isregularly varying at zero. The novel feature of the scheme is to approximatethe kernel function by a power function near zero and by a step functionelsewhere. The resulting approximation of the process is a combination ofWiener integrals of the power function and a Riemann sum, which is why we callthis method a hybrid scheme. Our main theoretical result describes theasymptotics of the mean square error of the hybrid scheme and we observe thatthe scheme leads to a substantial improvement of accuracy compared to theordinary forward Riemann-sum scheme, while having the same computationalcomplexity. We exemplify the use of the hybrid scheme by two numericalexperiments, where we examine the finite-sample properties of an estimator ofthe roughness parameter of a Brownian semistationary process and study MonteCarlo option pricing in the rough Bergomi model of Bayer et al. (2015),respectively.

    Griffié J, Shlomovich L, Williamson DJ, Shannon M, Aaron J, Khuon S, L Burn G, Boelen L, Peters R, Cope AP, Cohen EAK, Rubin-Delanchy P, Owen DMet al., 2017,

    3D Bayesian cluster analysis of super-resolution data reveals LAT recruitment to the T cell synapse.

    , Sci Rep, Vol: 7

    Single-molecule localisation microscopy (SMLM) allows the localisation of fluorophores with a precision of 10-30 nm, revealing the cell's nanoscale architecture at the molecular level. Recently, SMLM has been extended to 3D, providing a unique insight into cellular machinery. Although cluster analysis techniques have been developed for 2D SMLM data sets, few have been applied to 3D. This lack of quantification tools can be explained by the relative novelty of imaging techniques such as interferometric photo-activated localisation microscopy (iPALM). Also, existing methods that could be extended to 3D SMLM are usually subject to user defined analysis parameters, which remains a major drawback. Here, we present a new open source cluster analysis method for 3D SMLM data, free of user definable parameters, relying on a model-based Bayesian approach which takes full account of the individual localisation precisions in all three dimensions. The accuracy and reliability of the method is validated using simulated data sets. This tool is then deployed on novel experimental data as a proof of concept, illustrating the recruitment of LAT to the T-cell immunological synapse in data acquired by iPALM providing ~10 nm isotropic resolution.

    Pakkanen MS, Sottinen T, Yazigi A, 2017,

    On the conditional small ball property of multivariate Lévy-driven moving average processes

    , Stochastic Processes and their Applications, Vol: 127, Pages: 749-782, ISSN: 0304-4149

    © 2016 Elsevier B.V. We study whether a multivariate Lévy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call the conditional small ball property. Our main results establish the conditional small ball property for Lévy-driven moving average processes under natural non-degeneracy conditions on the kernel function of the process and on the driving Lévy process. We discuss in depth how to verify these conditions in practice. As concrete examples, to which our results apply, we consider fractional Lévy processes and multivariate Lévy-driven Ornstein–Uhlenbeck processes.

    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.

    Schon C, Adams N, Evangelou M, 2017,

    Clustering and Monitoring Edge Behaviour in Enterprise Network Traffic

    , 15th IEEE International Conference on Intelligence and Security Informatics - Security and Big Data (ISI), Publisher: IEEE, Pages: 31-36
    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.

    Schneider-Luftman D, Walden AT, 2016,

    Partial Coherence Estimation via Spectral Matrix Shrinkage under Quadratic Loss

    , IEEE TRANSACTIONS ON SIGNAL PROCESSING, Vol: 64, Pages: 5767-5777, ISSN: 1053-587X
    Lukkarinen J, Pakkanen MS, 2016,

    Arbitrage without borrowing or short selling?

    , Mathematics and Financial Economics, Vol: 11, Pages: 263-274, ISSN: 1862-9679

    We show that a trader, who starts with no initial wealth and is not allowedto borrow money or short sell assets, is theoretically able to attain positivewealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be constructed as a process of finite variation that satisfies a seemingly innocuous self-financing condition, formulated using a pathwiseRiemann-Stieltjes integral. Our result exemplifies the potential intricacies offormulating economically meaningful self-financing conditions in continuoustime, when one leaves the conventional arbitrage-free framework.

    Filippi S, Holmes C, 2016,

    A Bayesian nonparametric approach to testing for dependence between random variables

    , Bayesian Analysis, Vol: 12, Pages: 919-938, ISSN: 1931-6690

    Nonparametric and nonlinear measures of statistical dependence between pairsof random variables are important tools in modern data analysis. In particularthe emergence of large data sets can now support the relaxation of linearityassumptions implicit in traditional association scores such as correlation.Here we describe a Bayesian nonparametric procedure that leads to a tractable,explicit and analytic quantification of the relative evidence for dependence vsindependence. Our approach uses Polya tree priors on the space of probabilitymeasures which can then be embedded within a decision theoretic test fordependence. Polya tree priors can accommodate known uncertainty in the form ofthe underlying sampling distribution and provides an explicit posteriorprobability measure of both dependence and independence. Well known advantagesof having an explicit probability measure include: easy comparison of evidenceacross different studies; encoding prior information; quantifying changes independence across different experimental conditions, and; the integration ofresults within formal decision analysis.

    Lee SMS, Young GA, 2016,

    Distribution of likelihood-based p-values under a local alternative hypothesis

    , BIOMETRIKA, Vol: 103, Pages: 641-652, ISSN: 0006-3444
    Bakoben M, Bellotti A, Adams N, 2016,

    Improving clustering performance by incorporating uncertainty

    , PATTERN RECOGNITION LETTERS, Vol: 77, Pages: 28-34, ISSN: 0167-8655
    Bodenham DA, Adams NM, 2016,

    A comparison of efficient approximations for a weighted sum of chi-squared random variables

    , STATISTICS AND COMPUTING, Vol: 26, Pages: 917-928, ISSN: 0960-3174
    Battey H, Feng Q, Smith RJ, 2016,

    Improving confidence set estimation when parameters are weakly identified

    , Statistics and Probability Letters, Vol: 118, Pages: 117-123, ISSN: 0167-7152

    © 2016 Elsevier B.V. We consider inference in weakly identified moment condition models when additional partially identifying moment inequality constraints are available. We detail the limiting distribution of the estimation criterion function and consequently propose a confidence set estimator for the true parameter.

    Flaxman S, Sejdinovic D, Cunningham JP, Filippi Set al., 2016,

    Bayesian Learning of Kernel Embeddings

    , UAI'16

    Kernel methods are one of the mainstays of machine learning, but the problemof kernel learning remains challenging, with only a few heuristics and verylittle theory. This is of particular importance in methods based on estimationof kernel mean embeddings of probability measures. For characteristic kernels,which include most commonly used ones, the kernel mean embedding uniquelydetermines its probability measure, so it can be used to design a powerfulstatistical testing framework, which includes nonparametric two-sample andindependence tests. In practice, however, the performance of these tests can bevery sensitive to the choice of kernel and its lengthscale parameters. Toaddress this central issue, we propose a new probabilistic model for kernelmean embeddings, the Bayesian Kernel Embedding model, combining a Gaussianprocess prior over the Reproducing Kernel Hilbert Space containing the meanembedding with a conjugate likelihood function, thus yielding a closed formposterior over the mean embedding. The posterior mean of our model is closelyrelated to recently proposed shrinkage estimators for kernel mean embeddings,while the posterior uncertainty is a new, interesting feature with variouspossible applications. Critically for the purposes of kernel learning, ourmodel gives a simple, closed form marginal pseudolikelihood of the observeddata given the kernel hyperparameters. This marginal pseudolikelihood caneither be optimized to inform the hyperparameter choice or fully Bayesianinference can be used.

    Pakkanen MS, Réveillac A, 2016,

    Functional limit theorems for generalized variations of the fractional Brownian sheet

    , Bernoulli, Vol: 22, Pages: 1671-1708, ISSN: 1350-7265

    We prove functional central and non-central limit theorems for generalizedvariations of the anisotropic d-parameter fractional Brownian sheet (fBs) forany natural number d. Whether the central or the non-central limit theoremapplies depends on the Hermite rank of the variation functional and on thesmallest component of the Hurst parameter vector of the fBs. The limitingprocess in the former result is another fBs, independent of the original fBs,whereas the limit given by the latter result is an Hermite sheet, which isdriven by the same white noise as the original fBs. As an application, wederive functional limit theorems for power variations of the fBs and discusswhat is a proper way to interpolate them to ensure functional convergence.

    Nieto-Reyes A, Battey H, 2016,

    A Topologically Valid Definition of Depth for Functional Data

    , Statistical Science, Vol: 31, Pages: 61-79, ISSN: 0883-4237
    Bakoben M, Adams N, Bellotti A, 2016,

    Uncertainty aware clustering for behaviour in enterprise networks

    , 16th IEEE International Conference on Data Mining (ICDM), Publisher: IEEE, Pages: 269-272, ISSN: 2375-9232
    Noble J, Adams NM, 2016,

    Correlation-based Streaming Anomaly Detection in Cyber-Security

    , 16th IEEE International Conference on Data Mining (ICDM), Publisher: IEEE, Pages: 311-318, ISSN: 2375-9232
    Plasse J, Adams N, 2016,

    Handling Delayed Labels in Temporally Evolving Data Streams

    , 4th IEEE International Conference on Big Data (Big Data), Publisher: IEEE, Pages: 2416-2424
    Rubin-Delanchy P, Adams NM, Heard NA, 2016,

    Disassortativity of Computer Networks

    , 14th IEEE International Conference on Intelligence and Security Informatics - Cybersecurity and Big Data (IEEE ISI), Publisher: IEEE, Pages: 243-247
    Whitehouse M, Evangelou M, Adams NM, 2016,

    Activity-based temporal anomaly detection in enterprise-cyber security

    , 14th IEEE International Conference on Intelligence and Security Informatics - Cybersecurity and Big Data (IEEE ISI), Publisher: IEEE, Pages: 248-250
    Evangelou M, Adams NM, 2016,

    Predictability of NetFlow data

    , 14th IEEE International Conference on Intelligence and Security Informatics - Cybersecurity and Big Data (IEEE ISI), Publisher: IEEE, Pages: 67-72
    Young GA, 2015,

    Introduction to High-dimensional Statistics

    , INTERNATIONAL STATISTICAL REVIEW, Vol: 83, Pages: 515-516, ISSN: 0306-7734

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