Imperial College London

ProfessorMarkGirolami

Faculty of Natural SciencesDepartment of Mathematics

Chair in Statistics
 
 
 
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Contact

 

m.girolami Website

 
 
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Location

 

539Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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23 results found

Ellam L, Girolami M, Pavliotis GA, Wilson Aet al., 2018, Stochastic modelling of urban structure, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 474, ISSN: 1364-5021

JOURNAL ARTICLE

Ellam L, Strathmann H, Girolami M, Murray Iet al., 2017, A determinant-free method to simulate the parameters of large Gaussian fields, Stat, Vol: 6, Pages: 271-281, ISSN: 2049-1573

JOURNAL ARTICLE

Chkrebtii OA, Campbell DA, Calderhead B, Girolami MAet al., 2016, Bayesian Solution Uncertainty Quantification for Differential Equations, BAYESIAN ANALYSIS, Vol: 11, Pages: 1239-1267, ISSN: 1931-6690

JOURNAL ARTICLE

Chkrebtii OA, Campbell DA, Calderhead B, Girolami MAet al., 2016, o Rejoinder, BAYESIAN ANALYSIS, Vol: 11, Pages: 1295-1299, ISSN: 1931-6690

JOURNAL ARTICLE

Epstein M, Calderhead B, Girolami MA, Sivilotti LGet al., 2016, Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction, BIOPHYSICAL JOURNAL, Vol: 111, Pages: 333-348, ISSN: 0006-3495

JOURNAL ARTICLE

Girolami MA, 2014, Big Bayes Stories: A Collection of Vignettes, STATISTICAL SCIENCE, Vol: 29, Pages: 97-97, ISSN: 0883-4237

JOURNAL ARTICLE

Jiwaji M, Sandison ME, Reboud J, Stevenson R, Daly R, Barkess G, Faulds K, Kolch W, Graham D, Girolami MA, Cooper JM, Pitt ARet al., 2014, Quantification of Functionalised Gold Nanoparticle-Targeted Knockdown of Gene Expression in HeLa Cells, PLOS ONE, Vol: 9, ISSN: 1932-6203

JOURNAL ARTICLE

Stathopoulos V, Girolami MA, 2013, Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 371, ISSN: 1364-503X

JOURNAL ARTICLE

Jiwaji M, Daly R, Gibriel A, Barkess G, McLean P, Yang J, Pansare K, Cumming S, McLauchlan A, Kamola PJ, Bhutta MS, West AG, West KL, Kolch W, Girolami MA, Pitt ARet al., 2012, Unique Reporter-Based Sensor Platforms to Monitor Signalling in Cells, PLOS ONE, Vol: 7, ISSN: 1932-6203

JOURNAL ARTICLE

Good DM, Zuerbig P, Argiles A, Bauer HW, Behrens G, Coon JJ, Dakna M, Decramer S, Delles C, Dominiczak AF, Ehrich JHH, Eitner F, Fliser D, Frommberger M, Ganser A, Girolami MA, Golovko I, Gwinner W, Haubitz M, Herget-Rosenthal S, Jankowski J, Jahn H, Jerums G, Julian BA, Kellmann M, Kliem V, Kolch W, Krolewski AS, Luppi M, Massy Z, Melter M, Neusuess C, Novak J, Peter K, Rossing K, Rupprecht H, Schanstra JP, Schiffer E, Stolzenburg J-U, Tarnow L, Theodorescu D, Thongboonkerd V, Vanholder R, Weissinger EM, Mischak H, Schmitt-Kopplin Pet al., 2010, Naturally Occurring Human Urinary Peptides for Use in Diagnosis of Chronic Kidney Disease, MOLECULAR & CELLULAR PROTEOMICS, Vol: 9, Pages: 2424-2437, ISSN: 1535-9476

JOURNAL ARTICLE

Hopcroft LEM, McBride MW, Harris KJ, Sampson AK, McClure JD, Graham D, Young G, Holyoake TL, Girolami MA, Dominiczak AFet al., 2010, Predictive response-relevant clustering of expression data provides insights into disease processes, NUCLEIC ACIDS RESEARCH, Vol: 38, Pages: 6831-6840, ISSN: 0305-1048

JOURNAL ARTICLE

Psorakis I, Damoulas T, Girolami MA, 2010, Multiclass Relevance Vector Machines: Sparsity and Accuracy, IEEE TRANSACTIONS ON NEURAL NETWORKS, Vol: 21, Pages: 1588-1598, ISSN: 1045-9227

JOURNAL ARTICLE

Damoulas T, Girolami MA, 2008, Probabilistic multi-class multi-kernel learning: on protein fold recognition and remote homology detection, BIOINFORMATICS, Vol: 24, Pages: 1264-1270, ISSN: 1367-4803

JOURNAL ARTICLE

Overton IM, Padovani G, Girolami MA, Barton GJet al., 2008, ParCrys: a Parzen window density estimation approach to protein crystallization propensity prediction, BIOINFORMATICS, Vol: 24, Pages: 901-907, ISSN: 1367-4803

JOURNAL ARTICLE

Vyshemirsky V, Girolami MA, 2008, Bayesian ranking of biochemical system models, BIOINFORMATICS, Vol: 24, Pages: 833-839, ISSN: 1367-4803

JOURNAL ARTICLE

Fliser D, Novak J, Thongboonkerd V, Argiles A, Jankowski V, Girolami MA, Jankowski J, Mischak Het al., 2007, Advances in urinary proteome analysis and biomarker discovery, JOURNAL OF THE AMERICAN SOCIETY OF NEPHROLOGY, Vol: 18, Pages: 1057-1071, ISSN: 1046-6673

JOURNAL ARTICLE

Szymkowiak-Have A, Girolami MA, Larsen J, 2006, Clustering via kernel decomposition., IEEE Trans Neural Netw, Vol: 17, Pages: 256-264, ISSN: 1045-9227

Spectral clustering methods were proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this letter, the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership. Hyperparameters are selected using standard cross-validation methods.

JOURNAL ARTICLE

Barp A, Briol F-X, Kennedy AD, Girolami Met al., Geometry and Dynamics for Markov Chain Monte Carlo

Markov Chain Monte Carlo methods have revolutionised mathematical computationand enabled statistical inference within many previously intractable models. Inthis context, Hamiltonian dynamics have been proposed as an efficient way ofbuilding chains which can explore probability densities efficiently. The methodemerges from physics and geometry and these links have been extensively studiedby a series of authors through the last thirty years. However, there iscurrently a gap between the intuitions and knowledge of users of themethodology and our deep understanding of these theoretical foundations. Theaim of this review is to provide a comprehensive introduction to the geometrictools used in Hamiltonian Monte Carlo at a level accessible to statisticians,machine learners and other users of the methodology with only a basicunderstanding of Monte Carlo methods. This will be complemented with somediscussion of the most recent advances in the field which we believe willbecome increasingly relevant to applied scientists.

JOURNAL ARTICLE

Briol F-X, Oates CJ, Cockayne J, Chen WY, Girolami Met al., On the Sampling Problem for Kernel Quadrature, Pages: 586-595

The standard Kernel Quadrature method for numerical integration with randompoint sets (also called Bayesian Monte Carlo) is known to converge in root meansquare error at a rate determined by the ratio $s/d$, where $s$ and $d$ encodethe smoothness and dimension of the integrand. However, an empiricalinvestigation reveals that the rate constant $C$ is highly sensitive to thedistribution of the random points. In contrast to standard Monte Carlointegration, for which optimal importance sampling is well-understood, thesampling distribution that minimises $C$ for Kernel Quadrature does not admit aclosed form. This paper argues that the practical choice of samplingdistribution is an important open problem. One solution is considered; a novelautomatic approach based on adaptive tempering and sequential Monte Carlo.Empirical results demonstrate a dramatic reduction in integration error of upto 4 orders of magnitude can be achieved with the proposed method.

CONFERENCE PAPER

Briol F-X, Oates CJ, Girolami M, Osborne MAet al., Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees

There is renewed interest in formulating integration as an inference problem,motivated by obtaining a full distribution over numerical error that can bepropagated through subsequent computation. Current methods, such as BayesianQuadrature, demonstrate impressive empirical performance but lack theoreticalanalysis. An important challenge is to reconcile these probabilisticintegrators with rigorous convergence guarantees. In this paper, we present thefirst probabilistic integrator that admits such theoretical treatment, calledFrank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence to the truevalue of the integral is shown to be exponential and posterior contractionrates are proven to be superexponential. In simulations, FWBQ is competitivewith state-of-the-art methods and out-performs alternatives based onFrank-Wolfe optimisation. Our approach is applied to successfully quantifynumerical error in the solution to a challenging model choice problem incellular biology.

CONFERENCE PAPER

Briol F-X, Oates CJ, Girolami M, Osborne MA, Sejdinovic Det al., Probabilistic Integration: A Role in Statistical Computation?

A research frontier has emerged in scientific computation, wherein numericalerror is regarded as a source of epistemic uncertainty that can be modelled.This raises several statistical challenges, including the design of statisticalmethods that enable the coherent propagation of probabilities through a(possibly deterministic) computational work-flow. This paper examines the casefor probabilistic numerical methods in routine statistical computation. Ourfocus is on numerical integration, where a probabilistic integrator is equippedwith a full distribution over its output that reflects the presence of anunknown numerical error. Our main technical contribution is to establish, forthe first time, rates of posterior contraction for these methods. These showthat probabilistic integrators can in principle enjoy the "best of bothworlds", leveraging the sampling efficiency of Monte Carlo methods whilstproviding a principled route to assess the impact of numerical error onscientific conclusions. Several substantial applications are provided forillustration and critical evaluation, including examples from statisticalmodelling, computer graphics and a computer model for an oil reservoir.

JOURNAL ARTICLE

Oates CJ, Cockayne J, Briol F-X, Girolami Met al., Convergence Rates for a Class of Estimators Based on Stein's Method

Gradient information on the sampling distribution can be used to reduce thevariance of Monte Carlo estimators via Stein's method. An important applicationis that of estimating an expectation of a test function along the sample pathof a Markov chain, where gradient information enables convergence rateimprovement at the cost of a linear system which must be solved. Thecontribution of this paper is to establish theoretical bounds on convergencerates for a class of estimators based on Stein's method. Our analysis accountsfor (i) the degree of smoothness of the sampling distribution and testfunction, (ii) the dimension of the state space, and (iii) the case ofnon-independent samples arising from a Markov chain. These results provideinsight into the rapid convergence of gradient-based estimators observed forlow-dimensional problems, as well as clarifying a curse-of-dimension thatappears inherent to such methods.

JOURNAL ARTICLE

Oates CJ, Niederer S, Lee A, Briol F-X, Girolami Met al., Probabilistic Models for Integration Error in the Assessment of Functional Cardiac Models

This paper studies the numerical computation of integrals, representingestimates or predictions, over the output $f(x)$ of a computational model withrespect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to themodel. For the functional cardiac models that motivate this work, neither $f$nor $p$ possess a closed-form expression and evaluation of either requires$\approx$ 100 CPU hours, precluding standard numerical integration methods. Ourproposal is to treat integration as an estimation problem, with a joint modelfor both the a priori unknown function $f$ and the a priori unknowndistribution $p$. The result is a posterior distribution over the integral thatexplicitly accounts for dual sources of numerical approximation error due to aseverely limited computational budget. This construction is applied to account,in a statistically principled manner, for the impact of numerical errors that(at present) are confounding factors in functional cardiac model assessment.

CONFERENCE PAPER

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