Dr Anastasia Papavasiliou (University of Warwick)

Statistical Inference for differential equations driven by rough paths

Differential equations driven by rough paths (RDEs for short) generalize SDEs by allowing the equation to be driven by any type of noise and not just Brownian motion. As such, they are a very flexible modelling tool for randomly evolving dynamical systems. So far, however, they have been ignored by the statistics community, in my opinion for the two followin reasons: (i) the abstract theory of rough paths is still very young and under development, which makes it very hard to penetrate; (ii) there are no statistical tools available. In this talk, I will give an introduction to the theory and I will also discuss how to approach the problem of statistical inference given a discretely observed solution to an RDE.

Evangelos Evangelou (University of Bath)

Spatial sampling design under cost constraints in the presence of sampling errors

A sampling design scheme for spatial models for the prediction of the underlying Gaussian random field will be presented. The optimality criterion is the maximisation of the information about the random field contained in the sample. The model discussed departs from the typical spatial model by assuming measurement error in the observations, varying from location to location, while interest lies in prediction without the error term. In this case multiple samples need to be taken from each sampling location in order to reduce the measurement error. To that end, a hybrid algorithm which combines simulated annealing nested within an exchange algorithm will be presented for obtaining the optimal sampling design. Consideration is made with regards to optimal sampling under budget constraints accounting for initialisation and sampling costs.

Joint work with Zhengyuan Zhu (Iowa State)

Catriona Queen (The Open University)

A graphical dynamic approach to forecasting flows in road traffic networks

Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This talk considers how cubic splines can be used to incorporate information from these extra variables to enhance flow forecasts. The talk also introduces a new type of chain graph model for forecasting traffic flows. The models are applied to the problem of forecasting multivariate road traffic flows at the intersection of three busy motorways near Manchester, UK.

Philip Dawid (University of Cambridge

Theory and Applications of Proper Scoring Rules

We give an overview of the theory of proper scoring rules, and some recent applications.

A proper scoring rule encourages honest assessment of personal probabilities. It can also be used to define general entropy functions, discrepancy functions, M-estimators, etc., and to extend composite likelihood methods.

We have recently characterised those proper local scoring rules that can be computed without requiring the normalising constant of the density. This property is valuable for many purposes, including Bayesian model selection with improper priors.

Andrew Golightly (Newcastle University)

Auxiliary particle MCMC schemes for partially observed Markov jump processes

We consider Bayesian inference for parameters governing Markov jump processes (MJPs) using discretely observed data that may be incomplete and subject to measurement error. We use a recently proposed particle MCMC scheme which jointly updates parameters of interest and the latent process and present a vanilla implementation based on a bootstrap filter before considering improvements based around an auxiliary particle filter. In particular, we focus on a linear noise approximation to the MJP to construct a pre-weighting scheme and couple this with a bridging mechanism. Finally, we embed this approach within a 'delayed acceptance' framework to allow further computational gains. The methods are illustrated with some examples arising in systems biology.

Kevin Korb (Monash)

An Overview of Bayesian Network Research at Monash

Recent research on and around Bayesian net (BN) technology at Monash has featured: fog forecasting (the Bureau of Meteorology); environmental management (Victorian gov); biosecurity (ACERA); finding better discretizations, using cost-based data and Bayesian scoring rules; data mining dynamic Bayesian networks; re-activating MML causal discovery of linear models. I'll discuss these and some other BN activities, briefly describe other research happening at Monash FIT, and the opportunities for collaboration.

Heather Battey (University of Bristol)

Smooth projected density estimation

In this talk I will introduce a new class of estimators for multidimensional density estimation. The estimators are attractive in that they offer both flexibility and the possibility of incorporating structural constraints, whilst possessing a succinct representation that may be stored and evaluated easily. The latter property is of paramount importance when dealing with large datasets, which are now commonplace in many application areas. We show in a simulation study that the approach is universally unintimidated across a range of data generating mechanisms and often outperforms popular nonparametric estimators (including the kernel density estimator), even when structural constraints are not utilised. Moreover, its performance is shown to be somewhat robust to the choice of tuning parameters, which is an important practical advantage of our procedure.

Dr Jon Warren (University of Warwick)

Random matrices, Stochastic Growth models and the KPZ equation.

I will base this talk on two pieces of joint work. One with Peter Windridge, the other with Neil O'Connell. Firstly I will show you how the distribution of a largest eigenvalue of certain random matrix ( in fact having a Wishart distribution) arises also in a simple stochastic growth model. In fact this growth model belongs to a large universality class, which includes mathematical models for interfaces as diverse as the edge of a burning piece of paper, or a colony of bacteria on a petri dish. The KPZ equation is a stochastic partial differential equation that also belongs to this universality class, and in the work with Neil we set out to construct an analogue, for the KPZ equation, for the second, third and so on largest eigenvalues of the random matrix.

Ioanna Manolopoulou (University College London)

Bayesian observation modeling in presence-only data

The prevalence of presence-only samples eg. in ecology or criminology has led to a variety of statistical approaches. Aiming to predict ecological niches, species distribution models provide probability estimates of a binary response (presence/absence) in light of a set of environmental covariates. Similarly, statistical models to predict crime use propensity indicators from observable attributes inferred from incidental data. However, the associated challenges are confounded by non-uniform observation models; even in cases where observation is driven by seemingly irrelevant factors, these may distort estimates about the distribution of occurrences as a function of covariates due to unknown correlations. We present a Bayesian non-parametric approach to addressing sampling bias by carefully incorporating an observation model in a partially identifiable framework with selectively informative priors and linking it to the underlying process. Any available information about the role of various covariates in the observation process can then naturally enter the model. For example, in cases where sampling is driven by presumed likelihood of detecting an occurrence, the observation model becomes a proxy of the presence/absence model. We illustrate our methods on an example from species distribution modeling and a corporate accounting application.

Joint work with Richard Hahn from Chicago Booth.

Tom Palmer (Warwick Medical School)

Topics in instrumental variable estimation: structural mean models and bounds

One aim of epidemiological studies is to investigate the effect of a risk factor on a disease outcome. However, these studies are prone to unmeasured confounding and reverse causation. The use of genotypes as instrumental variables, known as Mendelian randomization studies, are one way to overcome this.

In this talk I describe some methods in instrumental variable estimation; structural mean models and nonparametric bounds for the average causal effect. Specifically, I describe how to estimate structural mean models using multiple instrumental variables in the generalized method of moments framework common in Econometrics. I describe the nonparametric bounds for the average causal effect of Balke and Pearl (JASA, 1997) which can be applied when each of the three variables; instrument, intermediate, and outcome are all binary.

I describe some methodological extensions to these bounds and their limitations.

To demonstrate the models I use a Mendelian randomization example investigating the effect of being overweight on the risk of hypertension in the Copenhagen General Population Study. I will also draw some comparisons with the application of instrumental variables to correct for noncompliance in randomized controlled trials.

Ajay Jasra (National University of Singapore)

On the convergence of Adaptive sequential Monte Carlo Methods

In several implementations of Sequential Monte Carlo (SMC) methods, it is natural and important in terms of algorithmic efficiency, to exploit the information on the history of the particles to optimally tune their subsequent propagations. In the following talk we provide an asymptotic theory for a class of such adaptive SMC methods. Our theoretical framework developed here will cover for instance, under assumptions, the algorithms in Chopin (2002), Jasra et al (2011), Schafer & Chopin (2013). There are limited results about the theoretical underpinning of such adaptive methods: we will bridge this gap by providing a weak law of large numbers (WLLN) and a central limit theorem (CLT) for some of the algorithms. The latter seems to be the first result of its kind in the literature and provides a formal justification of algorithms that are used in many practical scenarios. This is a joint work with Alex Beskos (NUS/UCL).

Piotr Fryzlewicz (London School of Economics)

Wild Binary Segmentation for multiple change-point detection

We propose a new technique, called Wild Binary Segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points, unlike standard Binary Segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to significant increase in computational complexity. WBS is also easy to code. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance. In addition, we provide a new proof of consistency of Binary Segmentation with improved rates of convergence, as well as a corresponding result for WBS.

Nicolai Meinshausen (University of Oxford)

Min-wise hashing for large-scale regression and classification.

We take a look at large-scale regression analysis in a "large p, large n" context for a linear regression or classification model.

In a high-dimensional "large p, small n" setting, we can typically only get good estimation if there exists a sparse regression vector that approximates the observations. No such assumptions are required for large-scale regression analysis where the number of observations n can (but does not have to) exceed the number of variables p. The main difficulty is that computing an OLS or ridge-type estimator is computationally infeasible for n and p in the millions and we need to find computationally efficient ways to approximate these solutions without increasing the prediction error by a large amount. Trying to find interactions amongst millions of variables seems to be an even more daunting task. We study a small variation of the b-bit minwse-hashing scheme (Li and Konig, 2011) for sparse datasets and show that the regression problem can be solved in a much lower-dimensional setting as long as the product of the number of non-zero elements in each observation and the l2-norm of a good approximation vector is small. We get finite-sample bounds on the prediction error. The min-wise hashing scheme is also shown to fit interaction models. Fitting interactions does not require an adjustment to the method used to approximate linear models, it just requires a higher-dimensional mapping.

Professor Donald Martin (North Carolina State University)

Computing probabilities for the discrete scan statistic through slack variables

The discrete scan statistic is used in many areas of applied probability and statistics to study local clumping of patterns.

Testing based on the statistic requires tail probabilities. Whereas the distribution has been studied extensively, most of the results are approximations, due to the difficulties associated with the computation. Results for exact tail probabilities for the statistic have been given for a binary sequence that is independent or first-order Markovian. We give an algorithm to obtain probabilities for the statistic over multi-state trials that are Markovian of a general order of dependence, and explore the algorithm’s usefulness.

François Caron (Oxford)
Bayesian nonparametric models for bipartite graphs

In this talk I will present a novel Bayesian nonparametric model for bipartite graphs, based on the theory of completely random measures. The model is able to handle a potentially infinite number of nodes and has appealing properties; in particular, it may exhibit a power-law behavior for some values of the parameters. I derive a posterior characterization, a generative process for network growth, and a simple Gibbs sampler for posterior simulation. Finally, the model is shown to provide a good fit to several large real-world bipartite social networks.

Davide Pigoli (Warwick)
Statistical methods for phonetic covariance operators in comparative linguistics

Comparative linguistics is concerned with the exploration of languages evolution. The traditional way of exploring relationships across languages consists of examining textual similarity. However, this neglects the phonetic characteristics of the languages. Here a novel approach is proposed to incorporate phonetic information, based on the comparison of frequency covariance structures in spoken languages. In particular, the aim is to explore the relationships among Romance languages and how they have developed from their common Latin root. The covariance operator being the statistical unit, a framework is illustrated for inference concerning the covariance operator of a functional random process. First, the problem of the definition of possible metrics for covariance operators is considered. In particular, an infinite dimensional analogue of the Procrustes reflection size and shape distance is developed. Then, distance-based inferential procedures are proposed for estimation and hypothesis testing. Finally, it is shown that the analysis of pairwise distances between phonetic covariance structures can provide insight into the relationships among Romance languages. Some languages also present features that are not completely expected from linguistics theory, indicatingnew directions for investigations.

Juhyun Park (Lancaster)
Functional average derivative regression
Abstract: Single index model is studied in the framework of regression estimation involving functional data. The model extends a linear model with an unknown link function and has the advantage of having low sensitivity to dimensional effects and flexibility and easiness of interpretation. However its usage in functional regression setting is still found to be limited, partly due to its complexity of fitting the model. In this work we develop a functional adaptation of the average derivative method that allows us to construct an explicit estimator for the functional single index.
Thanks to its explicit form of the estimator, implementation is made relatively simple and straightforward. Theoretical properties of the estimator of the index are studied based on asymptotic results on nonparametric functional derivatives estimation. In particular it is shown that the nonlinear regression component of the model can be estimated at the standard univariate rate, being therefore insensitive to the infinite dimensionality of the data.

Numerical examples are used to illustrate the method and to evaluate finite sample performance.

Ben Francis
Stochastic Control Methods to Individualise Drug Therapy by Incorporating Pharmacokinetic, Pharmacodynamic and Adverse Event Data
There are a number of methods available to aid determination of an individualised dosage regimen for a patient. However, often these methods are non-adaptive to the patient's requirements and do not allow for changing clinical targets throughout the course of therapy.

Research has been undertaken to include process noise in the Pharmacokinetic/Pharmacodynamic (PK/PD) response prediction to better simulate the patient response to the dose by allowing values sampled from the individual PK/PD parameter distributions to vary over time.

Further work explores different formulations of a cost function by considering probabilities from a Markov model.

Using the introduced methodology, the drug dose algorithm is shown to be adaptive to patient needs for imatinib and simvastatin therapy.

However, application of the drug dose algorithm in a wide range of clinical dosing decisions is possible.

Statistical modelling of summary values leads to accurate Approximate Bayesian Computations

Abstract: Approximate Bayesian Computations (ABC) are considered to be noisy. We present a statistical framework for accurate ABC parameter inference that rests on well-established results from indirect inference and decision theory. This framework guarantees that ABC estimates the mode of the true posterior density exactly and that the Kullback-Leibler divergence of the ABC approximation to the true posterior density is minimal, provided that verifiable conditions are met. Our approach requires appropriate statistical modelling of the distribution of "summary values" - data points on a summary level - from which the choice of summary statistics follows implicitly. This places elementary statistical modelling at the heart of ABC analyses, which we illustrate on several examples.

Selection of (ABC) summary statistics towards estimation and model choice

Abstract: The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true model. Those conditions, which amount to the expectations of the summary statistics to asymptotically differ under both models, are then usable in ABC settings to determine which summary statistics are appropriate, via a standard and quick Monte Carlo validation. We also discuss new schemes to automatically select efficient summary statistics from a large collection of those.

(Joint work with J.-M. Marin, N. Pillai, P. Pudlo & J. Rousseau)

John Fox (Oxford & UCL/Royal Free Hospital)
Arguing logically about risks: strengths, limitations and a request for assistance
Abstract: The standard mathematical treatment of risk combines numerical measures of uncertainty (usually probabilistic) and loss (money and other natural estimators of utility). There are significant practical and theoretical problems with this interpretation. A particular concern is that the estimation of quantitative parameters is frequently problematic, particularly when dealing with one-off events such as political, economic or environmental disasters.
Consequently practical decision-making under risk often requires extensions to the standard treatment.
An intuitive approach to reasoning under uncertainty has recently become established in computer science and cognitive science based on argumentation theory. On this approach theories about an application domain (formalised in a non-classical first-order logic) are applied to propositional facts about specific situations, and arguments are constructed for and/or against claims about what might happen in those situations. Arguments can also attack or support other arguments. Collections of arguments can be aggregated to characterize the type or degree of risk, based on the grounds of the arguments. The grounds and form of an argument can also be used to explain the supporting evidence for competing claims and assess their relative credibility. This approach has led to a novel framework for developing versatile risk management systems and has been validated in a number of domains, including clinical medicine and toxicology (e.g. www.infermed.com; www.lhasa.com). Argumentation frameworks are also being used to support open discussion and debates about important issues (e.g. see debate on "planet under pressure" at http://debategraph.org/Stream.aspx?nid=145319&vt=bubble&dc=focus).

Despite the practical success of argumentation methods in risk management and other kinds of decision making the main theories ignore quantitative measurement of uncertainty, or they combine qualitative reasoning with quantitative uncertainty in ad hoc ways. After a brief introduction to argumentation theory I will demonstrate some medical applications and invite suggestions for ways of incorporating uncertainty probabilistically that are mathematically satisfactory.

Chenlei Leng (Warwick)

High dimensional influence measure

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the sample size. Our proposal can be viewed as a high-dimensional counterpart to the classical Cook's distance. However, whereas the Cook's distance quantifies the individual observation's influence on the least squares regression coefficient estimate, our new diagnosis measure captures the influence on the marginal correlations, which in turn exerts serious influence on downstream analysis including coefficient estimation, variable selection and screening. Moreover, we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity. Availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection. Both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure. This is joint work with Junlong Zhao, Lexin Li, and Hansheng Wang.

A copy of the paper is downloadable from http://arxiv.org/abs/1311.6636.

Jean-Michel Marin

Consistency of the Adaptive Multiple Importance Sampling (joint work with Pierre Pudlo and Mohammed Sedki

Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a significant improvement in stability and Effective Sample Size due to the introduction of a recycling procedure. However, the consistency of the AMIS estimator remains largely open. In this work, we prove the convergence of the AMIS, at a cost of a slight modification in the learning process. Numerical experiments exhibit that this modification might even improve the original scheme.

Judith Rousseau

Asymptotic properties of Empirical Bayes procedures – in parametric and non parametric models

In this work we investigate frequentist properties of Empirical Bayes procedures. Empirical Bayes procedures are very much used in practice in more or less formalized ways as it is common practice to replace some hyperparameter in the prior by some data dependent quantity. There are typically two ways of constructing these data dependent quantities : using some king of moment estimator or some quantity whose behaviour is well understood or using a maximum marginal likelihood estimator. In this work we first give some general results on how to determine posterior concentration rates under the former setting, which we apply in particular to two types of Dirichlet process mixtures. We then shall discuss more parametric models in the context of maximum marginal likelihood estimation. We will in particular explain why some pathological behaviour can be expected in this case.

Amanda Turner (Lancaster)

Small particle limits in a regularized Laplacian random growth model
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In 1998 Hastings and Levitov proposed a one-parameter family of models for planar random growth in which clusters are represented as compositions of conformal mappings. This family includes physically occurring processes such as diffusion-limited aggregation (DLA), dielectric breakdown and the Eden model for biological cell growth. In the simplest case of the model (corresponding to the parameter alpha=0), James Norris and I showed how the Brownian web arises in the limit resulting from small particle size and rapid aggregation. In particular this implies that beyond a certain time, all newly aggregating particles share a single common ancestor. I shall show how small changes in alpha result in the emergence of branching structures within the model so that, beyond a certain time, the number of common ancestors is a random number whose distribution can be obtained. This is based on joint work with Fredrik Johansson Viklund (Columbia) and Alan Sola (Cambridge).

Vasileios Maroulas (Bath/Tennessee)

Filtering, drift homotopy and target tracking

Abstract:
Target tracking is a problem of paramount importance arising in Biology, Defense, Ecology and other scientific fields. We attack to this problem by employing particle filtering. Particle filtering is an importance sampling method which may fail in several occasions, e.g. in high dimensional data. In this talk, we present a novel approach for improving particle filters suited to target tracking with a nonlinear observation model. The suggested approach is based on what I
will call drift homotopy for stochastic differential equations which describe the dynamics of the moving target. Based on drift homotopy, we design a Markov Chain Monte Carlo step which is appended to the particle filter and aims to bring the particles closer to the observations while at the same time respecting the dynamics. The talk is based on joint works with Kai Kang and Panos Stinis.

Darren Wilkinson (Newcastle)
Stochastic Modelling of Genetic Interaction in Budding Yeast

Saccharomyces cerevisiae (often known as budding yeast, or brewers yeast) is a single-celled micro-organism that is easy to grow and genetically manipulate. As it has a cellular organisation that has much in common with the cells of humans, it is often used as a model organism for studying genetics. High-throughput robotic genetic technologies can be used to study the fitness of many thousands of genetic mutant strains of yeast, and the resulting data can be used to identify novel genetic interactions relevant to a target area of biology. The processed data consists of tens of thousands of growth curves with a complex hierarchical structure requiring sophisticated statistical modelling of genetic independence, genetic interaction (epistasis), and variation at multiple levels of the hierarchy. Starting from simple stochastic differential equation

(SDE) modelling of individual growth curves, a Bayesian hierarchical model can be built with variable selection indicators for inferring genetic interaction. The methods will be applied to data from experiments designed to highlight genetic interactions relevant to telomere biology.

Richard Everitt (Reading)

Inexact approximations for doubly and triply intractable problems

Markov random field models are used widely in computer science, statistical physics and spatial statistics and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to an intractable likelihood function. Several methods have been developed that permit exact, or close to exact, simulation from the posterior distribution. However, estimating the marginal likelihood and Bayes' factors for these models remains challenging in general. This talk will describe new methods for estimating Bayes' factors that use simulation to circumvent the evaluation of the intractable likelihood, and compare them to approximate Bayesian computation. We will also discuss more generally the idea of "inexact approximations".

Professor Adrian Raftery (Washington)

Bayesian Reconstruction of Past Populations for Developing and Developed Countries

I will describe Bayesian population reconstruction, a new method for estimating past populations by age and sex, with fully probabilistic statements of uncertainty. It simultaneously estimates age-specific
population counts, vital rates and net migration from fragmentary data while formally accounting for measurement error. As inputs, it takes initial bias-corrected estimates of age-specific population counts, vital rates and net migration. The output is a joint posterior probability distribution which yields fully probabilistic interval estimates of past vital rates and population numbers by age and sex. It is designed for the kind of data commonly collected in demographic surveys and censuses and can be applied to countries with widely varying levels of data quality. This is joint work with Mark Wheldon, Patrick Gerland and Samuel Clark.

David Dunson (Duke University)

Robust and scalable Bayes via the median posterior

Bayesian methods have great promise in big data sets, but this promise has not been fully realized due to the lack of scalable computational methods. Usual MCMC and SMC algorithms bog down as the size of the data and number of parameters increase. For massive data sets, it has become routine to rely on penalized optimization approaches implemented on distributed computing systems. The most popular scalable approximation algorithms rely on variational Bayes, which lacks theoretical guarantees and badly under-estimates posterior covariance. Another problem with Bayesian inference is the lack of robustness; data contamination and corruption is particularly common in large data applications and cannot easily be dealt with using traditional methods. We propose to solve both the robustness and the scalability problem using a new alternative to exact Bayesian inference we refer to as the median posterior. Data are divided into subsets and stored on different computers prior to analysis. For each subset, we obtain a stochastic approximation to the full data posterior, and run MCMC to generate samples from this approximation. The median posterior is defined as the geometric median of the subset-specific approximations, and can be rapidly approximated. We show several strong theoretical results for the median posterior, including general theorems on concentration rates and robustness. The methods are illustrated through simple examples, including Gaussian process regression with outliers.

Eric Moulines (Télécom ParisTech)

Proximal Metropolis adjusted Langevin algorithm for sampling sparse distribution over high-dimensional spaces

This talk introduces a new Markov Chain Monte Carlo method to sampling sparse distributions or to perform Bayesian model choices in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines (i) a Metropolis adjusted Langevin step to propose local moves associated with the differentiable part of the target density with (ii) a proximal step based on the non-differentiable part of the target density which provides sparse solutions such that small components are shrunk toward zero. Several implementations of the proximal step will be investigated adapted to different sparsity priors or allowing to perform variable selections, in high-dimensional settings. The performance of these new procedures are illustrated on both simulated and real data sets. Preliminary convergence results will also be presented.

Mark Fiecas (Warwick)
Modeling the Evolution of Neurophysiological Signals

In recent years, research into analyzing brain signals has dramatically increased, and these rich data sets require more advanced statistical tools in order to perform proper statistical analyses. Consider an experiment where a stimulus is presented many times, and after each stimulus presentation (trial), time series data is collected. The time series data per trial exhibit nonstationary characteristics. Moreover, across trials the time series are non-identical because their spectral properties change over the course of the experiment. In this talk, we will look at a novel approach for analyzing nonidentical nonstationary time series data. We consider two sources of nonstationarity: 1) within each trial of the experiment and 2) across the trials, so that the spectral properties of the time series data are evolving over time within a trial, and are also evolving over the course of the experiment. We extend the locally stationary time series model to account for nonidentical data. We analyze a local field potential data set to study how the spectral properties of the local field potentials obtained from the nucleus accumbens and the hippocampus of a monkey evolve over the course of a learning association experiment.

David Leslie (Bristol)
Applied abstract stochastic approximation

Stochastic approximation was introduced as a tool to find the zeroes of a function under only noisy observations of the function value. A classical statistical example is to find the zeroes of the score function when observations can only be processed sequentially. The method has since been developed and used mainly in the control theory, machine learning and economics literature to analyse iterative learning algorithms, but I contend that it is time for statistics to re-discover the power of stochastic approximation. I will introduce the main ideas of the method, and describe an extension; the parameter of interest is an element of a function space, and we wish to analyse its stochastic evolution through time. This extension allows the analysis of online nonparametric algorithms - we present an analysis of Newton's algorithm to estimate nonparametric mixing distributions. It also allows the investigation of learning in games with a continuous strategy set, where a mixed strategy is an arbitrary distribution on an interval.

(Joint work with Steven Perkins)

Rajen Shah (Cambridge)

Random Intersection Trees for finding interactions in large, sparse datasets

Many large-scale datasets are characterised by a large number (possibly tens of thousands or millions) of sparse variables. Examples range from medical insurance data to text analysis. While estimating main effects in regression problems involving such data is now a reasonably well-studied problem, finding interactions between variables remains a serious computational challenge. As brute force searches through all possible interactions are infeasible, most approaches build up interaction sets incrementally, adding variables in a greedy fashion. The drawback is that potentially informative high-order interactions may be overlooked. Here, we propose an alternative approach for classification problems with binary predictor variables, called Random Intersection Trees. It works by starting with a maximal interaction that includes all variables, and then gradually removing variables if they fail to appear in randomly chosen observations of a class of interest. We show that with this method, under some weak assumptions, interactions can be found with high probability, and that the computational complexity of our procedure is much smaller than for a brute force search.