## Operational Research and Statistics Seminars 2013-2014

### Programme

All seminars will commence at 12:10pm in room M/2.06, The Mathematics Building, Cardiff University, Senghennydd Road (unless otherwise stated).

Please contact Dr Iskander Aliev for more details regarding Operational Research/WIMCS lectures and Dr Jonathan Gillard for more details regarding Statistics lectures.

##### 9 October 2013

**Speaker: **Dr Mark Kelbert (Swansea University).

**Title:** Earthquake forecasting: Statistics and Information.

**Abstract:** We present an axiomatic approach to the earthquake forecasting in terms of multi-component random fields on the lattice. This approach provides a method for constructing point estimates and confidence intervals for conditional probabilities of strong earthquakes under conditions on the levels of precursors. Also, it provides an approach for setting multilevel alarm system and hypothesis testing for binary alarms. We propose a method of comparison for different earthquake forecasts in terms of the increase of Shannon information. 'Forecasting' and 'prediction' of earthquakes are equivalent in this approach.

##### 23 October 2013

**Speaker: **Prof. Anatoly Zhigljavsky (Cardiff University).

**Title:** Stochastic methods in multiobjective optimization.

**Abstract:** TBC.

##### 30 October 2013

**Speaker: **Dr Andreas Artemiou (Cardiff University).

**Title:** Dimension Reduction in Regression.

**Abstract:** Firstly I will go through a historical overview of how dimension reduction is achieved in regression problems (with a focus on linear regression). I will be spending more time explaining why unsupervised methods like Principal Component Analysis will not work and I will be sufficient dimension reduction, a class of supervised dimension reduction techniques, that have been developed the last 25 years. After the general introduction (and probably in a second talk) I will focus on the use of machine learning algorithm and more specifically the use of Support Vector Machine to achieve linear and nonlinear dimension reduction in a unified framework. I will discuss the advantages of this type of methodology over previous methods, as well as ways to improve the shortcomings of it, (by the end of it, I will discuss in detail current research I am doing on this topic).

##### 13 November 2013 at 12:10

**Speaker: **Dr Andreas Artemiou (Cardiff University).

**Title:** Using support vector machines in sufficient dimension reduction.

**Abstract:** Having introduced the general framework for sufficient dimension reduction in the first part of the talk, in this part I will discuss how Support Vector Machine can be used to achieve both linear and nonlinear sufficient dimension reduction under a unified framework (idea discussed in Li, Artemiou and Li (2011)). Then I will discuss possible problems of the algorithms as well as possible solutions we are currently working on.

##### 27 November 2013

**Speaker: **Gareth Davies (Cardiff University).

**Title:** Calibration in Survey Sampling.

**Abstract:** Calibration is a technique frequently used in sample surveys. It consists of determining a set of final estimation weights that satisfy some benchmark constraints and that are as close as possible to a set of initial design weights. The motivation for the calibration problem and the main reasons for calibration in practice are introduced.
In this talk, we consider various methods of calibration. When constraints are 'hard' it is not guaranteed that the weights will remain positive or 'close' to the initial design weights. A variety of distance functions are considered and their relative merits explored. The chi-square distance function receives most attention in calibration literature, but is this the most appropriate function? Alternative calibration approaches will be introduced, namely empirical likelihood calibration, soft calibration and model calibration.

##### 15 January 2014

**Speaker: **Dr David Hodge (University of Nottingham).

**Title:** Restless bandits for resource allocation.

**Abstract:** I will give an overview of restless bandit theory and talk about some applications. Areas of application may involve queues, stock control and machine maintenance and all concern the dynamic sequential allocation of divisible resources between `competing' projects/bandits. I will discuss some problems where bandit `indices' can yield excellent scalable heuristics for high dimensional resource allocation problems. I will also try to discuss some work on asymptotic optimality with a view to highlighting the many areas where the result could be of use. The talk will attempt to provide an overview to a number of papers of work in this area with authors including K. Glazebrook, C. Kirkbride (both at Lancaster), and J. Minty.

##### 19 February 2014

**Speaker: **Dr Felix Fischer (Cambridge).

**Title:** Optimal Impartial Selection.

**Abstract:** We study the problem of selecting a member of a set of agents based on impartial nominations by agents from that set. The problem was studied previously by Alon et al. and by Holzman and Moulin and has important applications in situations where representatives are selected from within a group or where publishing or funding decisions are made based on a process of peer review. Our main result concerns a randomized mechanism that in expectation selects an agent with at least half the maximum number of nominations. Subject to impartiality, this is best possible. (joint work with Max Klimm).

##### 26 March 2014

**Speaker: **Danijel Grahovac (University of Osijek).

**Title:** Asymptotic properties of the partition function and applications.

**Abstract:** The so-called partition function is a sample moment statistic based on blocks of data and it is often usedin the context of multifractal processes. It will be shown that its behavior is strongly influenced by the tailof the distribution underlying the data both in i.i.d. and weakly dependent cases. As a fi rst applicationof this result, graphical and estimation methods for the tail index are developed. Proposed methods aretested against some well-known estimators on simulated and real world data. Second application involvesdetermining scaling properties of stochastic processes. It is shown that scaling functions method is unreliableand may produce spurious multifractality in the presence of heavy tails.

##### 7 May 2014

**Speaker: **Dr Paulavicius Remigijus (Imperial College).

**Title:** Simplicial Global Optimization.

**Abstract:** TBC.

##### 4 June 2014

**Speaker: **Prof. Joerg Fliege (Uniiversity of Southampton).

**Title:** Robust Multiobjective Optimisation.

**Abstract:** Motivated by Markowitz portfolio optimization problems under

uncertainty in the problem data, we consider general convex parametric multiobjective optimization problems under data uncertainty. For the first time, this uncertainty is treated by a robust multiobjective formulation in the gist of Ben-Tal and Nemirovski. For this novel formulation, we investigate its relationship to the original multiobjective formulation as well as to its scalarizations. A further reformulation, based on set-valued optimisation, leads to a framework for descent algorithms with semi-infinite direction search programs.

##### 23 June 2014 at 3pm in M/1.25

**Speaker: **Dr Mark Kelbert (Swansea University).

**Title:** Dobrushin interface in classical multi-type lattice Widom-Rowlinson models.

**Abstract:** A classical $q$-type WR (Widom--Rowlinson) model is analyzed, on a lattice ${\bf Z}^d$, to establish properties of Dobrushin`s interface phases. The analysis is restricted to $q=2,3,4$ and large values of (equal) fugacities. We consider an interface between (a) two stable phases,(b) a stable and an unstable phase, and (c) two unstable phases. In case (a) the interface turns out to be rigid; in cases (b) and (c) rigidity/non-rigidity depends on the pattern of attraction for the unstable phase(s).

##### 2 July 2014

**Speaker: ** Matthew John (Cardiff).

**Title:** An Overview of the Urban Transit Network Design Problem and an Improved Multi-Objective Algorithm Approach.

**Abstract: **The determination of efficient routes and schedules in public transport systems is complex due to the vast search space and multiple constraints involved. In this presentation we focus on the Urban Transit Routing Problem concerned with the physical network design of public transport systems. Historically, route planners have used their local knowledge coupled with simple guidelines to produce network designs. Several major studies have identified the need for automated tools to aid in the design and evaluation of public transport networks. We propose a new construction heuristic used to seed a multi-objective evolutionary algorithm. Several problem specific mutation operators are then combined with an NSGAII framework leading to improvements upon previously published results. Algorithm parallelisation is then discussed using a hybrid approach together with a real world application.

##### 9 July 2014 at 11:10 in M/0.40

**Speaker: ** Dr. Alla Sikorskii (Michigan State University).

**Title:** Fractional Pearson Diffusions.

**Abstract:** Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equations that are used for modeling of sub-diffusive phenomena, caused by particle sticking and trapping. We define fractional Pearson diffusion processes using a non-Markovian inverse stable time change. The distributional properties and the correlation functions of fractional Pearson diffusions are discussed.

Joint work with N. N. Leonenko and M. M. Meerschaert.

##### 16 July 2014 at 12:10 in M/0.40

**Speaker: ** Dr Quentin Louveaux (University of Liege).

**Title:** Relaxation schemes for min max generalization in batch mode reinforcement learning.

**Abstract:** Reinforcement learning is a control paradigm where an agent tries to interact with its environment in order to maximize a reward. We assume that the space in which the agent lies is a discrete-time Markov

process whose only knowledge is given through a batch collection of trajectories. In this talk, we are interested in providing a worst-case performance guarantee of a given policy. It was shown that such a guarantee can be modeled through a quadratically constrained quadratic program. We show that such a problem is NP-hard and we propose two tractable relaxation schemes to tackle it. The first relaxation scheme works by dropping some constraints in order to obtain a problem that is solvable in polynomial time. The second relaxation scheme, based on a Lagrangian relaxation where all constraints are dualized, can also be solved in polynomial time. We also theoretically prove and empirically illustrate that both relaxation schemes provide better results than those previously proposed in the literature.

This is a joint work with Raphaël Fonteneau, Bernard Boigelot and Damien Ernst.