spring_2023

This talk will focus on recent work about the sequential detection of anomalies within partially observed functional data, motivated by a problem encountered by an industrial collaborator. Classical sequential changepoint detection approaches look for changes in the parameters, or structure, of a data sequence and are not equipped to handle the complex non-stationarity and dependency structure of functional data. Conversely, existing functional data approaches require the full observation of the curve before anomaly detection can take place. We propose a new method, FAST, that performs sequential detection of anomalies in partially observed functional data. This talk will introduce the approach, and some associated theoretical results, and highlight its application on telecommunications data.

This is joint work with Idris Eckley and Lawrence Bardwell.

A flexible predictive density combination is introduced for large financial data sets which allows for model set incompleteness. Dimension reduction procedures that include learning allocate the large sets of predictive densities and combination weights to relatively small subsets.  Given the representation of the probability model in extended nonlinear state-space form, efficient simulation-based Bayesian inference is proposed using parallel dynamic clustering as well as nonlinear filtering, implemented on graphics processing units. The approach is applied to combine predictive densities based on a large number of individual US stock returns of daily observations over a period that includes the Covid-19 crisis period.  Evidence on dynamic cluster composition, weight patterns and model set incompleteness gives valuable signals for improved modelling. This enables higher predictive accuracy and better assessment of uncertainty and risk for investment fund management.

Online changepoint detection algorithms based on likelihood-ratio tests have excellent statistical properties. However, a simple exact online implementation is computationally infeasible as, at time T, it involves considering O(T) possible locations for the change. To improve on this, we use functional pruning ideas to reduce the set of changepoint locations that need to be stored at time T to approximately log T. Furthermore, we show how we need only maximise the likelihood-ratio test statistic over a small subset of these possible locations. Empirical results show that the resulting exact online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average. We consider applications of this algorithm in the context of detecting increases in radiation count that represent astronomical or nuclear events of interest.

This talk will introduce a recent suite of research focussed on the statistical detection of anomalous structure in online data settings. The challenge of efficiently identifying anomalies in data sequences is an important statistical problem that now arises in many applications. Whilst there has been substantial work aimed at making statistical analyses robust to outliers, or point anomalies, there has been much less work on detecting anomalous segments, or collective anomalies, particularly in those settings where point anomalies might also occur. This is the challenge we seek to address, demonstrating theoretical results in both the offline and online settings as well as introducing some applied case studies.

Douglas Wiens (Department of Mathematics and Statistical Sciences, University of Alberta, CAN) will give a talk on Wednesday April 19th at 14:15 in the Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor.

Variable selection methods based on L₀ penalties have excellent theoretical properties to select sparse models in a high-dimensional setting. There exist modifications of BIC which either control the family wise error rate (mBIC) or the false discovery rate (mBIC2) in terms of which regressors are selected to enter a model. However, the minimization of L₀ penalties comprises a mixed integer problem which is known to be NP hard and therefore becomes computationally challenging with increasing numbers of regressor variables. This is one reason why alternatives like the LASSO have become so popular, which involve convex optimization problems which are easier to solve. The last few years have seen some real progress in developing new algorithms to minimize  L₀ penalties. We will compare the performance of these algorithms in terms of minimizing L₀ based selection criteria.
Simulation studies covering a wide range of scenarios which are inspired by genetic association studies are used to compare the values of selection criteria obtained with different algorithms. Additionally some statistical characteristics of the selected models and the runtime of algorithms are compared.

Estimates of environmental extremes are needed for a multitude of applications. For example, buildings, roads, bridges and dams must be designed to withstand extreme precipitation and flooding events of a certain size. Obtaining such estimates requires a combination of statistical theory and environmental process understanding to overcome data deficiencies: data on extremes are by definition sparse and regulations often require estimates for events that have yet to be observed. We will present approaches to obtain consistent estimates across spatial locations and accumulation periods, and discuss a few open questions on this topic.