Pieter Segaert

Multivariate and functional classification using depth and distance

We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data.

Rejoinder to ‘multivariate functional outlier detection’

First of all we would like to thank the editor, Professor Andrea Cerioli, for inviting us to submit our work and for requesting comments from some esteemed colleagues. We were surprised by the number of invited comments and grateful to their contributing authors, all of whom raised important points and/or offered valuable suggestions. We are happy for the opportunity to rejoin the discussion. Rather than addressing the comments in turn we will organize our rejoinder by topic, starting with comments directly related to concepts we proposed in the paper and continuing with some extensions.

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures.

Analysis of Travel Activity Determinants Using Robust Statistics

This study investigates travel behavior determinants based on a multiday travel survey conducted in the region of Ghent, Belgium. Due to the limited data reliability of the data sample and the influence of outliers exerted on classical principal component analysis, robust principal component analysis (ROBPCA) is employed in order to reveal the explanatory variables responsible for most of the variability. Interpretation of the results is eased by utilizing ROSPCA. The application of ROSPCA reveals six distinct principal components where each is determined by a few variables. Among others, our results suggest a key role of variable categories such as journey purpose-related impedance and journey inherent constraints. Surprisingly, the variables associated with journey timing turn out to be less important. Finally, our findings reveal the critical role of outliers in travel behavior analysis. This suggests that a systematic understanding of how outliers contribute to observed mobility behavior patterns, as derived from travel surveys, is needed. In this regard, the proposed methods serve for processing raw data typically used in activity-based modelling.

Fit to speak - Physical fitness is associated with reduced language decline in healthy ageing

Healthy ageing is associated with decline in cognitive abilities such as language. Aerobic fitness has been shown to ameliorate decline in some cognitive domains, but the potential benefits for language have not been examined. In a cross-sectional sample, we investigated the relationship between aerobic fitness and tip-of-the-tongue states. These are among the most frequent cognitive failures in healthy older adults and occur when a speaker knows a word but is unable to produce it. We found that healthy older adults indeed experience more tip-of-the-tongue states than young adults. Importantly, higher aerobic fitness levels decrease the probability of experiencing tip-of-the-tongue states in healthy older adults. Fitness-related differences in word finding abilities are observed over and above effects of age. This is the first demonstration of a link between aerobic fitness and language functioning in healthy older adults.Healthy ageing is associated with decline in cognitive abilities such as language. Aerobic fitness has been shown to ameliorate decline in some cognitive domains, but the potential benefits for language have not been examined. We investigated the relationship between aerobic fitness and tip-of-the-tongue states. These are among the most frequent cognitive failures in healthy older adults and occur when a speaker knows a word but is unable to produce it. We found that the healthy older adults indeed experience more tip-of-the-tongue states, and that when they do they have access to less information about the word9s sound structure, compared to young controls. Importantly, higher aerobic fitness levels decrease the probability of experiencing tip-of-the-tongue states in healthy older adults, over and above the effect of age. This is the first demonstration of a link between aerobic fitness and language functioning in healthy older adults.

Robust identification of target genes and outliers in triple-negative breast cancer data

Correct classification of breast cancer subtypes is of high importance as it directly affects the therapeutic options. We focus on triple-negative breast cancer which has the worst prognosis among breast cancer types. Using cutting edge methods from the field of robust statistics, we analyze Breast Invasive Carcinoma transcriptomic data publicly available from The Cancer Genome Atlas data portal. Our analysis identifies statistical outliers that may correspond to misdiagnosed patients. Furthermore, it is illustrated that classical statistical methods may fail to identify outliers due to their heavy influence, prompting the need for robust statistics. Using robust sparse logistic regression we obtain 36 relevant genes, of which ca. 60% have been previously reported as biologically relevant to triple-negative breast cancer, reinforcing the validity of the method. The remaining 14 genes identified are new potential biomarkers for triple-negative breast cancer. Out of these, JAM3, SFT2D2, and PAPSS1 were previously associated to breast tumors or other types of cancer. The relevance of these genes is confirmed by the new DetectDeviatingCells outlier detection technique. A comparison of gene networks on the selected genes showed significant differences between triple-negative breast cancer and non-triple-negative breast cancer data. The individual role of FOXA1 in triple-negative breast cancer and non-triple-negative breast cancer, and the strong FOXA1-AGR2 connection in triple-negative breast cancer stand out. The goal of our paper is to contribute to the breast cancer/triple-negative breast cancer understanding and management. At the same time it demonstrates that robust regression and outlier detection constitute key strategies to cope with high-dimensional clinical data such as omics data.

Higher physical fitness levels are associated with less language decline in healthy ageing

Healthy ageing is associated with decline in cognitive abilities such as language. Aerobic fitness has been shown to ameliorate decline in some cognitive domains, but the potential benefits for language have not been examined. In a cross-sectional sample, we investigated the relationship between aerobic fitness and tip-of-the-tongue states. These are among the most frequent cognitive failures in healthy older adults and occur when a speaker knows a word but is unable to produce it. We found that healthy older adults indeed experience more tip-of-the-tongue states than young adults. Importantly, higher aerobic fitness levels decrease the probability of experiencing tip-of-the-tongue states in healthy older adults. Fitness-related differences in word finding abilities are observed over and above effects of age. This is the first demonstration of a link between aerobic fitness and language functioning in healthy older adults.