Related papers: Depth Patterns and their Applications in Animal Tr…
Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…
The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…
The goal of animal movement analysis is to understand how organisms explore and exploit the complex and varying environment. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviors to highly random…
The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…
We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given $d$-dimensional data set for any $d\geq 2$, the algorithm is based on representation of level sets as intersections of balls in $R^d$, and can…
The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…
Statistical depths provide a fundamental generalization of quantiles and medians to data in higher dimensions. This paper proposes a new type of globally defined statistical depth, based upon control theory and eikonal equations, which…
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
Tukey's depth offers a powerful tool for nonparametric inference and estimation, but also encounters serious computational and methodological difficulties in modern statistical data analysis. This paper studies how to generalize and compute…
Deep neural networks are a family of computational models that are naturally suited to the analysis of hierarchical data such as, for instance, sequential data with the use of recurrent neural networks. In the other hand, ordinal regression…
Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward…
The information contained in a time series is more than what the values themselves are. In this paper, the Time-variant Local Autocorrelated Polynomial model with Kalman filter is proposed to model the underlying dynamics of a time series…
Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal…
Determining the representativeness of a point within a data cloud has recently become a desirable task in multivariate analysis. The concept of statistical depth function, which reflects centrality of an arbitrary point, appears to be…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal patterns describes the average diversity of the ordinal patterns succeeding a given…