Related papers: Depth Patterns and their Applications in Animal Tr…

Half-space depth (also called Tukey depth or location depth) is one of the most commonly studied data depth measures because it possesses many desirable properties for data depth functions. The data depth contours bound regions of…

We investigate in real-life conditions and with very high accuracy the dynamics of body rotation, or yawing, of walking pedestrians - an highly complex task due to the wide variety in shapes, postures and walking gestures. We propose a…

The task of detecting anomalous data patterns is as important in practical applications as challenging. In the context of spatial data, recognition of unexpected trajectories brings additional difficulties, such as high dimensionality and…

Linear regression is a fundamental tool for statistical analysis. This has motivated the development of linear regression methods that also satisfy differential privacy and thus guarantee that the learned model reveals little about any one…

In this paper, we show that the halfspace depth random variable for samples from a univariate distribution with a notion of center is distributed as a uniform distribution on the interval [0,1/2]. The simplicial depth random variable has a…

The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…

Many real-world datasets are labeled with natural orders, i.e., ordinal labels. Ordinal regression is a method to predict ordinal labels that finds a wide range of applications in data-rich domains, such as natural, health and social…

Starting with Tukey's pioneering work in the 1970's, the notion of depth in statistics has been widely extended especially in the last decade. These extensions include high dimensional data, functional data, and manifold-valued data. In…

In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance…

We propose a framework for descriptively analyzing sets of partial orders based on the concept of depth functions. Despite intensive studies of depth functions in linear and metric spaces, there is very little discussion on depth functions…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

Data mining is the task of discovering interesting patterns from large amounts of data. There are many data mining tasks, such as classification, clustering, association rule mining, and sequential pattern mining. Sequential pattern mining…

Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…

We consider trawl processes, which are stationary and infinitely divisible stochastic processes and can describe a wide range of statistical properties, such as heavy tails and long memory. In this paper, we develop the first…

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…

We analyze the ordinal structure of long-range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points. We provide two estimators for the probabilities of ordinal…

We introduce a general framework for testing temporal symmetries in time series based on the distribution of ordinal patterns. While previous approaches have focused on specific forms of asymmetry, such as time reversal, our method provides…

Estimated density is often interpreted as indicating how typical a sample is under a model. Yet deep models trained on one dataset can assign higher density to simpler out-of-distribution (OOD) data than to in-distribution test data. We…

Uncertainty awareness is crucial to develop reliable machine learning models. In this work, we propose the Natural Posterior Network (NatPN) for fast and high-quality uncertainty estimation for any task where the target distribution belongs…