Related papers: Depth for curve data and applications
This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…
A data marketplace is an online venue that brings data owners, data brokers, and data consumers together and facilitates commoditisation of data amongst them. Data pricing, as a key function of a data marketplace, demands quantifying the…
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature function defined on $[0,1]$. The construction of these feature…
The Tukey (or halfspace) depth extends nonparametric methods toward multivariate data. The multivariate analogues of the quantiles are the central regions of the Tukey depth, defined as sets of points in the $d$-dimensional space whose…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
Quantifying numerical data involves addressing two key challenges: first, determining whether the data can be naturally quantified, and second, identifying the numerical intervals or ranges of values that correspond to specific value…
Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses…
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…
We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…
One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al.…
In the 1990s, statisticians began thinking in a principled way about how computation could better support the learning and doing of statistics. Since then, the pace of software development has accelerated, advancements in computing and data…
Large observational clinical datasets become increasingly available for mining associations between various disease traits and administered therapy. These datasets can be considered as representations of the landscape of all possible…
Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…
Depth of the Tukey median is investigated for empirical distributions. A sharper upper bound is provided for this value for data sets in general position. This bound is lower than the existing one in the literature, and more importantly…
Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its…
It is difficult to collect data on a large scale in a monocular depth estimation because the task requires the simultaneous acquisition of RGB images and depths. Data augmentation is thus important to this task. However, there has been…