Related papers: General notions of depth for functional data
In this work, we present a panoramic metric depth foundation model that generalizes across diverse scene distances. We explore a data-in-the-loop paradigm from the view of both data construction and framework design. We collect a…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
The spatial distribution has been widely used to develop various nonparametric procedures for finite dimensional multivariate data. In this paper, we investigate the concept of spatial distribution for data in infinite dimensional Banach…
We propose and analyze the moving median absolute deviation (MMAD) as a robust depth construction based on the median absolute distance functional with particular emphasis on its local geometry and probabilistic structure. In the univariate…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…
Tukey depth, aka halfspace depth, has attracted much interest in data analysis, because it is a natural way of measuring the notion of depth relative to a cloud of points or, more generally, to a probability measure. Given an i.i.d. sample,…
A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…
In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other methods that try to select the best…
The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Tukey's depth (or halfspace depth) is a widely used measure of centrality for multivariate data. However, exact computation of Tukey's depth is known to be a hard problem in high dimensions. As a remedy, randomized approximations of Tukey's…
It is not unusual for a data analyst to encounter data sets distributed across several computers. This can happen for reasons such as privacy concerns, efficiency of likelihood evaluations, or just the sheer size of the whole data set. This…
Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…
We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a…
Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
Post-data statistical inference concerns making probability statements about model parameters conditional on observed data. When a priori knowledge about parameters is available, post-data inference can be conveniently made from Bayesian…
Depth estimation is a fundamental task in 3D computer vision, crucial for applications such as 3D reconstruction, free-viewpoint rendering, robotics, autonomous driving, and AR/VR technologies. Traditional methods relying on hardware…
We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent representation formulae for the score function introduced…
According to the Integrated Information Theory of Consciousness, consciousness is a fundamental observer-independent property of physical systems, and the measure Phi of integrated information is identical to the quantity or level of…