4,451 research outputs found
Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection
We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to estimate minimum entropy sets. These sets are relevant to detect anomalous or outlier functional data. A numerical experiment illustrates the performance of the proposed method; in addition, we conduct an analysis of mortality rate curves as an interesting application in a real-data context to explore functional anomaly detection.The first and third authors acknowledge financial support from the Spanish Ministry
of Economy and Competitiveness ECO2015-66593-P. The Second author acknowledges CONICET
Argentina Project 20020150200110BA. The fourth author acknowledges the Spanish Ministry of
Economy and Competitiveness Projects GROMA(MTM2015-63710-P), PPI (RTC-2015-3580-7) and
UNIKO(RTC-2015-3521-7) and the “methaodos.org” research group at URJC
Discovering Functional Communities in Dynamical Networks
Many networks are important because they are substrates for dynamical
systems, and their pattern of functional connectivity can itself be dynamic --
they can functionally reorganize, even if their underlying anatomical structure
remains fixed. However, the recent rapid progress in discovering the community
structure of networks has overwhelmingly focused on that constant anatomical
connectivity. In this paper, we lay out the problem of discovering_functional
communities_, and describe an approach to doing so. This method combines recent
work on measuring information sharing across stochastic networks with an
existing and successful community-discovery algorithm for weighted networks. We
illustrate it with an application to a large biophysical model of the
transition from beta to gamma rhythms in the hippocampus.Comment: 18 pages, 4 figures, Springer "Lecture Notes in Computer Science"
style. Forthcoming in the proceedings of the workshop "Statistical Network
Analysis: Models, Issues and New Directions", at ICML 2006. Version 2: small
clarifications, typo corrections, added referenc
Statistical learning methods for functional data with applications to prediction, classification and outlier detection
In the era of big data, Functional Data Analysis has become increasingly important insofar
as it constitutes a powerful tool to tackle inference problems in statistics. In particular
in this thesis we have proposed several methods aimed to solve problems of
prediction of time series, classification and outlier detection from a functional approach.
The thesis is organized as follows: In Chapter 1 we introduce the concept of functional
data and state the overview of the thesis. In Chapter 2 of this work we present
the theoretical framework used to we develop the proposed methodologies.
In Chapters 3 and 4 two new ordering mappings for functional data are proposed.
The first is a Kernel depth measure, which satisfies the corresponding theoretical properties,
while the second is an entropy measure. In both cases we propose a parametric
and non-parametric estimation method that allow us to define an order in the data set
at hand. A natural application of these measures is the identification of atypical observations
(functions).
In Chapter 5 we study the Functional Autoregressive Hilbertian model. We also
propose a new family of basis functions for the estimation and prediction of the aforementioned
model, which belong to a reproducing kernel Hilbert space. The properties
of continuity obtained in this space allow us to construct confidence bands for the corresponding
predictions in a detracted time horizon.
In order to boost different classification methods, in Chapter 6 we propose a divergence
measure for functional data. This metric allows us to determine in which part of
the domain two classes of functional present divergent behavior. This methodology is
framed in the field of domain selection, and it is aimed to solve classification problems
by means of the elimination of redundant information.
Finally in Chapter 7 the general conclusions of this work and the future research
lines are presented.Financial support received from the Spanish Ministry of Economy and Competitiveness ECO2015-66593-P and the UC3M PIF scholarship for doctoral studies.Programa de Doctorado en EconomĂa de la Empresa y MĂ©todos Cuantitativos por la Universidad Carlos III de MadridPresidente: Santiago Velilla Cerdán; Secretario: Kalliopi Mylona; Vocal: Luis Antonio Belanche Muño
- …