Search results for "Stochastic gradient."

Estimation of Granger causality through Artificial Neural Networks: applications to physiological systems and chaotic electronic oscillators

2021

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Sq…

Binary logistic regression versus stochastic gradient boosted decision trees in assessing landslide susceptibility for multiple-occurring landslide e…

2015

This study aims to compare binary logistic regression (BLR) and stochastic gradient treeboost (SGT) methods in assessing landslide susceptibility within the Mediterranean region for multiple-occurrence regional landslide events. A test area was selected in the north-eastern sector of Sicily (southern Italy) where thousands of debris flows and debris avalanches triggered on the first October 2009 due to an extreme storm. Exploiting the same set of predictors and the 2009 event landslide archive, BLR- and SGT-based susceptibility models have been obtained for the two catchments separately, adopting a random partition (RP) technique for validation. In addition, the models trained in one catchm…

Average Performance Analysis of the Stochastic Gradient Method for Online PCA

2019

International audience; This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the practical relevance of the plain stochastic gradient approach and that drastic improvements can be achieved by learning the learning rate.

Comparing binary logistic regression and stochastic gradient boosting techniques in debris-flows susceptibility modelling: application in North-Easte…

2013

Online shortest paths with confidence intervals for routing in a time varying random network

2018

International audience; The increase in the world's population and rising standards of living is leading to an ever-increasing number of vehicles on the roads, and with it ever-increasing difficulties in traffic management. This traffic management in transport networks can be clearly optimized by using information and communication technologies referred as Intelligent Transport Systems (ITS). This management problem is usually reformulated as finding the shortest path in a time varying random graph. In this article, an online shortest path computation using stochastic gradient descent is proposed. This routing algorithm for ITS traffic management is based on the online Frank-Wolfe approach.…

OPTIMIZING STOCHASTIC SUSCEPTIBILITY MODELLING FOR DEBRIS FLOW LANDSLIDES: MODEL EXPORTATION, STATISTICAL TECHNIQUES COMPARISON AND USE OF REMOTE SEN…

Il presente lavoro di ricerca è stato sviluppato al fine di approfondire approcci metodologici nell'ambito della sucscettibilità da frana. In particolare, il tema centrale della ricerca è rappresentato dal tema specifico dell'esportazione spaziale di modelli di suscettibilità nell'area mediterranea. All'interno del topic specifico dell'esportazione di modelli predittivi spaziali sono state approfondite tematiche relative all'utilizzo di differenti algoritmi o di differenti sorgenti, derivate da DEM o da coperture satellitari. The present work has been developed in order to enhance current methodological approaches within the big picture of the landslide susceptibility. In particular, the ce…

A fast and recursive algorithm for clustering large datasets with k-medians

2012

Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class of recursive stochastic gradient algorithms designed for the $k$-medians loss criterion is proposed. By their recursive nature, these algorithms are very fast and are well adapted to deal with large samples of data that are allowed to arrive sequentially. It is proved that the stochastic gradient algorithm converges almost surely to the set of stationary points of the underlying loss criterion. A particular attention is paid to the averaged versions, which…

Fast Estimation of the Median Covariation Matrix with Application to Online Robust Principal Components Analysis

2017

International audience; The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at each new observation and are able to deal rapidly with large samples of high dimensional data without being obliged to store all the data in memory. Asymptotic convergence properties of the recursive algorithms are studied under weak conditions. The computation of the principal components can also be performed online and this approach can be useful for online outlier detection. A simulation study clearly shows that this robust indicat…

Recursive estimation of the conditional geometric median in Hilbert spaces

2012

International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…

Stochastic algorithms for robust statistics in high dimension

2016

This thesis focus on stochastic algorithms in high dimension as well as their application in robust statistics. In what follows, the expression high dimension may be used when the the size of the studied sample is large or when the variables we consider take values in high dimensional spaces (not necessarily finite). In order to analyze these kind of data, it can be interesting to consider algorithms which are fast, which do not need to store all the data, and which allow to update easily the estimates. In large sample of high dimensional data, outliers detection is often complicated. Nevertheless, these outliers, even if they are not many, can strongly disturb simple indicators like the me…