Consider a non-linear function $G(X_t)$ where $X_t$ is a stationary Gaussian sequence with long-range dependence. The usual reduction principle states that the partial sums of $G(X_t)$ behave asymptotically like the partial sums of the first term in the expansion of $G$ in Hermite polynomials. In the context of the wavelet estimation of the long-range dependence parameter, one replaces the partial sums of $G(X_t)$ by the wavelet scalogram, namely the partial sum of squares of the wavelet coefficients. Is there a reduction principle in the wavelet setting, namely is the asymptotic behavior of the scalogram for $G(X_t)$ the same as that for the first term in the expansion of $G$ in Hermite polynomial? The answer is negative in general. This paper provides a minimal growth condition on the scales of the wavelet coefficients which ensures that the reduction principle also holds for the scalogram. The results are applied to testing the hypothesis that the long-range dependence parameter takes a specific value. Joint work with François Roueff and Murad S. Taqqu

Keywords: long-range dependence; long memory; self-similarity; wavelet transform; estimation; hypothesis
testing[-]

This course introduces fundamental concepts in machine learning and presents some classical approaches and algorithms. The scikit-learn library is presented during the practical sessions. The course aims at providing fundamental basics for using machine learning techniques.
Class (4h)
General Introduction to Machine Learning (learning settings, curse of dimensionality, overfitting/underfitting, etc.)
Overview of Supervised Learning: True risk/Empirical risk, loss functions, regularization, sparsity, norms, bias/variance trade-off, PAC generalization bounds, model selection.
Classical machine learning models: Support Vector Machines, Kernel Methods, Decision trees and Random Forests.
An introduction to uncertainty in ML: Gaussian Processes, Quantile Regression with RF
Labs (4h)
Introduction to scikit-learn
Classical Machine learning Models with scikit-learn
Uncertainty in ML[-]

This course introduces fundamental concepts in machine learning and presents some classical approaches and algorithms. The scikit-learn library is presented during the practical sessions. The course aims at providing fundamental basics for using machine learning techniques.
Class (4h)
General Introduction to Machine Learning (learning settings, curse of dimensionality, overfitting/underfitting, etc.)
Overview of Supervised Learning: True risk/Empirical risk, loss functions, regularization, sparsity, norms, bias/variance trade-off, PAC generalization bounds, model selection.
Classical machine learning models: Support Vector Machines, Kernel Methods, Decision trees and Random Forests
An introduction to uncertainty in ML: Gaussian Processes, Quantile Regression with RF
Labs (4h)
Introduction to scikit-learn
Classical Machine learning Models with scikit-learn
Uncertainty in ML[-]

This course introduces fundamental concepts in machine learning and presents some classical approaches and algorithms. The scikit-learn library is presented during the practical sessions. The course aims at providing fundamental basics for using machine learning techniques.
Class (4h)
General Introduction to Machine Learning (learning settings, curse of dimensionality, overfitting/underfitting, etc.)
Overview of Supervised Learning: True risk/Empirical risk, loss functions, regularization, sparsity, norms, bias/variance trade-off, PAC generalization bounds, model selection.
Classical machine learning models: Support Vector Machines, Kernel Methods, Decision trees and Random Forests
An introduction to uncertainty in ML: Gaussian Processes, Quantile Regression with RF
Labs (4h)
Introduction to scikit-learn
Classical Machine learning Models with scikit-learn
Uncertainty in ML[-]

This course introduces fundamental concepts in machine learning and presents some classical approaches and algorithms. The scikit-learn library is presented during the practical sessions. The course aims at providing fundamental basics for using machine learning techniques.
Class (4h)
General Introduction to Machine Learning (learning settings, curse of dimensionality, overfitting/underfitting, etc.)
Overview of Supervised Learning: True risk/Empirical risk, loss functions, regularization, sparsity, norms, bias/variance trade-off, PAC generalization bounds, model selection.
Classical machine learning models: Support Vector Machines, Kernel Methods, Decision trees and Random Forests.
An introduction to uncertainty in ML: Gaussian Processes, Quantile Regression with RF
Labs (4h)
Introduction to scikit-learn
Classical Machine learning Models with scikit-learn
Uncertainty in ML[-]