arXiv subjects

Amaury Durand

Publications and source records attributed to Amaury Durand.

10 recordsLinked to original sources

arXiv2025

Power comparison of sequential testing by betting procedures

In this paper, we derive power guarantees of some sequential tests for bounded mean under general alternatives. We focus on testing procedures using nonnegative supermartingales which are anytime valid and consider alternatives which coincide asymptotically with the null (e.g. vanishing mean) while still allowing to reject in finite time. Introducing variance constraints, we show that the alternative can be broaden while keeping power guarantees for certain second-order testing procedures. We also compare different test procedures in multidimensional setting using characteristics of the rejection times. Finally, we extend our analysis to other functionals as well as testing and comparing forecasters. Our results are illustrated with numerical simulations including bounded mean testing and comparison of forecasters.

math.ST↗

arXiv2025

AutoML Algorithms for Online Generalized Additive Model Selection: Application to Electricity Demand Forecasting

Electricity demand forecasting is key to ensuring that supply meets demand lest the grid would blackout. Reliable short-term forecasts may be obtained by combining a Generalized Additive Models (GAM) with a State-Space model (Obst et al., 2021), leading to an adaptive (or online) model. A GAM is an over-parameterized linear model defined by a formula and a state-space model involves hyperparameters. Both the formula and adaptation parameters have to be fixed before model training and have a huge impact on the model's predictive performance. We propose optimizing them using the DRAGON package of Keisler (2025), originally designed for neural architecture search. This work generalizes it for automated online generalized additive model selection by defining an efficient modeling of the search space (namely, the space of the GAM formulae and adaptation parameters). Its application to short-term French electricity demand forecasting demonstrates the relevance of the approach

stat.ML↗

arXiv2022

Hilbert valued fractionally integrated autoregressive moving average processes with long memory operators

Fractionally integrated autoregressive moving average (FIARMA) processes have been widely and successfully used to model and predict univariate time series exhibiting long range dependence. Vector and functional extensions of these processes have also been considered more recently. Here we study these processes by relying on a spectral domain approach in the case where the processes are valued in a separable Hilbert space H0. In this framework, the usual univariate long memory parameter d is replaced by a long memory operator D acting on H0, leading to a class of H0-valued FIARMA(D, p, q) processes, where p and q are the degrees of the AR and MA polynomials. When D is a normal operator, we provide a necessary and sufficient condition for the D-fractional integration of an H0-valued ARMA(p, q) process to be well defined. Then, we derive the best predictor for a class of causal FIARMA processes and study how this best predictor can be consistently estimated from a finite sample of the process. To this end, we provide a general result on quadratic functionals of the periodogram, which incidentally yields a result of independent interest. Namely, for any ergodic stationary process valued in H0 with finite second moment, the empirical autocovariance operator converges, in trace-norm, to the true autocovariance operator almost surely at each lag.

math.FA↗

arXiv2022

Weakly stationary stochastic processes valued in a separable Hilbert space: Gramian-Cramér representations and applications

The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time domain. The key point is to build the Gramian-Cramér representation as an isomorphic mapping from the modular spectral domain to the modular time domain. We also discuss the general Bochner theorem and provide useful results on the composition and inversion of lag-invariant linear filters. Finally, we derive the Cramér-Karhunen-Loève decomposition and harmonic functional principal component analysis, which are established without relying on additional assumptions.

math.ST↗

arXiv2022

New penalized criteria for smooth non-negative tensor factorization with missing entries

Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we focus in understanding how this issue should be dealt with for nonnegative tensor factorization. We investigate several criteria used for non-negative tensor factorization in the case where some entries are missing. In particular we show how smoothness penalties can compensate the presence of missing values in order to ensure the existence of an optimum. This lead us to propose new criteria with efficient numerical optimization algorithms. Numerical experiments are conducted to support our claims.

eess.SP↗

arXiv2021

Duals of linearized Reed-Solomon codes

We give a description of the duals of linearized Reed-Solomon codes in terms of codes obtained by taking residues of Ore rational functions. Our construction shows in particular that, under some assumptions on the base field, the class of linearized Reed-Solomon codes is stable under duality. As a byproduct of our work, we develop a theory of residues in the Ore setting.

cs.IT↗

arXiv2021

Smooth nonnegative tensor factorization for multi-sites electrical load monitoring

The analysis of load curves collected from smart meters is a key step for many energy management tasks ranging from consumption forecasting to customers characterization and load monitoring. In this contribution, we propose a model based on a functional formulation of nonnegative tensor factorization and derive updates for the corresponding optimization problem. We show on the concrete example of multi-sites load curves disaggregation how this formulation is helpful for 1) exhibiting smooth intraday consumption patterns and 2) taking into account external variables such as the outside temperature. The benefits are demonstrated on simulated and real data by exhibiting a meaningful clustering of the observed sites based on the obtained decomposition.

eess.SP↗

arXiv2019

Reed-Solomon-Gabidulin Codes

We introduce Reed-Solomon-Gabidulin codes which is, at the same time, an extension to Reed-Solomon codes on the one hand and Gabidulin codes on the other hand. We prove that our codes have good properties with respect to the minimal distance and design an efficient decoding algorithm.

cs.IT↗

arXiv2017

The ACCompanion v0.1: An Expressive Accompaniment System

In this paper we present a preliminary version of the ACCompanion, an expressive accompaniment system for MIDI input. The system uses a probabilistic monophonic score follower to track the position of the soloist in the score, and a linear Gaussian model to compute tempo updates. The expressiveness of the system is powered by the Basis-Mixer, a state-of-the-art computational model of expressive music performance. The system allows for expressive dynamics, timing and articulation.

cs.SD↗

arXiv2016

Live Score Following on Sheet Music Images

In this demo we show a novel approach to score following. Instead of relying on some symbolic representation, we are using a multi-modal convolutional neural network to match the incoming audio stream directly to sheet music images. This approach is in an early stage and should be seen as proof of concept. Nonetheless, the audience will have the opportunity to test our implementation themselves via 3 simple piano pieces.

cs.SD↗