Publications

2020

• Inside Quasimodo: Exploring Construction and Usage of Commonsense Knowledge
  
  • Romero Julien
  • Razniewski Simon
  , 2020, pp.3445-3448. Quasimodo [10] is an open-source commonsense knowledge base that significantly advanced the state of salient commonsense knowledge base construction. It introduced a pipeline that gathers, normalizes, validates and scores statements coming from query log and question answering forums. In this demonstration, we present a companion web portal which allows (i) to explore the data, (ii) to run and analyze the extraction pipeline live, and (iii) inspect the usage of Quasimodo's knowledge in several downstream use cases. The web portal is available at https://quasimodo.r2.enst.fr. (10.1145/3340531.3417416)
  DOI : 10.1145/3340531.3417416
• Extending Deep Rhythm for Tempo and Genre Estimation Using Complex Convolutions, Multitask Learning and Multi-input Network
  
  • Foroughmand Hadrien
  • Peeters Geoffroy
  , 2020. Tempo and genre are two inter-leaved aspects of music, genres are often associated to rhythm patterns which are played in specific tempo ranges. In this paper, we focus on the recent Deep Rhythm system based on a harmonic representation of rhythm used as an input to a convolutional neural network. To consider the relationships between frequency bands, we process complex-valued inputs through complexconvolutions. We also study the joint estimation of tempo/genre using a multitask learning approach. Finally, we study the addition of a second input branch to the system based on a VGG-like architecture applied to a mel-spectrogram input. This multi-input approach allows to improve the performances for tempo and genre estimation.
• Unsupervised Concept Drift Detection Using a Student-Teacher Approach
  
  • Cerqueira Vítor
  • Gomes Heitor Murilo
  • Bifet Albert
  , 2020, 12323, pp.190--204. Concept drift detection is a crucial task in data stream evolving environments. Most of the state of the art approaches designed to tackle this problem monitor the loss of predictive models. Accordingly, an alarm is launched when the loss increases significantly, which triggers some adaptation mechanism (e.g. retrain the model). However, this modus operandi falls short in many real-world scenarios, where the true labels are not readily available to compute the loss. These often take up to several weeks to be available. In this context, there is increasing attention to approaches that perform concept drift detection in an unsupervised manner, i.e., without access to the true labels. We propose a novel approach to unsupervised concept drift detection, which is based on a student-teacher learning paradigm. Essentially, we create an auxiliary model (student) to mimic the behaviour of the main model (teacher). At run-time, our approach is to use the teacher for predicting new instances and monitoring the mimicking loss of the student for concept drift detection. In a set of controlled experiments, we discovered that the proposed approach detects concept drift effectively. Relative to the gold standard, in which the labels are immediately available after prediction, our approach is more conservative: it signals less false alarms, but it requires more time to detect changes. We also show the competitiveness of our approach relative to other unsupervised methods. (10.1007/978-3-030-61527-7_13)
  DOI : 10.1007/978-3-030-61527-7_13
• FEAT: A Fairness-Enhancing and Concept-Adapting Decision Tree Classifier
  
  • Zhang Wenbin
  • Bifet Albert
  , 2020, 12323, pp.175--189. Fairness-aware learning is increasingly important in socially-sensitive applications for the sake of achieving optimal and non-discriminative decision-making. Most of the proposed fairness-aware learning algorithms process the data in offline settings and assume that the data is generated by a single concept without drift. Unfortunately, in many real-world applications, data is generated in a streaming fashion and can only be scanned once. In addition, the underlying generation process might also change over time. In this paper, we propose and illustrate an efficient algorithm for mining fair decision trees from discriminatory and continuously evolving data streams. This algorithm, called FEAT (Fairness-Enhancing and concept-Adapting Tree), is based on using the change detector to learn adaptively from non-stationary data streams, that also accounts for fairness. We study FEAT’s properties and demonstrate its utility through experiments on a set of discriminated and time-changing data streams. (10.1007/978-3-030-61527-7_12)
  DOI : 10.1007/978-3-030-61527-7_12
• On-Chip Voltage and Temperature Digital Sensor for Security, Reliability, and Portability
  
  • Hasan Anik Md Toufiq
  • Ebrahimabadi Mohammad
  • Pirsiavash Hamed
  • Danger Jean-Luc
  • Guilley Sylvain
  • Karimi Naghmeh
  , 2020, pp.506-509. (10.1109/ICCD50377.2020.00091)
  DOI : 10.1109/ICCD50377.2020.00091
• SysML Models: Studying Safety and Security Measures Impact on Performance Using Graph Tainting
  
  • Zoor Maysam
  • Apvrille Ludovic
  • Pacalet Renaud
  , 2020. Designing safe, secure and efficient embedded systems implies understanding interdependencies between safety, security and performance requirements and mechanisms. In this paper, we introduce a new technique for analyzing the performance impact of safety/security implemented as hardware and software mechanisms and described in SysML models. Our analysis approach extracts a dependency graph from a SysML model. The SysML model is then simulated to obtain a list of simulation transactions. Then, to study the latency between two events of interest, we progressively taint the dependency graph according to simulation transactions and to dependencies between all software and hardware components. The simulation transactions are finally classified according to which vertex taint they correspond, and are displayed according to their timing and related hardware device. Thus a designer can easily spot which components need to be re-modeled in order to meet the performance requirement. A Rail Carriage use case studied in the scope of the H2020 AQUAS project illustrates our approach, in particular how tainting can handle the multiple occurrences of the same event. CCS CONCEPTS • Computer systems organization → Embedded software.
• Space-Ground Coherent Optical Links: Ground Receiver Performance With Adaptive Optics and Digital Phase-Locked Loop
  
  • Paillier Laurie
  • Le Bidan Raphaël
  • Conan Jean-Marc
  • Artaud Géraldine
  • Vedrenne Nicolas
  • Jaouën Yves
  Journal of Lightwave Technology, Institute of Electrical and Electronics Engineers (IEEE)/Optical Society of America(OSA), 2020, 38 (20), pp.5716-5727. In the framework of high-data-rate free-space optical low Earth orbit satellite-to-ground communication, we investigate, by means of a refined end-to-end numerical model of the link, the performance of a coherent receiver that combines an adaptive optics system and a specific digital receiver architecture. The design of a fine carrier recovery stage based on a phase-locked loop is presented and its performance is characterized. The end-to-end model includes the impact of atmospheric turbulence, adaptive optics correction, laser phase noise and of the frequency mismatch between the transmit and receiver lasers. The results show that adaptive optics coupled with classical digital phase-locked loop techniques can provide a reliable solution to the problem of carrier frequency and phase tracking in coherent satellite-to-ground optical links, after prior coarse frequency estimation. The phase-locked loop converges after a few hundreds of microseconds and accurately tracks the phase fluctuations. The residual amplitude fluctuations and laser phase noise are shown to be the dominant impairments for the link performance. (10.1109/JLT.2020.3003561)
  DOI : 10.1109/JLT.2020.3003561
• CONTENT BASED SINGING VOICE SOURCE SEPARATION VIA STRONG CONDITIONING USING ALIGNED PHONEMES
  
  • Meseguer-Brocal Gabriel
  • Peeters Geoffroy
  , 2020. Informed source separation has recently gained renewed interest with the introduction of neural networks and the availability of large multitrack datasets containing both the mixture and the separated sources. These approaches use prior information about the target source to improve separation. Historically, Music Information Retrieval researchers have focused primarily on scoreinformed source separation, but more recent approaches explore lyrics-informed source separation. However, because of the lack of multitrack datasets with time-aligned lyrics, models use weak conditioning with non-aligned lyrics. In this paper, we present a multimodal multitrack dataset with lyrics aligned in time at the word level with phonetic information as well as explore strong conditioning using the aligned phonemes. Our model follows a U-Net architecture and takes as input both the magnitude spectrogram of a musical mixture and a matrix with aligned phonetic information. The phoneme matrix is embedded to obtain the parameters that control Feature-wise Linear Modulation (FiLM) layers. These layers condition the U-Net feature maps to adapt the separation process to the presence of different phonemes via affine transformations. We show that phoneme conditioning can be successfully applied to improve singing voice source separation.
• Architecture de récepteur cohérent pour les liens optiques satellite-sol avec optique adaptative
  
  • Paillier Laurie
  , 2020. L’émergence et la multiplication de moyens d’observation du sol de résolution croissante et de réseaux de télécommunication spatiaux à très haut débit pour l’internet globalisé rendent nécessaire d’accroître la capacité de transmission de données entre l’espace et le sol de plusieurs ordres de grandeur. Les liens optiques, avec des débits de plusieurs dizaines de Gbps par canal, constituent une solution à très fort potentiel si les techniques de modulation de phase exploitées dans les réseaux fibrés peuvent y être appliquées. L’enjeu de cette thèse est d’investiguer le recours à des méthodes de modulation de phase pour des liens optiques satellite-sol en prenant en compte les spécificités propres à l’application : bruits de phase des lasers, effet Doppler, et impact de la propagation à travers l’atmosphère turbulente corrigé par optique adaptative pour maximiser l’efficacité de la détection cohérente. Dans ce but, j’ai développé un outil de simulation complète d’une transmission cohérente BPSK incluant les étapes de propagation à travers l’atmosphère, de détection et de démodulation. En s’appuyant sur cet outil, nous avons proposé deux architectures de récepteur numérique : l’une exploitant une boucle à verrouillage de phase, l’autre reposant sur une synchronisation en boucle ouverte. La méthodologie de conception développée à cette occasion permet de réduire l’impact du bruit de phase des lasers sur la précision de synchronisation, ce terme restant néanmoins prépondérant. L’étude menée montre que les deux architectures présentent des performances comparables en termes de précision de synchronisation, de seuil de convergence et de taux d’erreur dans différentes conditions de turbulence. Les performances en taux d’erreur obtenues soulignent l’importance de la qualité de la correction par optique adaptative. Une confirmation par modélisation du faible impact du bruit de phase turbulent sur la performance est apportée. Ces travaux laissent envisager la possibilité d’un accroissement très significatif du débit atteignable pour des liens de télémesure cohérents dans le cas de l’emploi de constellations d’ordre supérieur (QPSK et au-delà) au prix d’une correction par optique adaptative de bonne qualité.
• Brief announcement: on decidability of 2-process affine models
  
  • Kuznetsov Petr
  • Rieutord Thibault
  , 2020, 179, pp.54:1-54:3. Affine models of computation, defined as subsets of iterated immediate-snapshot runs, capture a wide variety of shared-memory systems: wait-freedom, t-resilience, k-concurrency, and fair shared-memory adversaries. The question of whether a given task is solvable in a given affine model is, in general, undecidable. In this paper, we focus on affine models defined for a system of two processes. We show that task computability of 2-process affine models is decidable and presents a complete hierarchy of five equivalence classes of 2-process affine models. (10.4230/LIPIcs.DISC.2020.54)
  DOI : 10.4230/LIPIcs.DISC.2020.54
• Innovative Dynamic SRAM PUF Authentication for Trusted Internet of Things
  
  • Urien Pascal
  , 2020, pp.374-377. (10.1109/WiMob50308.2020.9253432)
  DOI : 10.1109/WiMob50308.2020.9253432
• SHOULD WE CONSIDER THE USERS IN CONTEXTUAL MUSIC AUTO-TAGGING MODELS?
  
  • Ibrahim Karim M
  • Epure Elena V
  • Peeters Geoffroy
  • Richard Gael
  , 2020. Music tags are commonly used to describe and categorize music. Various auto-tagging models and datasets have been proposed for the automatic music annotation with tags. However, the past approaches often neglect the fact that many of these tags largely depend on the user, especially the tags related to the context of music listening. In this paper, we address this problem by proposing a user-aware music auto-tagging system and evaluation protocol. Specifically, we use both the audio content and user information extracted from the user listening history to predict contextual tags for a given user/track pair. We propose a new dataset of music tracks annotated with contextual tags per user. We compare our model to the traditional audio-based model and study the influence of user embeddings on the classification quality. Our work shows that explicitly modeling the user listening history into the automatic tagging process could lead to more accurate estimation of contextual tags. (10.5281/zenodo.3961560)
  DOI : 10.5281/zenodo.3961560
• Asynchronous Reconfiguration with Byzantine Failures
  
  • Kuznetsov Petr
  • Tonkikh Andrei
  , 2020.
• Multi-cell Downlink Dimensioning in NB-IoT Networks
  
  • Nguyen Tuan Anh
  • Martins Philippe
  , 2020, pp.117-122. (10.1109/WiMob50308.2020.9253401)
  DOI : 10.1109/WiMob50308.2020.9253401
• Affine Tasks for k-Test-and-Set
  
  • Kuznetsov Petr
  • Rieutord Thibault
  , 2020. The paper proposes a surprisingly simple characterization of a classical class of models of distributed computing, captured by an affine task : A subcomplex of the second iteration of the standard chromatic subdivision. We show that the class of affine task we propose has an element equivalent, regarding task solvability, to any wait-free shared-memory model in which processes have additionally access to k-test-and-set objects. Our results thus extend existing affine characterization beyond fair models.
• A configuration tool for MQTT based OPC UA PubSub
  
  • Bellot Patrick
  • Liu Zepeng
  , 2020.
• Ordonnancement par similarité pour la biométrie : théorie et pratique
  
  • Vogel Robin
  , 2020. The rapid growth in population, combined with the increased mobility of people has created a need for sophisticated identity management systems.For this purpose, biometrics refers to the identification of individuals using behavioral or biological characteristics. The most popular approaches, i.e. fingerprint, iris or face recognition, are all based on computer vision methods. The adoption of deep convolutional networks, enabled by general purpose computing on graphics processing units, made the recent advances incomputer vision possible. These advances have led to drastic improvements for conventional biometric methods, which boosted their adoption in practical settings, and stirred up public debate about these technologies. In this respect, biometric systems providers face many challenges when learning those networks.In this thesis, we consider those challenges from the angle of statistical learning theory, which leads us to propose or sketch practical solutions. First, we answer to the proliferation of papers on similarity learningfor deep neural networks that optimize objective functions that are disconnected with the natural ranking aim sought out in biometrics. Precisely, we introduce the notion of similarity ranking, by highlighting the relationship between bipartite ranking and the requirements for similarities that are well suited to biometric identification. We then extend the theory of bipartite ranking to this new problem, by adapting it to the specificities of pairwise learning, particularly those regarding its computational cost. Usual objective functions optimize for predictive performance, but recentwork has underlined the necessity to consider other aspects when training a biometric system, such as dataset bias, prediction robustness or notions of fairness. The thesis tackles all of those three examplesby proposing their careful statistical analysis, as well as practical methods that provide the necessary tools to biometric systems manufacturers to address those issues, without jeopardizing the performance of their algorithms.
• Harvesting commonsense and hidden knowledge from web services
  
  • Romero Julien
  , 2020. In this thesis, we harvest knowledge of two different types from online resources . The first one is commonsense knowledge, i.e. intuitive knowledge shared by most people like ``the sky is blue''. We extract salient statements from query logs and question-answering by carefully designing question patterns. Next, we validate our statements by querying other web sources such as Wikipedia, Google Books, or image tags from Flickr. We aggregate these signals to create a final score for each statement. We obtain a knowledge base, QUASIMODO, which, compared to its competitors, has better precision and captures more salient facts.The other kind of knowledge we investigate is hidden knowledge, i.e. knowledge not directly given by a data provider. More concretely, some Web services allow accessing the data only through predefined access functions. To answer a user query, we have to combine different such access functions, i.e., we have to rewrite the query in terms of the functions. We study two different scenarios: In the first scenario, the access functions have the shape of a path, the knowledge base respects constraints called ``Unary Inclusion Dependencies'', and the query is atomic. We show that the problem is decidable in polynomial time, and we provide an algorithm with theoretical evidence. In the second scenario, we remove the constraints and create a new class of relevant plans called "smart plans". We show that it is decidable to find these plans and we provide an algorithm.
• Persistent Fault Analysis With Few Encryptions
  
  • Carré Sébastien
  • Guilley Sylvain
  • Rioul Olivier
  , 2020. Persistent fault analysis (PFA) consists in guessing block cipher secret keys by biasing their substitution box. This paper improves the original attack of Zhang et al. on AES-128 presented at CHES 2018. By a thorough analysis, the exact probability distribution of the ciphertext (under a uniformly distributed plaintext) is derived, and the maximum likelihood key recovery estimator is computed exactly. Its expression is turned into an attack algorithm, which is shown to be twice more efficient in terms of number of required encryptions than the original attack of Zhang et al. This algorithm is also optimized from a computational complexity standpoint. In addition, our optimal attack is naturally amenable to key enumeration, which expedites full 16-bytes key extraction. Various tradeoffs between data and computational complexities are investigated.
• Knowledge distillation from multi-modal to mono-modal segmentation networks
  
  • Hu Minhao
  • Maillard Matthis
  • Zhang Ya
  • Ciceri Tommaso
  • La Barbera Giammarco
  • Bloch Isabelle
  • Gori Pietro
  , 2020, LNCS 12261, pp.772-781. The joint use of multiple imaging modalities for medical image segmentation has been widely studied in recent years. The fusion of information from different modalities has demonstrated to improve the segmentation accuracy, with respect to mono-modal segmentations, in several applications. However, acquiring multiple modalities is usually not possible in a clinical setting due to a limited number of physicians and scanners, and to limit costs and scan time. Most of the time, only one modality is acquired. In this paper, we propose KD-Net, a framework to transfer knowledge from a trained multi-modal network (teacher) to a mono-modal one (student). The proposed method is an adaptation of the generalized distillation framework where the student network is trained on a subset (1 modality) of the teacher's inputs (n modalities). We illustrate the effectiveness of the proposed framework in brain tumor segmentation with the BraTS 2018 dataset. Using different architectures, we show that the student network effectively learns from the teacher and always outperforms the baseline mono-modal network in terms of seg-mentation accuracy.
• Weighted Emprirical Risk Minimization: Transfer Learning based on Importance Sampling
  
  • Vogel Robin
  • Achab Mastane
  • Clémençon Stéphan
  , 2020. We consider statistical learning problems, when the distribution P 0 of the training observations Z01, . . . , Z0n differs from the distribution P involved in the risk one seeks to minimize (referred to as the test distribution) but is still defined on the same measurable space as P and dominates it. In the unrealistic case where the likelihood ratio Φ(z) = dP/dP0 (z) is known, one may straightforwardly extends the Empirical Risk Minimization (ERM) approach to this specific transfer learning setup using the same idea as that behind Importance Sampling, by minimizing a weighted version of the empirical risk functional computed from the ’biased’ training data Z0 iwith weights Φ(Z0i). Although the importance function Φ(z) is generally unknown in practice, we show that, in various situations frequently encountered in practice, it takes a simple form and can be directly estimated from the Z 0 i ’s and some auxiliary information on the statistical population P. By means of linearization techniques, we then prove that the generalization capacity of the approach aforementioned is preserved when plugging the resulting estimates of the Φ(Z0i)’s into the weighted empirical risk. Beyond these theoretical guarantees, numerical results provide strong empirical evidence of the relevance of the approach promoted in this article.
• Variance-Reduced Methods for Machine Learning
  
  • Gower Robert M
  • Schmidt Mark
  • Bach Francis
  • Richtárik Peter
  Proceedings of the IEEE, Institute of Electrical and Electronics Engineers, 2020, 108 (11). Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago. The last 8 years have seen an exciting new development: variance reduction (VR) for stochastic optimization methods. These VR methods excel in settings where more than one pass through the training data is allowed, achieving a faster convergence than SGD in theory as well as practice. These speedups underline the surge of interest in VR methods and the fast-growing body of work on this topic. This review covers the key principles and main developments behind VR methods for optimization with finite data sets and is aimed at non-expert readers. We focus mainly on the convex setting, and leave pointers to readers interested in extensions for minimizing non-convex functions. optimization, machine learning, variance reduction * The classic way to implement GD is to determine γ as the approximate solution to min γ>0 f (x k − γ∇f (x k)). This is called a line search since it is an optimization over a (10.1109/JPROC.2020.3028013)
  DOI : 10.1109/JPROC.2020.3028013
• MULTILINGUAL LYRICS-TO-AUDIO ALIGNMENT
  
  • Vaglio Andrea
  • Hennequin Romain
  • Moussallam Manuel
  • Richard Gael
  • d'Alché-Buc Florence
  , 2020. Lyrics-to-audio alignment methods have recently reported impressive results, opening the door to practical applications such as karaoke and within song navigation. However , most studies focus on a single language-usually En-glish-for which annotated data are abundant. The question of their ability to generalize to other languages, especially in low (or even zero) training resource scenarios has been so far left unexplored. In this paper, we address the lyrics-to-audio alignment task in a generalized multilingual setup. More precisely, this investigation presents the first (to the best of our knowledge) attempt to create a language-independent lyrics-to-audio alignment system. Building on a Recurrent Neural Network (RNN) model trained with a Connectionist Temporal Classification (CTC) algorithm, we study the relevance of different intermediate representations, either character or phoneme, along with several strategies to design a training set. The evaluation is conducted on multiple languages with a varying amount of data available, from plenty to zero. Results show that learning from diverse data and using a universal phoneme set as an intermediate representation yield the best generalization performances.
• NeuroPycon: An open-source python toolbox for fast multi-modal and reproducible brain connectivity pipelines
  
  • Meunier David
  • Pascarella Annalisa
  • Altukhov Dmitrii
  • Jas Mainak
  • Combrisson Etienne
  • Lajnef Tarek
  • Bertrand-Dubois Daphné
  • Hadid Vanessa
  • Alamian Golnoush
  • Alves Jordan
  • Barlaam Fanny
  • Saive Anne-Lise
  • Dehgan Arthur
  • Jerbi Karim
  NeuroImage, Elsevier, 2020, 219, pp.117020. Keywords: Magnetoencephalography (MEG) Electroencephalography (EEG) Electrophysiology MRI Functional connectivity Graph theory Multi-modality Python MNE Source reconstruction Brain networks Nipype Brain imaging Reproducible science Pipelines A B S T R A C T Recent years have witnessed a massive push towards reproducible research in neuroscience. Unfortunately, this endeavor is often challenged by the large diversity of tools used, project-specific custom code and the difficulty to track all user-defined parameters. NeuroPycon is an open-source multi-modal brain data analysis toolkit which provides Python-based template pipelines for advanced multi-processing of MEG, EEG, functional and anatomical MRI data, with a focus on connectivity and graph theoretical analyses. Importantly, it provides shareable parameter files to facilitate replication of all analysis steps. NeuroPycon is based on the NiPype framework which facilitates data analyses by wrapping many commonly-used neuroimaging software tools into a common Python environment. In other words, rather than being a brain imaging software with is own implementation of standard algorithms for brain signal processing, NeuroPycon seamlessly integrates existing packages (coded in python, Matlab or other languages) into a unified python framework. Importantly, thanks to the multi-threaded processing and computational efficiency afforded by NiPype, NeuroPycon provides an easy option for fast parallel processing, which critical when handling large sets of multi-dimensional brain data. Moreover, its flexible design allows users to easily configure analysis pipelines by connecting distinct nodes to each other. Each node can be a Python-wrapped module, a user-defined function or a well-established tool (e.g. MNE-Python for MEG analysis, Rada-tools for graph theoretical metrics, etc.). Last but not least, the ability to use NeuroPycon parameter files to fully describe any pipeline is an important feature for reproducibility, as they can be shared and used for easy repli-cation by others. The current implementation of NeuroPycon contains two complementary packages: The first, called ephypype, includes pipelines for electrophysiology analysis and a command-line interface for on the fly pipeline creation. Current implementations allow for MEG/EEG data import, pre-processing and cleaning by automatic removal of ocular and cardiac artefacts, in addition to sensor or source-level connectivity analyses. The second package, called graphpype, is designed to investigate functional connectivity via a wide range of graph-theoretical metrics, including modular partitions. The present article describes the philosophy, architecture, and functionalities of the toolkit and provides illustrative examples through interactive notebooks. NeuroPycon is available for download via github (https://github.com/neuropycon) and the two principal packages are documented online (https://neuropycon.github.io/ephypype/index.html, and https://neuropycon.github.io/graph pype/index.html). Future developments include fusion of multi-modal data (eg. MEG and fMRI or intracranial EEG and fMRI). We hope that the release of NeuroPycon will attract many users and new contributors, and (10.1016/j.neuroimage.2020.117020)
  DOI : 10.1016/j.neuroimage.2020.117020
• SECRET KEY ESTIMATION METHODS AND DEVICES
  
  • Rioul Olivier
  • Guilley Sylvain
  , 2020. A secret key estimation device is provided for determining an estimate of at least one secret key used during a number of executions of a cryptographic function used by at least one cryptographic algorithm. The number of executions of the cryptographic function is at least equal to two. The secret key estimation device comprises an analysis unit for determining a plurality of sets of leakage traces from a side-channel information acquired during the number of executions of the cryptographic function. Each set of leakage traces corresponds to an execution of the cryptographic function and comprising at least one leakage trace. The secret key estimation device further comprises a processing unit configured to determine a statistical distribution of the acquired plurality of sets of leakage traces. The statistical distribution is dependent on a leakage function, the leakage function being represented in a basis of functions by a set of real values. The secret key estimation device is configured to determine the secret key from the statistical distribution of the plurality of sets of leakage traces using an estimation algorithm according to the maximization of a performance metric.