Tensor-based regression models and applications

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2017-2018Avec l’avancement des technologies modernes, les tenseurs d’ordre élevé sont assez répandus et abondent dans un large éventail d’applications telles que la neuroscience informatique, la vision par ordinateur, le traitement du signal et ainsi de suite. La principale raison pour laquelle les méthodes de régression classiques ne parviennent pas à traiter de façon appropriée des tenseurs d’ordre élevé est due au fait que ces données contiennent des informations structurelles multi-voies qui ne peuvent pas être capturées directement par les modèles conventionnels de régression vectorielle ou matricielle. En outre, la très grande dimensionnalité de l’entrée tensorielle produit une énorme quantité de paramètres, ce qui rompt les garanties théoriques des approches de régression classique. De plus, les modèles classiques de régression se sont avérés limités en termes de difficulté d’interprétation, de sensibilité au bruit et d’absence d’unicité. Pour faire face à ces défis, nous étudions une nouvelle classe de modèles de régression, appelés modèles de régression tensor-variable, où les prédicteurs indépendants et (ou) les réponses dépendantes prennent la forme de représentations tensorielles d’ordre élevé. Nous les appliquons également dans de nombreuses applications du monde réel pour vérifier leur efficacité et leur efficacité.With the advancement of modern technologies, high-order tensors are quite widespread and abound in a broad range of applications such as computational neuroscience, computer vision, signal processing and so on. The primary reason that classical regression methods fail to appropriately handle high-order tensors is due to the fact that those data contain multiway structural information which cannot be directly captured by the conventional vector-based or matrix-based regression models, causing substantial information loss during the regression. Furthermore, the ultrahigh dimensionality of tensorial input produces huge amount of parameters, which breaks the theoretical guarantees of classical regression approaches. Additionally, the classical regression models have also been shown to be limited in terms of difficulty of interpretation, sensitivity to noise and absence of uniqueness. To deal with these challenges, we investigate a novel class of regression models, called tensorvariate regression models, where the independent predictors and (or) dependent responses take the form of high-order tensorial representations. We also apply them in numerous real-world applications to verify their efficiency and effectiveness. Concretely, we first introduce hierarchical Tucker tensor regression, a generalized linear tensor regression model that is able to handle potentially much higher order tensor input. Then, we work on online local Gaussian process for tensor-variate regression, an efficient nonlinear GPbased approach that can process large data sets at constant time in a sequential way. Next, we present a computationally efficient online tensor regression algorithm with general tensorial input and output, called incremental higher-order partial least squares, for the setting of infinite time-dependent tensor streams. Thereafter, we propose a super-fast sequential tensor regression framework for general tensor sequences, namely recursive higher-order partial least squares, which addresses issues of limited storage space and fast processing time allowed by dynamic environments. Finally, we introduce kernel-based multiblock tensor partial least squares, a new generalized nonlinear framework that is capable of predicting a set of tensor blocks by merging a set of tensor blocks from different sources with a boosted predictive power

Principled methods for mixtures processing

This document is my thesis for getting the habilitation à diriger des recherches, which is the french diploma that is required to fully supervise Ph.D. students. It summarizes the research I did in the last 15 years and also provides the short­term research directions and applications I want to investigate. Regarding my past research, I first describe the work I did on probabilistic audio modeling, including the separation of Gaussian and α­stable stochastic processes. Then, I mention my work on deep learning applied to audio, which rapidly turned into a large effort for community service. Finally, I present my contributions in machine learning, with some works on hardware compressed sensing and probabilistic generative models.My research programme involves a theoretical part that revolves around probabilistic machine learning, and an applied part that concerns the processing of time series arising in both audio and life sciences

An Adaptive Strategy for Sensory Processing

Recognizing objects and detecting associations among them is essential for the survival of organisms. The ability to perform these tasks is derived from the representations of objects obtained through processing information along sensory pathways. Our current understanding of sensory processing is based on two sets of foundational theories – The Efficient Coding Hypothesis and hierarchical assembly of object representations. These theories suggest that sensory processing aims to identify independent features of the environment and progressively represent objects in terms of comprehensive combinations of these features. Separately, the two sets of theories have successfully explained the detection of associations and perceptual invariance, respectively; however, reconciling them together in one unified theory has remained challenging. Independent features are deemed essential for detecting association by the Efficient coding hypothesis, but to achieve consistency in representations, multiple comprehensive structures corresponding to the same object must be hierarchically assembled, ignoring independence among such structures. Here we propose an alternative framework for sensory processing in which the system, instead of finding the truly independent components of the environment, aims to represent objects based on their most informative structures. Using theoretical arguments, we show that following such a strategy allows the system to efficiently represent sensory cues without necessarily acquiring knowledge about statistical properties of all possible inputs. Through mathematical simulations, we find that the framework can describe the known characteristics of early sensory processing stages and permits consistent input representations observed at later stages of processing. We also demonstrate that the framework can be implemented in a biologically plausible neuronal circuit and explain aspects of experience and learning from corrupted inputs. Thus, this framework provides a novel perspective and a unified description of sensory processing in its entirety

Online Audio-Visual Multi-Source Tracking and Separation: A Labeled Random Finite Set Approach

The dissertation proposes an online solution for separating an unknown and time-varying number of moving sources using audio and visual data. The random finite set framework is used for the modeling and fusion of audio and visual data. This enables an online tracking algorithm to estimate the source positions and identities for each time point. With this information, a set of beamformers can be designed to separate each desired source and suppress the interfering sources

Efficient and Robust Methods for Audio and Video Signal Analysis

This thesis presents my research concerning audio and video signal processing and machine learning. Specifically, the topics of my research include computationally efficient classifier compounds, automatic speech recognition (ASR), music dereverberation, video cut point detection and video classification.Computational efficacy of information retrieval based on multiple measurement modalities has been considered in this thesis. Specifically, a cascade processing framework, including a training algorithm to set its parameters has been developed for combining multiple detectors or binary classifiers in computationally efficient way. The developed cascade processing framework has been applied on video information retrieval tasks of video cut point detection and video classification. The results in video classification, compared to others found in the literature, indicate that the developed framework is capable of both accurate and computationally efficient classification. The idea of cascade processing has been additionally adapted for the ASR task. A procedure for combining multiple speech state likelihood estimation methods within an ASR framework in cascaded manner has been developed. The results obtained clearly show that without impairing the transcription accuracy the computational load of ASR can be reduced using the cascaded speech state likelihood estimation process.Additionally, this thesis presents my work on noise robustness of ASR using a nonnegative matrix factorization (NMF) -based approach. Specifically, methods for transformation of sparse NMF-features into speech state likelihoods has been explored. The results reveal that learned transformations from NMF activations to speech state likelihoods provide better ASR transcription accuracy than dictionary label -based transformations. The results, compared to others in a noisy speech recognition -challenge show that NMF-based processing is an efficient strategy for noise robustness in ASR.The thesis also presents my work on audio signal enhancement, specifically, on removing the detrimental effect of reverberation from music audio. In the work, a linear prediction -based dereverberation algorithm, which has originally been developed for speech signal enhancement, was applied for music. The results obtained show that the algorithm performs well in conjunction with music signals and indicate that dynamic compression of music does not impair the dereverberation performance

SIS 2017. Statistics and Data Science: new challenges, new generations

The 2017 SIS Conference aims to highlight the crucial role of the Statistics in Data Science. In this new domain of ‘meaning’ extracted from the data, the increasing amount of produced and available data in databases, nowadays, has brought new challenges. That involves different fields of statistics, machine learning, information and computer science, optimization, pattern recognition. These afford together a considerable contribute in the analysis of ‘Big data’, open data, relational and complex data, structured and no-structured. The interest is to collect the contributes which provide from the different domains of Statistics, in the high dimensional data quality validation, sampling extraction, dimensional reduction, pattern selection, data modelling, testing hypotheses and confirming conclusions drawn from the data

Proceedings of the 19th Sound and Music Computing Conference

Proceedings of the 19th Sound and Music Computing Conference - June 5-12, 2022 - Saint-Étienne (France). https://smc22.grame.f