Modulation Spaces and the Curse of Dimensionality

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A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic descripti ...

Dexterous in-hand manipulation in robotics, particularly with multi-fingered robotic hands, poses significant challenges due to the intricate avoidance of collisions among fingers and the object being manipulated. Collision-free paths for all fingers must ...

Principal component analysis (PCA) is an essential algorithm for dimensionality reduction in many data science domains. We address the problem of performing a federated PCA on private data distributed among multiple data providers while ensuring data confi ...

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is therefore key to unde ...

In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...

We study the problem of learning unknown parameters of stochastic dynamical models from data. Often, these models are high dimensional and contain several scales and complex structures. One is then interested in obtaining a reduced, coarse-grained descript ...

During the last twenty years, Random matrix theory (RMT) has produced numerous results that allow a better understanding of large random matrices. These advances have enabled interesting applications in the domain of communication. Although this theory can ...

Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient algorithm for detecti ...

In this work, we study graph-based multi-arms bandit (MAB) problems aimed at optimizing actions on irregular and high-dimensional graphs. More formally, we consider a decision-maker that takes sequential actions over time and observes the experienced rewar ...

How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ...

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: ...

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the c ...

SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to ...

Amplitude and frequency are the two primary features of one-dimensional signals, and thus both are widely utilized to analysis data in numerous fields. While amplitude can be examined directly, frequency requires more elaborate approaches, except in the si ...

Modulation Spaces and the Curse of Dimensionality

Chattez avec Graph Search

Spectral Estimators for High-Dimensional Matrix Inference

Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression

Enhancing Dexterity in Confined Spaces: Real-Time Motion Planning for Multifingered In-Hand Manipulation

Scalable and Privacy-Preserving Federated Principal Component Analysis

Fluctuations, bias, variance and ensemble of learners: exact asymptotics for convex losses in high-dimension

Structure-preserving approaches and data-driven closure modeling for model order reduction

Filtered data and eigenfunction estimators for statistical inference of multiscale and interacting diffusion processes

Statistical Applications of Random Matrix Theory: Comparison of Two Populations

Streaming Principal Component Analysis From Incomplete Data

Spectral MAB for Unknown Graph Processes

Spectrally approximating large graphs with smaller graphs

Graph-based Methods for Visualization and Clustering

Fast Robust PCA on Graphs

LDAHash: Improved Matching with Smaller Descriptors

Efficient Schemes for Adaptive Frequency Tracking and their Relevance for EEG and ECG