Principal Polynomial Analysis

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In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

In the past few years, Machine Learning (ML) techniques have ushered in a paradigm shift, allowing the harnessing of ever more abundant sources of data to automate complex tasks. The technical workhorse behind these important breakthroughs arguably lies in ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of nature. We stud ...

In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

This dataset contains a collection of ultrafast ultrasound acquisitions from nine volunteers and the CIRS 054G phantom. For a comprehensive understanding of the dataset, please refer to the paper: Viñals, R.; Thiran, J.-P. A KL Divergence-Based Loss for In ...

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...

We introduce robust principal component analysis from a data matrix in which the entries of its columns have been corrupted by permutations, termed Unlabeled Principal Component Analysis (UPCA). Using algebraic geometry, we establish that UPCA is a well-de ...

Machine learning (ML) enables artificial intelligent (AI) agents to learn autonomously from data obtained from their environment to perform tasks. Modern ML systems have proven to be extremely effective, reaching or even exceeding human intelligence. Altho ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

In this thesis we explore the applications of projective geometry, a mathematical theory of the relation between 3D scenes and their 2D images, in modern learning-based computer vision systems. This is an interesting research question which contradicts the ...

Modern neuroscience research is generating increasingly large datasets, from recording thousands of neurons over long timescales to behavioral recordings of animals spanning weeks, months, or even years. Despite a great variety in recording setups and expe ...

Principal Polynomial Analysis

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From low-rank retractions to dynamical low-rank approximation and back

Random matrix methods for high-dimensional machine learning models

Topics in statistical physics of high-dimensional machine learning

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Social Opinion Formation and Decision Making Under Communication Trends

Understanding generalization and robustness in modern deep learning

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (1/6)

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (4/6)

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (6/6)

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (5/6)

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (3/6)

A KL Divergence-Based Loss for In Vivo Ultrafast Ultrasound Image Enhancement with Deep Learning: Dataset (2/6)

Towards Trustworthy Deep Learning for Image Reconstruction

Interpret3C: Interpretable Student Clustering Through Individualized Feature Selection

Unlabeled Principal Component Analysis and Matrix Completion

Few-shot Learning for Efficient and Effective Machine Learning Model Adaptation

Anomalous and Chern topological waves in hyperbolic networks

Incorporating Projective Geometry into Deep Learning

Robust machine learning for neuroscientific inference