Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

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Fuel performance codes are essential for predicting fuel rod behavior in nuclear reactors. These codes comprise a complex system of models with empirical constants that require calibration against experimental data. To support this calibration, this study ...

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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 ...

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representatio ...

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 ...

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 ...

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 ...

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In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...

In the current era of big data, aggregation queries on high-dimensional datasets are frequently utilized to uncover hidden patterns, trends, and correlations critical for effective business decision-making. Data cubes facilitate such queries by employing p ...

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been ...

We present Sudokube, a novel system that supports interactive speed querying on high-dimensional data using partially materialized data cubes. Given a storage budget, it judiciously chooses what projections to precompute and materialize during cube constru ...

Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

Chattez avec Graph Search

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Learning Privacy from Visual Entities

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How Deep Neural Networks Learn Compositional Data: The Random Hierarchy Model

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

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

Topics in statistical physics of high-dimensional machine learning

Random matrix methods for high-dimensional machine learning models

Aggregating Spatial and Photometric Context for Photometric Stereo

Spectral Estimators for High-Dimensional Matrix Inference

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Sparse Autoencoders for Speech Modeling and Recognition

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Short homology bases for hyperelliptic hyperbolic surfaces

Interactive-time Exploration, Querying, and Analysis of Large High-dimensional Datasets

Robust Collaborative Learning with Linear Gradient Overhead

Aggregation and Exploration of High-Dimensional Data Using the Sudokube Data Cube Engine