Statistical Structure

Statistical structure analysis focuses on uncovering the underlying patterns and dependencies within complex datasets, aiming to move beyond simple pairwise relationships to capture higher-order interactions. Current research employs diverse approaches, including deep learning architectures like physics-informed neural networks for solving stochastic dynamics and random matrix theory to analyze eigenvalue statistics of covariance matrices, as well as exploring the limitations of graph neural networks in handling certain random structures. These investigations are crucial for improving the performance of machine learning algorithms, enhancing our understanding of complex systems across various scientific domains, and enabling more accurate modeling of real-world phenomena.

Papers

November 8, 2023

Solution of FPK Equation for Stochastic Dynamics Subjected to Additive Gaussian Noise via Deep Learning Approach
Amir H. Khodabakhsh, Seid H. Pourtakdoust
Solution Path Deep Learning Approach Gaussian Noise Stochastic Dynamical System Statistical Structure

June 26, 2023

The Underlying Scaling Laws and Universal Statistical Structure of Complex Datasets
Noam Levi, Yaron Oz
Scaling Law Random Matrix Complex Datasets Power Law Scaling Statistical Structure Eigenvalue Distribution

June 5, 2023

Barriers for the performance of graph neural networks (GNN) in discrete random structures. A comment on~\cite{schuetz2022combinatorial},\cite{angelini2023modern},\cite{schuetz2023reply}
David Gamarnik
Neural Network Graph Neural Network Graph Drawing Combinatorial Optimization Problem Knowledge Barrier Independent Set Statistical Structure

June 1, 2023

Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions
Zhaolu Liu, Robert L. Peach, Pedro A. M. Mediano, Mauricio Barahona
Order Interaction Distributive Lattice Kernel Test Statistical Structure

March 6, 2023

Learning multi-scale local conditional probability models of images
Zahra Kadkhodaie, Florentin Guth, Stéphane Mallat, Eero P Simoncelli
LeArning Abstract Receptive Field Digital Image Score Based Diffusion Low Dimensional Multi Scale Decomposition Statistical Structure

March 3, 2023

Linear CNNs Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequencies
Hannah Pinson, Joeri Lenaerts, Vincent Ginis
Convolutional Neural Network Data Set Convolutional Structure Dominant Low Frequency Statistical Structure

January 20, 2022

Learning with latent group sparsity via heat flow dynamics on networks
Subhroshekhar Ghosh, Soumendu Sundar Mukherjee
LeArning Abstract Network Programming Stochastic Block Model Network Science Spatial Network Group Sparsity Statistical Structure

Statistical Structure

Papers

Solution of FPK Equation for Stochastic Dynamics Subjected to Additive Gaussian Noise via Deep Learning Approach

The Underlying Scaling Laws and Universal Statistical Structure of Complex Datasets

Barriers for the performance of graph neural networks (GNN) in discrete random structures. A comment on~\cite{schuetz2022combinatorial},\cite{angelini2023modern},\cite{schuetz2023reply}

Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions

Learning multi-scale local conditional probability models of images

Linear CNNs Discover the Statistical Structure of the Dataset Using Only the Most Dominant Frequencies

Learning with latent group sparsity via heat flow dynamics on networks