Depth Function

Statistical depth functions quantify the centrality of data points within a distribution, providing a measure of how "deep" a point lies within the data cloud. Current research focuses on extending depth functions to non-standard data types like partial orders and high-dimensional spaces, particularly for applications in machine learning (e.g., uncertainty quantification in neural networks, classifier comparison, and text embedding analysis) and other fields (e.g., power grid optimization). These methods offer improved ways to analyze complex datasets, enabling more robust uncertainty estimation, more insightful comparisons of machine learning algorithms, and more effective scenario selection in risk management. The development and application of depth functions are thus significantly impacting various scientific fields by providing powerful tools for data analysis and decision-making.

Papers

April 12, 2024

Combining Statistical Depth and Fermat Distance for Uncertainty Quantification
Hai-Vy Nguyen, Fabrice Gamboa, Reda Chhaibi, Sixin Zhang, Serge Gratton, Thierry Giaccone
Neural Network Uncertainty Quantification Depth Estimation Feature Space Parameter Uncertainty Select and Combine Better Uncertainty Estimation Depth Function Fermat Distance

December 20, 2023

Comparing Machine Learning Algorithms by Union-Free Generic Depth
Hannah Blocher, Georg Schollmeyer, Malte Nalenz, Christoph Jansen
Machine Learning Algorithm Large Depth Simplicial Complex Infinite Depth Depth Function

October 30, 2023

DiffEnc: Variational Diffusion with a Learned Encoder
Beatrix M. G. Nielsen, Anders Christensen, Andrea Dittadi, Ole Winther
Diffusion Model Hierarchical Variational Deep Encoder Diffusion Loss Depth Function

October 23, 2023

Statistical Depth for Ranking and Characterizing Transformer-Based Text Embeddings
Parker Seegmiller, Sarah Masud Preum
Text Embeddings Partial Ranking Text Transformation NLP Pipeline Depth Function Statistical Depth

September 20, 2023

Extreme Scenario Selection in Day-Ahead Power Grid Operational Planning
Guillermo Terrén-Serrano, Michael Ludkovski
Renewable Generation Operational Risk Depth Function Scenario Selection

April 19, 2023

Depth Functions for Partial Orders with a Descriptive Analysis of Machine Learning Algorithms
Hannah Blocher, Georg Schollmeyer, Christoph Jansen, Malte Nalenz
Machine Learning Algorithm Large Depth Description Library Simplicial Complex Partial Order Depth Function

March 21, 2023

Learning a Depth Covariance Function
Eric Dexheimer, Andrew J. Davison
LeArning Abstract Depth Completion Direct Sparse Odometry Geometric Vision Depth Function

July 26, 2022

Differentially Private Estimation via Statistical Depth
Ryan Cumings-Menon
Differential Privacy Privacy Budget Private Estimation Private Linear Regression Approximate Differential Privacy Depth Function

January 20, 2022

Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications
Morgane Goibert, Stéphan Clémençon, Ekhine Irurozki, Pavlo Mozharovskyi
Financial Application Consensus Group Decision Statistical Learning Definition Defining Redefinition Machine Permutation Random Permutation Geometric Median Depth Function