Principal Differences Analysis: Interpretable Characterization of Differences between Distributions
We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate populations. Relying on the Cramer-Wold device, it requires no assumptions about the form of the underlying distributions, nor the nature of their inter-class differences. A sparse variant of the method is introduced to identify features responsible for the differences. We provide algorithms for both the original minimax formulation as well as its semidefinite relaxation. In addition to deriving some convergence results, we illustrate how the approach may be applied to identify differences between cell populations in the somatosensory cortex and hippocampus as manifested by single cell RNA-seq. Our broader framework extends beyond the specific choice of Wasserstein divergence.
Code (1)
Tasks
HippocampusSimilar Papers 제목 키워드 기반
Principal Component Analysis When n < p: Challenges and Solutions
Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by t…
Dimensionality ReductionJoint Characterization of the Cryospheric Spectral Feature Space
Hyperspectral feature spaces are useful for many remote sensing applications ranging from spectral mixture modeling to discrete thematic classification. In such cases, characterization of the feature space dimensionality…
ClusteringDimensionality ReductionXAI-Driven Spectral Analysis of Cough Sounds for Respiratory Disease Characterization
This paper proposes an eXplainable Artificial Intelligence (XAI)-driven methodology to enhance the understanding of cough sound analysis for respiratory disease management. We employ occlusion maps to highlight relevant …
An online algorithm for contrastive Principal Component Analysis
Finding informative low-dimensional representations that can be computed efficiently in large datasets is an important problem in data analysis. Recently, contrastive Principal Component Analysis (cPCA) was proposed as a…
Contrastive LearningInterpretable Machine Learning for Kronecker Coefficients
We analyze the saliency of neural networks and employ interpretable machine learning models to predict whether the Kronecker coefficients of the symmetric group are zero or not. Our models use triples of partitions as in…
Interpretable Machine Learning