Inverse Dimensionality Reduction

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Inverse dimensionality reduction studies how compact representations relate to the original data: how to reconstruct or synthesize data from embeddings, identify what projections preserve, and find reduced representations sufficient for prediction. Methods include parametric and invertible autoencoders with uncertainty estimates, continuous neural-operator embeddings, local attribution and distortion analysis, and sufficient-dimension-reduction techniques such as kernel gradient methods, MAVE, and generative regression. Applications include visualization, scientific data analysis, hyperspectral imaging, and distributional prediction, where compact representations can aid interpretation or reduce computation. A central challenge is balancing local and global geometric fidelity, reconstruction and predictive sufficiency, and computational or sample efficiency; low-dimensional coordinates do not necessarily recover meaningful original variables.

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Sufficiently Reduced Distributional Regression
Sep 24, 2026Alexander Henzi, Tiange Liu, Xinwei ShenConditional Distribution Estimation Inverse Dimensionality Reduction
Tsinghua University, Department of Statistics and Data Science · University of Washington
Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework
Sep 21, 2026Arjun KM, Shashi JainPrincipal Component Analysis Algorithmic Fairness
Department of Management Studies Indian Institute of Science, Bangalore
Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression
Sep 20, 2026Wenxi Tan, Bing Li, Lingzhou XueConditional Distribution Estimation Inverse Dimensionality Reduction
Department of Statistics, The Pennsylvania State University
FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction
Jul 29, 2026Lucas Greff Meneses, Evandro S. Ortigossa, Claudio Silva +1Feature Attribution Inverse Dimensionality Reduction
University of São Paulo · Weizmann Institute of Science · New York University
Riemannian Stochastic Optimization for Sufficient Dimension Reduction
May 29, 2026Thibault Pautrel, François PortierStochastic Optimization Riemannian Optimization
Laboratoire des Signaux et Systèmes (L2S), CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France · ENSAI, CREST, Bruz, France
Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models
May 14, 2026Libin Zhu, Damek Davis, Dmitriy Drusvyatskiy +1Kernel Ridge Regression Representation Learning
Department of Mathematics, University of Washington, Seattle, WA 98195 · Wharton Department of Statistics and Data Science, University of Pennsylvania, Philadelphia, PA 19104, USA · Department of Mathematics, U. Washington, Seattle, WA 98195 +1
Color Constancy in Hyperspectral Imaging via Reduced Spectral Spaces
May 13, 2026G. Dofri Vidarsson, Liying Lu, Sabine SüsstrunkColor Constancy Hyperspectral Imaging
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
NOFE - Neural Operator Function Embedding
May 12, 2026Lars Uebbing, Harald L. Joakimsen, Siyan Chen +6Inverse Dimensionality Reduction Sheaf Neural Networks
1UiT The Arctic University of Norway · 2Norwegian Computing Center · University of South Brittany +1
PCA-Based Interpretable Knowledge Representation and Analysis of Geometric Design Parameters
Mar 18, 2026Alexander Köhler, Michael BreußPrincipal Component Analysis Inverse Dimensionality Reduction
Brandenburgische Technische Universität Platz der deutschen Einheit 1, 03046 Cottbus, Germany
DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy
Aug 16, 2025Frederik L. Dennig, Daniel A. KeimVariational Autoencoders Uncertainty Quantification
University of Konstanz

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Sufficiently Reduced Distributional Regression

Alexander Henzi, Tiange Liu, Xinwei Shen

Tsinghua University, Department of Statistics and Data Science · University of Washington

Conditional Distribution Estimation Inverse Dimensionality Reduction Dimensionality Reduction Distributional Regression Conditional Generative Modeling

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We propose Sufficiently Reduced Distributional Regression (SRDR), a generative method that combines conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). It builds on a characterization of sufficiency through strictly proper scoring rules: a dimension reduction is sufficient if and only if predicting the response from the reduced covariates incurs no loss in expected score relative to the full covariates. Sufficient dimension reduction thus becomes a risk minimization problem. SRDR jointly trains a dimension reduction map and a generative prediction model by minimizing the energy score, which can be estimated by sampling without density evaluation or adversarial training. The framework extends to multi-environment data and to classification. We prove that the estimated conditional distributions converge in energy distance to the true ones, which implies that the learned representation is asymptotically sufficient. In simulations and applications to CT slice localization, superconductivity, and digit classification, SRDR recovers low-dimensional sufficient structure and matches or outperforms state-of-the-art nonlinear SDR methods in representation quality and predictive performance.