Deep Single-Index Fréchet Regression
Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fréchet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index structure for the conditional Fréchet mean. DeSI estimates an interpretable index direction, which quantifies the relative importance of inputs, using a deep neural network, and performs Fréchet regression along the resulting one-dimensional index in the targ...
| Authors | Muqing Cui, Yidong Zhou, Su I Iao et al. |
|---|---|
| Primary category | stat.ML |
| Published | 5 June 2026 |
| Last updated at source | 5 June 2026 |
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