Distribution-Based Invariant Deep Networks for Learning Meta-Features

TL;DR

This paper introduces Dida, a neural architecture that achieves permutation invariance over features for learning dataset meta-features, demonstrating superior performance on dataset-level tasks compared to existing methods.

Contribution

The paper extends distribution-based neural networks to be invariant under feature permutation and empirically validates its effectiveness on dataset characterization tasks.

Findings

Dida outperforms state-of-the-art methods on dataset matching tasks.

Dida effectively characterizes datasets for hyper-parameter performance prediction.

The architecture is robust to Lipschitz-bounded transformations.

Abstract

Recent advances in deep learning from probability distributions successfully achieve classification or regression from distribution samples, thus invariant under permutation of the samples. The first contribution of the paper is to extend these neural architectures to achieve invariance under permutation of the features, too. The proposed architecture, called Dida, inherits the NN properties of universal approximation, and its robustness w.r.t. Lipschitz-bounded transformations of the input distribution is established. The second contribution is to empirically and comparatively demonstrate the merits of the approach on two tasks defined at the dataset level. On both tasks, Dida learns meta-features supporting the characterization of a (labelled) dataset. The first task consists of predicting whether two dataset patches are extracted from the same initial dataset. The second task consists of predicting whether the learning performance achieved by a hyper-parameter configuration under a fixed algorithm (ranging in k-NN, SVM, logistic regression and linear classifier with SGD) dominates that of another configuration, for a dataset extracted from the OpenML benchmarking suite. On both tasks, Dida outperforms the state of the art: DSS (Maron et al., 2020) and Dataset2Vec (Jomaa et al., 2019) architectures, as well as the models based on the hand-crafted meta-features of the literature.