What is the Effect of Importance Weighting in Deep Learning?
This addresses a gap in understanding importance weighting for over-parameterized models, which is incremental as it builds on prior theoretical work but has practical implications for practitioners in fields like causal inference and domain adaptation.
The study investigated the impact of importance weighting in deep neural networks, finding that its effect diminishes over training epochs and is partially restored by L2 regularization and batch normalization, but not dropout, across various architectures and datasets.
Importance-weighted risk minimization is a key ingredient in many machine learning algorithms for causal inference, domain adaptation, class imbalance, and off-policy reinforcement learning. While the effect of importance weighting is well-characterized for low-capacity misspecified models, little is known about how it impacts over-parameterized, deep neural networks. This work is inspired by recent theoretical results showing that on (linearly) separable data, deep linear networks optimized by SGD learn weight-agnostic solutions, prompting us to ask, for realistic deep networks, for which many practical datasets are separable, what is the effect of importance weighting? We present the surprising finding that while importance weighting impacts models early in training, its effect diminishes over successive epochs. Moreover, while L2 regularization and batch normalization (but not dropout), restore some of the impact of importance weighting, they express the effect via (seemingly) the wrong abstraction: why should practitioners tweak the L2 regularization, and by how much, to produce the correct weighting effect? Our experiments confirm these findings across a range of architectures and datasets.