Transformers can optimally learn regression mixture models
This addresses the challenge of flexible, general-purpose prediction in mixture models, which are common in regression but often rely on model-specific methods, though it is incremental in applying transformers to this setting.
The paper tackles the problem of learning optimal predictors for mixtures of linear regressions, showing that transformers achieve low mean-squared error and closely approximate the optimal predictor in experiments, with sample-efficient learning and some robustness to distribution shifts.
Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.