Javier Abad

Piersilvio De Bartolomeis, Javier Abad, Guanbo Wang et al. · eth-zurich

Randomized experiments are the preferred approach for evaluating the effects of interventions, but they are costly and often yield estimates with substantial uncertainty. On the other hand, in silico experiments leveraging foundation models offer a cost-effective alternative that can potentially attain higher statistical precision. However, the benefits of in silico experiments come with a significant risk: statistical inferences are not valid if the models fail to accurately predict experimental responses to interventions. In this paper, we propose a novel approach that integrates the predictions from multiple foundation models with experimental data while preserving valid statistical inference. Our estimator is consistent and asymptotically normal, with asymptotic variance no larger than the standard estimator based on experimental data alone. Importantly, these statistical properties hold even when model predictions are arbitrarily biased. Empirical results across several randomized experiments show that our estimator offers substantial precision gains, equivalent to a reduction of up to 20% in the sample size needed to match the same precision as the standard estimator based on experimental data alone.

Javier Abad, Umang Bhatt, Adrian Weller et al.

Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level $\varepsilon$, CP guarantees that the error rate is at most $\varepsilon$, irrespective of whether the underlying model is misspecified. However, the prohibitive computational costs of "full" CP led researchers to design scalable alternatives, which alas do not attain the same guarantees or statistical power of full CP. In this paper, we use influence functions to efficiently approximate full CP. We prove that our method is a consistent approximation of full CP, and empirically show that the approximation error becomes smaller as the training set increases; e.g., for $10^{3}$ training points the two methods output p-values that are $<10^{-3}$ apart: a negligible error for any practical application. Our methods enable scaling full CP to large real-world datasets. We compare our full CP approximation (ACP) to mainstream CP alternatives, and observe that our method is computationally competitive whilst enjoying the statistical predictive power of full CP.