NeurIPS 2024 Papers

Canonical work handling distribution shifts typically necessitates an entire target distribution that lands inside the training distribution. However, practical scenarios often involve only a handful target samples, potentially lying outside the training support, which requires the capability of extrapolation. In this work, we aim to provide a theoretical understanding of when extrapolation is possible and offer principled methods to achieve it without requiring an on-support target distribution. To this end, we formulate the extrapolation problem with a latent-variable model that embodies the minimal change principle in causal mechanisms. Under this formulation, we cast the extrapolation problem into a latent-variable identification problem. We provide realistic conditions on shift properties and the estimation objectives that lead to identification even when only one off-support target sample is available, tackling the most challenging scenarios. Our theory reveals the intricate interplay between the underlying manifold's smoothness and the shift properties. We showcase how our theoretical results inform the design of practical adaptation algorithms. Through experiments on both synthetic and real-world data, we validate our theoretical findings and their practical implications.

A fundamental task in AI is providing performance guarantees for predictions made in unseen domains. In practice, there can be substantial uncertainty about the distribution of new data, and corresponding variability in the performance of existing predictors. Building on the theory of partial identification and transportability, this paper introduces new results for bounding the value of a functional of the target distribution, such as the generalization error of a classifiers, given data from source domains and assumptions about the data generating mechanisms, encoded in causal diagrams. Our contribution is to provide the first general estimation technique for transportability problems, adapting existing parameterization schemes such Neural Causal Models to encode the structural constraints necessary for cross-population inference. We demonstrate the expressiveness and consistency of this procedure and further propose a gradient-based optimization scheme for making scalable inferences in practice. Our results are corroborated with experiments.

We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require matrix inversions nor mini-batches thereby providing a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, we derive rates of convergence in expectation, that are of order $\mathcal{O}(\log T/T)$ and $\mathcal{O}(1/T^{1-\epsilon})$ for any $\epsilon>0$, respectively under the availability of two-sample and one-sample oracles respectively. Importantly, under the availability of the two-sample oracle, the aforementioned rate is actually agnostic to the relationship between confounder and the instrumental variable demonstrating the flexibility of the proposed approach in alleviating the need for explicit model assumptions required in recent works based on reformulating the problem as min-max optimization problems. Experimental validation is provided to demonstrate the advantages of the proposed algorithms over classical approaches like the 2SLS method.