We consider learning from labeled data collected across multiple environments, where the data distribution may vary across these environments. This problem is commonly approached from a causal perspective, seeking invariant representations that retain causal factors while discarding spurious ones. However, this framework assumes that the environment has no direct effect on the target. In contrast, we consider settings in which this assumption fails, but still aim to learn representations that support robust prediction on average across previously unseen environments. To this end, we study representations learned by explicitly modeling variation across environments and then marginalizing that variation out. We analyze the resulting representations and characterize when they are preferable to those learned by causal invariant-representation methods. We propose a concrete method based on generalized random-intercept models, a class of predictors in which such marginalization is possible, and study their generalization properties. Empirically, we show that these models outperform invariant-learning methods across a range of challenging settings.

Foundation models are powerful technologies: how they are released publicly directly shapes their societal impact. In this position paper, we focus on open foundation models, defined here as those with broadly available model weights (e.g. Llama 2, Stable Diffusion XL). We identify five distinctive properties (e.g. greater customizability, poor monitoring) of open foundation models that lead to both their benefits and risks. Open foundation models present significant benefits, with some caveats, that span innovation, competition, the distribution of decision-making power, and transparency. To understand their risks of misuse, we design a risk assessment framework for analyzing their marginal risk. Across several misuse vectors (e.g. cyberattacks, bioweapons), we find that current research is insufficient to effectively characterize the marginal risk of open foundation models relative to pre-existing technologies. The framework helps explain why the marginal risk is low in some cases, clarifies disagreements about misuse risks by revealing that past work has focused on different subsets of the framework with different assumptions, and articulates a way forward for more constructive debate. Overall, our work helps support a more grounded assessment of the societal impact of open foundation models by outlining what research is needed to empirically validate their theoretical benefits and risks.

We study the task of learning from non-i.i.d. data. In particular, we aim at learning predictors that minimize the conditional risk for a stochastic process, i.e. the expected loss of the predictor on the next point conditioned on the set of training samples observed so far. For non-i.i.d. data, the training set contains information about the upcoming samples, so learning with respect to the conditional distribution can be expected to yield better predictors than one obtains from the classical setting of minimizing the marginal risk. Our main contribution is a practical estimator for the conditional risk based on the theory of non-parametric time-series prediction, and a finite sample concentration bound that establishes uniform convergence of the estimator to the true conditional risk under certain regularity assumptions on the process.