Yiran Jia

Yiran Jia

Learning models that can handle distribution shifts is a key challenge in domain generalization. Invariance learning, an approach that focuses on identifying features invariant across environments, improves model generalization by capturing stable relationships, which may represent causal effects when the data distribution is encoded within a structural equation model (SEM) and satisfies modularity conditions. This has led to a growing body of work that builds on invariance learning, leveraging the inherent heterogeneity across environments to develop methods that provide causal explanations while enhancing robust prediction. However, in many practical scenarios, obtaining complete outcome data from each environment is challenging due to the high cost or complexity of data collection. This limitation in available data hinders the development of models that fully leverage environmental heterogeneity, making it crucial to address missing outcomes to improve both causal insights and robust prediction. In this work, we derive an estimator from the invariance objective under missing outcomes. We establish non-asymptotic guarantees on variable selection property and $\ell_2$ error convergence rates, which are influenced by the proportion of missing data and the quality of imputation models across environments. We evaluate the performance of the new estimator through extensive simulations and demonstrate its application using the UCI Bike Sharing dataset to predict the count of bike rentals. The results show that despite relying on a biased imputation model, the estimator is efficient and achieves lower prediction error, provided the bias is within a reasonable range.

Eric Yeats, Aaron Jacobson, Darryl Hannan et al.

The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered that diffusion models capture the LID of data through the spectra of their score estimates and through the rate of change of their density estimates under various noise perturbations. While these methods can accurately quantify LID, they require either many forward passes of the diffusion model or use of gradient computation, limiting their applicability in compute- and memory-constrained scenarios. We show that the LID is a lower bound on the denoising score matching loss, motivating use of the denoising score matching loss as a LID estimator. Moreover, we show that the equivalent implicit score matching loss also approximates LID via the normal dimension and is closely related to a recent LID estimator, FLIPD. Our experiments on a manifold benchmark and with Stable Diffusion 3.5 indicate that the denoising score matching loss is a highly competitive and scalable LID estimator, achieving superior accuracy and memory footprint under increasing problem size and quantization level.