Kang Du

Kang Du, Yu Xiang

Causal inference from observational data following the restricted structural causal models (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or non-linearity. This methodology can be adapted to stationary time series, yet inferring causal relationships from nonstationary time series remains a challenging task. In this work, we propose a new class of restricted SCM, via a time-varying filter and stationary noise, and exploit the asymmetry from nonstationarity for causal identification in both bivariate and network settings. We propose efficient procedures by leveraging powerful estimates of the bivariate evolutionary spectra for slowly varying processes. Various synthetic and real datasets that involve high-order and non-smooth filters are evaluated to demonstrate the effectiveness of our proposed methodology.

Kang Du, Yu Xiang

We study the data-generating mechanism for reconstructive SSL to shed light on its effectiveness. With an infinite amount of labeled samples, we provide a sufficient and necessary condition for perfect linear approximation. The condition reveals a full-rank component that preserves the label classes of Y, along with a redundant component. Motivated by the condition, we propose to approximate the redundant component by a low-rank factorization and measure the approximation quality by introducing a new quantity $ε_s$, parameterized by the rank of factorization s. We incorporate $ε_s$ into the excess risk analysis under both linear regression and ridge regression settings, where the latter regularization approach is to handle scenarios when the dimension of the learned features is much larger than the number of labeled samples n for downstream tasks. We design three stylized experiments to compare SSL with supervised learning under different settings to support our theoretical findings.