Yuxiang Wang

Dan Qiao, Yu-Xiang Wang

We consider the problem of generalization of arbitrarily overparameterized two-layer ReLU Neural Networks with univariate input. Recent work showed that under square loss, flat solutions (motivated by flat / stable minima and Edge of Stability phenomenon) provably cannot overfit, but it remains unclear whether the same phenomenon holds for logistic loss. This is a puzzling open problem because existing work on logistic loss shows that gradient descent with increasing step size converges to interpolating solutions (at infinity, for the margin-separable cases). In this paper, we prove that the \emph{flatness implied generalization} is more delicate under logistic loss. On the positive side, we show that flat solutions enjoy near-optimal generalization bounds within a region between the left-most and right-most \emph{uncertain} sets determined by each candidate solution. On the negative side, we show that there exist arbitrarily flat yet overfitting solutions at infinity that are (falsely) certain everywhere, thus certifying that flatness alone is insufficient for generalization in general. We demonstrate the effects predicted by our theory in a well-controlled simulation study.

Chieh-Chi Kao, Yuxiang Wang, Jonathan Waltman et al.

Image hallucination and super-resolution have been studied for decades, and many approaches have been proposed to upsample low-resolution images using information from the images themselves, multiple example images, or large image databases. However, most of this work has focused exclusively on small magnification levels because the algorithms simply sharpen the blurry edges in the upsampled images - no actual new detail is typically reconstructed in the final result. In this paper, we present a patch-based algorithm for image hallucination which, for the first time, properly synthesizes novel high frequency detail. To do this, we pose the synthesis problem as a patch-based optimization which inserts coherent, high-frequency detail from contextually-similar images of the same physical scene/subject provided from either a personal image collection or a large online database. The resulting image is visually plausible and contains coherent high frequency information. We demonstrate the robustness of our algorithm by testing it on a large number of images and show that its performance is considerably superior to all state-of-the-art approaches, a result that is verified to be statistically significant through a randomized user study.

Seth Flaxman, Danica J. Sutherland, Yu-Xiang Wang et al.

We combine fine-grained spatially referenced census data with the vote outcomes from the 2016 US presidential election. Using this dataset, we perform ecological inference using distribution regression (Flaxman et al, KDD 2015) with a multinomial-logit regression so as to model the vote outcome Trump, Clinton, Other / Didn't vote as a function of demographic and socioeconomic features. Ecological inference allows us to estimate "exit poll" style results like what was Trump's support among white women, but for entirely novel categories. We also perform exploratory data analysis to understand which census variables are predictive of voting for Trump, voting for Clinton, or not voting for either. All of our methods are implemented in Python and R, and are available online for replication.