Adaptive Huber Regression

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded $(1+\delta)$-th moment for any $\delta > 0$. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when $\delta \geq 1$, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime $0<\delta< 1$. Furthermore, this transition is smooth and optimal. In addition, we extend the methodology to allow both heavy-tailed predictors and observation noise. Simulation studies lend further support to the theory. In a genetic study of cancer cell lines that exhibit heavy-tailedness, the proposed methods are shown to be more robust and predictive.Comment: final versio

Distant Supervision for Entity Linking

Entity linking is an indispensable operation of populating knowledge repositories for information extraction. It studies on aligning a textual entity mention to its corresponding disambiguated entry in a knowledge repository. In this paper, we propose a new paradigm named distantly supervised entity linking (DSEL), in the sense that the disambiguated entities that belong to a huge knowledge repository (Freebase) are automatically aligned to the corresponding descriptive webpages (Wiki pages). In this way, a large scale of weakly labeled data can be generated without manual annotation and fed to a classifier for linking more newly discovered entities. Compared with traditional paradigms based on solo knowledge base, DSEL benefits more via jointly leveraging the respective advantages of Freebase and Wikipedia. Specifically, the proposed paradigm facilitates bridging the disambiguated labels (Freebase) of entities and their textual descriptions (Wikipedia) for Web-scale entities. Experiments conducted on a dataset of 140,000 items and 60,000 features achieve a baseline F1-measure of 0.517. Furthermore, we analyze the feature performance and improve the F1-measure to 0.545