Hedging predictions in machine learning

Recent advances in machine learning make it possible to design efficient prediction algorithms for data sets with huge numbers of parameters. This paper describes a new technique for "hedging" the predictions output by many such algorithms, including support vector machines, kernel ridge regression, kernel nearest neighbours, and by many other state-of-the-art methods. The hedged predictions for the labels of new objects include quantitative measures of their own accuracy and reliability. These measures are provably valid under the assumption of randomness, traditional in machine learning: the objects and their labels are assumed to be generated independently from the same probability distribution. In particular, it becomes possible to control (up to statistical fluctuations) the number of erroneous predictions by selecting a suitable confidence level. Validity being achieved automatically, the remaining goal of hedged prediction is efficiency: taking full account of the new objects' features and other available information to produce as accurate predictions as possible. This can be done successfully using the powerful machinery of modern machine learning.Comment: 24 pages; 9 figures; 2 tables; a version of this paper (with discussion and rejoinder) is to appear in "The Computer Journal

When Social Influence Meets Item Inference

Research issues and data mining techniques for product recommendation and viral marketing have been widely studied. Existing works on seed selection in social networks do not take into account the effect of product recommendations in e-commerce stores. In this paper, we investigate the seed selection problem for viral marketing that considers both effects of social influence and item inference (for product recommendation). We develop a new model, Social Item Graph (SIG), that captures both effects in form of hyperedges. Accordingly, we formulate a seed selection problem, called Social Item Maximization Problem (SIMP), and prove the hardness of SIMP. We design an efficient algorithm with performance guarantee, called Hyperedge-Aware Greedy (HAG), for SIMP and develop a new index structure, called SIG-index, to accelerate the computation of diffusion process in HAG. Moreover, to construct realistic SIG models for SIMP, we develop a statistical inference based framework to learn the weights of hyperedges from data. Finally, we perform a comprehensive evaluation on our proposals with various baselines. Experimental result validates our ideas and demonstrates the effectiveness and efficiency of the proposed model and algorithms over baselines.Comment: 12 page

Stochastic Optimization for Spectral Risk Measures

Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic algorithms to optimize these quantities by characterizing their subdifferential and addressing challenges such as biasedness of subgradient estimates and non-smoothness of the objective. We show theoretically and experimentally that out-of-the-box approaches such as stochastic subgradient and dual averaging are hindered by bias and that our approach outperforms them