A Greedy Homotopy Method for Regression with Nonconvex Constraints

Constrained least squares regression is an essential tool for high-dimensional data analysis. Given a partition $\mathcal{G}$ of input variables, this paper considers a particular class of nonconvex constraint functions that encourage the linear model to select a small number of variables from a small number of groups in $\mathcal{G}$. Such constraints are relevant in many practical applications, such as Genome-Wide Association Studies (GWAS). Motivated by the efficiency of the Lasso homotopy method, we present RepLasso, a greedy homotopy algorithm that tries to solve the induced sequence of nonconvex problems by solving a sequence of suitably adapted convex surrogate problems. We prove that in some situations RepLasso recovers the global minima of the nonconvex problem. Moreover, even if it does not recover global minima, we prove that in relevant cases it will still do no worse than the Lasso in terms of support and signed support recovery, while in practice outperforming it. We show empirically that the strategy can also be used to improve over other Lasso-style algorithms. Finally, a GWAS of ankylosing spondylitis highlights our method's practical utility

Neural Ranking Models with Weak Supervision

Despite the impressive improvements achieved by unsupervised deep neural networks in computer vision and NLP tasks, such improvements have not yet been observed in ranking for information retrieval. The reason may be the complexity of the ranking problem, as it is not obvious how to learn from queries and documents when no supervised signal is available. Hence, in this paper, we propose to train a neural ranking model using weak supervision, where labels are obtained automatically without human annotators or any external resources (e.g., click data). To this aim, we use the output of an unsupervised ranking model, such as BM25, as a weak supervision signal. We further train a set of simple yet effective ranking models based on feed-forward neural networks. We study their effectiveness under various learning scenarios (point-wise and pair-wise models) and using different input representations (i.e., from encoding query-document pairs into dense/sparse vectors to using word embedding representation). We train our networks using tens of millions of training instances and evaluate it on two standard collections: a homogeneous news collection(Robust) and a heterogeneous large-scale web collection (ClueWeb). Our experiments indicate that employing proper objective functions and letting the networks to learn the input representation based on weakly supervised data leads to impressive performance, with over 13% and 35% MAP improvements over the BM25 model on the Robust and the ClueWeb collections. Our findings also suggest that supervised neural ranking models can greatly benefit from pre-training on large amounts of weakly labeled data that can be easily obtained from unsupervised IR models.Comment: In proceedings of The 40th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR2017