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Fen Xia

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3 papers

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JMLR Journal 2017 Journal Article

A General Distributed Dual Coordinate Optimization Framework for Regularized Loss Minimization

Shun Zheng
Jialei Wang
Fen Xia
Wei Xu
Tong Zhang

In modern large-scale machine learning applications, the training data are often partitioned and stored on multiple machines. It is customary to employ the data parallelism approach, where the aggregated training loss is minimized without moving data across machines. In this paper, we introduce a novel distributed dual formulation for regularized loss minimization problems that can directly handle data parallelism in the distributed setting. This formulation allows us to systematically derive dual coordinate optimization procedures, which we refer to as Distributed Alternating Dual Maximization (DADM). The framework extends earlier studies described in (Boyd et al., 2011; Ma et al., 2017; Jaggi et al., 2014; Yang, 2013) and has rigorous theoretical analyses. Moreover, with the help of the new formulation, we develop the accelerated version of DADM (Acc-DADM) by generalizing the acceleration technique from (Shalev-Shwartz and Zhang, 2014) to the distributed setting. We also provide theoretical results for the proposed accelerated version, and the new result improves previous ones (Yang, 2013; Ma et al., 2017) whose iteration complexities grow linearly on the condition number. Our empirical studies validate our theory and show that our accelerated approach significantly improves the previous state- of-the-art distributed dual coordinate optimization algorithms. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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NeurIPS Conference 2009 Conference Paper

Statistical Consistency of Top-k Ranking

Fen Xia
Tie-Yan Liu
Hang Li

This paper is concerned with the consistency analysis on listwise ranking methods. Among various ranking methods, the listwise methods have competitive performances on benchmark datasets and are regarded as one of the state-of-the-art approaches. Most listwise ranking methods manage to optimize ranking on the whole list (permutation) of objects, however, in practical applications such as information retrieval, correct ranking at the top k positions is much more important. This paper aims to analyze whether existing listwise ranking methods are statistically consistent in the top-k setting. For this purpose, we define a top-k ranking framework, where the true loss (and thus the risks) are defined on the basis of top-k subgroup of permutations. This framework can include the permutation-level ranking framework proposed in previous work as a special case. Based on the new framework, we derive sufficient conditions for a listwise ranking method to be consistent with the top-k true loss, and show an effective way of modifying the surrogate loss functions in existing methods to satisfy these conditions. Experimental results show that after the modifications, the methods can work significantly better than their original versions.

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ICML Conference 2008 Conference Paper

Listwise approach to learning to rank: theory and algorithm

Fen Xia
Tie-Yan Liu
Jue Wang 0004
Wensheng Zhang 0002
Hang Li 0001

This paper aims to conduct a study on the listwise approach to learning to rank. The listwise approach learns a ranking function by taking individual lists as instances and minimizing a loss function defined on the predicted list and the ground-truth list. Existing work on the approach mainly focused on the development of new algorithms; methods such as RankCosine and ListNet have been proposed and good performances by them have been observed. Unfortunately, the underlying theory was not sufficiently studied so far. To amend the problem, this paper proposes conducting theoretical analysis of learning to rank algorithms through investigations on the properties of the loss functions, including consistency, soundness, continuity, differentiability, convexity, and efficiency. A sufficient condition on consistency for ranking is given, which seems to be the first such result obtained in related research. The paper then conducts analysis on three loss functions: likelihood loss, cosine loss, and cross entropy loss. The latter two were used in RankCosine and ListNet. The use of the likelihood loss leads to the development of a new listwise method called ListMLE, whose loss function offers better properties, and also leads to better experimental results.

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