We consider the problem of combining ranking results from various sources. In the context of the Web, the main applications include building meta-search engines, combining ranking functions, selecting documents based on multiple criteria, and improving search precision through word associations. Wedevelop a set of techniques for the rank aggregation problem and compare their performance to that of well-known methods. A primary goal of our work is to design rank aggregation techniques that can effectively combat "spam," a serious problem in Web searches. Experiments show that our methods are simple, efficient, and effective. Keywords: rank aggregation, ranking functions, metasearch, multi-word queries, spam 1.

We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.

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

Data Cleaning is an important process that has been at the center of research interest in recent years. An important end goal of effective data cleaning is to identify the relational tuple or tuples that are “most related ” to a given query tuple. Various techniques have been proposed in the literature for efficiently identifying approximate matches to a query string against a single attribute of a relation. In addition to constructing a ranking (i.e., ordering) of these matches, the techniques often associate, with each match, scores that quantify the extent of the match. Since multiple attributes could exist in the query tuple, issuing approximate match operations for each of them separately will effectively create a number of ranked lists of the relation tuples. Merging these lists to identify a final ranking and scoring, and returning the top-K tuples, is a challenging task. In this paper, we adapt the well-known footrule distance (for merging ranked lists) to effectively deal with scores. We study efficient algorithms to merge rankings, and produce the top-K tuples, in a declarative way. Since techniques for approximately matching a query string against a single attribute in a relation are typically best deployed in a database, we introduce and describe two novel algorithms for this problem and we provide SQL specifications for them. Our experimental case study, using real application data along with a realization of our proposed techniques on a commercial data base system, highlights the benefits of the proposed algorithms and attests to the overall effectiveness and practicality of our approach. 1

The Bradley–Terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs. Among the many studies of the model in the past 75 years, numerous authors have generalized it in several directions, sometimes providing iterative algorithms for obtaining maximum likelihood estimates for the generalizations. Building on a theory of algorithms known by the initials MM, for minorization–maximization, this paper presents a powerful technique for producing iterative maximum likelihood estimation algorithms for a wide class of generalizations of the Bradley–Terry model. While algorithms for problems of this type have tended to be custom-built in the literature, the techniques in this paper enable their mass production. Simple conditions are stated that guarantee that each algorithm described will produce a sequence that converges to the unique maximum likelihood estimator. Several of the algorithms and convergence results herein are new. 1. Introduction. In

Preference learning is an emerging topic that appears in different guises in the recent literature. This work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a finite number of labels. Our approach for learning such a mapping, called ranking by pairwise comparison (RPC), first induces a binary preference relation from suitable training data using a natural extension of pairwise classification. A ranking is then derived from the preference relation thus obtained by means of a ranking procedure, whereby different ranking methods can be used for minimizing different loss functions. In particular, we show that a simple (weighted) voting strategy minimizes risk with respect to the well-known Spearman rank correlation. We compare RPC to existing label ranking methods, which are based on scoring individual labels instead of comparing pairs of labels. Both empirically and theoretically, it is shown that RPC is superior in terms of computational efficiency, and at least competitive in terms of accuracy.

Abstract. We give the first analysis of a systematic scan version of the Metropolis algorithm. Our examples include generating random elements of a Coxeter group with probability determined by the length function. The analysis is based on interpreting Metropolis walks in terms of the multiplication in the Iwahori-Hecke algebra. 1.

Statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration. We explore the use of non-parametric models for partially ranked data and derive computationally efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. A bias-variance analysis and an experimental study demonstrate the applicability of the proposed method.

This revision of the ICML 2007 proceedings article corrects an error in Sec. 3. Cluster analysis of ranking data, which occurs in consumer questionnaires, voting forms or other inquiries of preferences, attempts to identify typical groups of rank choices. Empirically measured rankings are often incomplete, i.e. different numbers of filled rank positions cause heterogeneity in the data. We propose a mixture approach for clustering of heterogeneous rank data. Rankings of different lengths can be described and compared by means of a single probabilistic model. A maximum entropy approach avoids hidden assumptions about missing rank positions. Parameter estimators and an efficient EM algorithm for unsupervised inference are derived for the ranking mixture model. Experiments on both synthetic data and real-world data demonstrate significantly improved parameter estimates on heterogeneous data when the incomplete rankings are included in the inference process. 1.

A recommender system must be able to suggest items that are likely to be preferred by the user. In most systems, the degree of preference is represented by a rating score. Given a database of users ’ past ratings on a set of items, traditional collaborative filtering algorithms are based on predicting the potential ratings that a user would assign to the unrated items so that they can be ranked by the predicted ratings to produce a list of recommended items. In this paper, we propose a collaborative filtering approach that addresses the item ranking problem directly by modeling user preferences derived from the ratings. We measure the similarity between users based on the correlation between their rankings of the items rather than the rating values and propose new collaborative filtering algorithms for ranking items based on the preferences of similar users. Experimental results on real world movie rating data sets show that the proposed approach outperforms traditional collaborative filtering algorithms significantly on the NDCG measure for evaluating ranked results.