Name
Abstract | ||
|---|---|---|
This article is devoted to the problem of predicting the value taken by a random permutation $Sigma$, describing the preferences of an individual over a set of numbered items ${1,; ldots,; n}$ say, based on the observation of an input/explanatory r.v. $X$ e.g. characteristics of the individual), when error is measured by the Kendall $tau$ distance. In the probabilistic formulation of the u0027Learning to Orderu0027 problem we propose, which extends the framework for statistical Kemeny ranking aggregation developped in citet{CKS17}, this boils down to recovering conditional Kemeny medians of $Sigma$ given $X$ from i.i.d. training examples $(X_1, Sigma_1),; ldots,; (X_N, Sigma_N)$. For this reason, this statistical learning problem is referred to as textit{ranking median regression} here. Our contribution is twofold. We first propose a probabilistic theory of ranking median regression: the set of optimal elements is characterized, the performance of empirical risk minimizers is investigated in this context and situations where fast learning rates can be achieved are also exhibited. Next we introduce the concept of local consensus/median, in order to derive efficient methods for ranking median regression. The major advantage of this local learning approach lies in its close connection with the widely studied Kemeny aggregation problem. From an algorithmic perspective, this permits to build predictive rules for ranking median regression by implementing efficient techniques for (approximate) Kemeny median computations at a local level in a tractable manner. In particular, versions of $k$-nearest neighbor and tree-based methods, tailored to ranking median regression, are investigated. Accuracy of piecewise constant ranking median regression rules is studied under a specific smoothness assumption for $Sigma$u0027s conditional distribution given $X$. |
Year | Venue | Field |
|---|---|---|
2018 | ALT | Econometrics,Aggregation problem,Conditional probability distribution,Ranking,Regression,Random permutation,Probabilistic logic,Smoothness,Statistics,Mathematics,Piecewise |
DocType | Citations | PageRank |
Conference | 0 | 0.34 |
References | Authors | |
9 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stéphan Clémençon | 1 | 214 | 30.59 |
| Anna Korba | 2 | 3 | 3.42 |
| Eric Sibony | 3 | 1 | 1.38 |