Ranking Median Regression: Learning to Order through Local Consensus

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 'Learning to Order' 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 $\Sigma$'s conditional distribution given $X$

Jointly Modeling Topics and Intents with Global Order Structure

Modeling document structure is of great importance for discourse analysis and related applications. The goal of this research is to capture the document intent structure by modeling documents as a mixture of topic words and rhetorical words. While the topics are relatively unchanged through one document, the rhetorical functions of sentences usually change following certain orders in discourse. We propose GMM-LDA, a topic modeling based Bayesian unsupervised model, to analyze the document intent structure cooperated with order information. Our model is flexible that has the ability to combine the annotations and do supervised learning. Additionally, entropic regularization can be introduced to model the significant divergence between topics and intents. We perform experiments in both unsupervised and supervised settings, results show the superiority of our model over several state-of-the-art baselines.Comment: Accepted by AAAI 201

Label Ranking with Probabilistic Models

Diese Arbeit konzentriert sich auf eine spezielle Prognoseform, das sogenannte Label Ranking. Auf den Punkt gebracht, kann Label Ranking als eine Erweiterung des herkömmlichen Klassifizierungproblems betrachtet werden. Bei einer Anfrage (z. B. durch einen Kunden) und einem vordefinierten Set von Kandidaten Labels (zB AUDI, BMW, VW), wird ein einzelnes Label (zB BMW) zur Vorhersage in der Klassifizierung benötigt, während ein komplettes Ranking aller Label (zB BMW> VW> Audi) für das Label Ranking erforderlich ist. Da Vorhersagen dieser Art, bei vielen Problemen der realen Welt nützlich sind, können Label Ranking-Methoden in mehreren Anwendungen, darunter Information Retrieval, Kundenwunsch Lernen und E-Commerce eingesetzt werden. Die vorliegende Arbeit stellt eine Auswahl an Methoden für Label-Ranking vor, die Maschinelles Lernen mit statistischen Bewertungsmodellen kombiniert. Wir konzentrieren wir uns auf zwei statistische Ranking-Modelle, das Mallows- und das Plackett-Luce-Modell und zwei Techniken des maschinellen Lernens, das Beispielbasierte Lernen und das Verallgemeinernde Lineare Modell