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 $X$

Uniqueness and minimal obstructions for tree-depth

A k-ranking of a graph G is a labeling of the vertices of G with values from {1,...,k} such that any path joining two vertices with the same label contains a vertex having a higher label. The tree-depth of G is the smallest value of k for which a k-ranking of G exists. The graph G is k-critical if it has tree-depth k and every proper minor of G has smaller tree-depth. We establish partial results in support of two conjectures about the order and maximum degree of k-critical graphs. As part of these results, we define a graph G to be 1-unique if for every vertex v in G, there exists an optimal ranking of G in which v is the unique vertex with label 1. We show that several classes of k-critical graphs are 1-unique, and we conjecture that the property holds for all k-critical graphs. Generalizing a previously known construction for trees, we exhibit an inductive construction that uses 1-unique k-critical graphs to generate large classes of critical graphs having a given tree-depth.Comment: 14 pages, 4 figure

Learning Tree-based Deep Model for Recommender Systems

Model-based methods for recommender systems have been studied extensively in recent years. In systems with large corpus, however, the calculation cost for the learnt model to predict all user-item preferences is tremendous, which makes full corpus retrieval extremely difficult. To overcome the calculation barriers, models such as matrix factorization resort to inner product form (i.e., model user-item preference as the inner product of user, item latent factors) and indexes to facilitate efficient approximate k-nearest neighbor searches. However, it still remains challenging to incorporate more expressive interaction forms between user and item features, e.g., interactions through deep neural networks, because of the calculation cost. In this paper, we focus on the problem of introducing arbitrary advanced models to recommender systems with large corpus. We propose a novel tree-based method which can provide logarithmic complexity w.r.t. corpus size even with more expressive models such as deep neural networks. Our main idea is to predict user interests from coarse to fine by traversing tree nodes in a top-down fashion and making decisions for each user-node pair. We also show that the tree structure can be jointly learnt towards better compatibility with users' interest distribution and hence facilitate both training and prediction. Experimental evaluations with two large-scale real-world datasets show that the proposed method significantly outperforms traditional methods. Online A/B test results in Taobao display advertising platform also demonstrate the effectiveness of the proposed method in production environments.Comment: Accepted by KDD 201

Improved branch and bound method for control structure screening

The main aim of this paper is to present an improved algorithm of “Branch and Bound” method for control structure screening. The new algorithm uses a best- first search approach, which is more efficient than other algorithms based on depth-first search approaches. Detailed explanation of the algorithms is provided in this paper along with a case study on Tennessee–Eastman process to justify the theory of branch and bound method. The case study uses the Hankel singular value to screen control structure for stabilization. The branch and bound method provides a global ranking to all possible input and output combinations. Based on this ranking an efficient control structure with least complexity for stabilizing control is detected which leads to a decentralized proportional cont

The Translation Evidence Mechanism. The Compact between Researcher and Clinician.

Currently, best evidence is a concentrated effort by researchers. Researchers produce information and expect that clinicians will implement their advances in improving patient care. However, difficulties exist in maximizing cooperation and coordination between the producers, facilitators, and users (patients) of best evidence outcomes. The Translational Evidence Mechanism is introduced to overcome these difficulties by forming a compact between researcher, clinician and patient. With this compact, best evidence may become an integral part of private practice when uncertainties arise in patient health status, treatments, and therapies. The mechanism is composed of an organization, central database, and decision algorithm. Communication between the translational evidence organization, clinicians and patients is through the electronic chart. Through the chart, clinical inquiries are made, patient data from provider assessments and practice cost schedules are collected and encrypted (HIPAA standards), then inputted into the central database. Outputs are made within a timeframe suitable to private practice and patient flow. The output consists of a clinical practice guideline that responds to the clinical inquiry with decision, utility and cost data (based on the "average patient") for shared decision-making within informed consent. This shared decision-making allows for patients to "game" treatment scenarios using personal choice inputs. Accompanying the clinical practice guideline is a decision analysis that explains the optimized clinical decision. The resultant clinical decision is returned to the central database using the clinical practice guideline. The result is subsequently used to update current best evidence, indicate the need for new evidence, and analyze the changes made in best evidence implementation. When updates in knowledge occur, these are transmitted to the provider as alerts or flags through patient charts and other communication modalities

The Flexible Group Spatial Keyword Query

We present a new class of service for location based social networks, called the Flexible Group Spatial Keyword Query, which enables a group of users to collectively find a point of interest (POI) that optimizes an aggregate cost function combining both spatial distances and keyword similarities. In addition, our query service allows users to consider the tradeoffs between obtaining a sub-optimal solution for the entire group and obtaining an optimimized solution but only for a subgroup. We propose algorithms to process three variants of the query: (i) the group nearest neighbor with keywords query, which finds a POI that optimizes the aggregate cost function for the whole group of size n, (ii) the subgroup nearest neighbor with keywords query, which finds the optimal subgroup and a POI that optimizes the aggregate cost function for a given subgroup size m (m <= n), and (iii) the multiple subgroup nearest neighbor with keywords query, which finds optimal subgroups and corresponding POIs for each of the subgroup sizes in the range [m, n]. We design query processing algorithms based on branch-and-bound and best-first paradigms. Finally, we provide theoretical bounds and conduct extensive experiments with two real datasets which verify the effectiveness and efficiency of the proposed algorithms.Comment: 12 page