Equitable orientations of sparse uniform hypergraphs

Caro, West, and Yuster studied how $r$-uniform hypergraphs can be oriented in such a way that (generalizations of) indegree and outdegree are as close to each other as can be hoped. They conjectured an existence result of such orientations for sparse hypergraphs, of which we present a proof

Scaling Graph-based Semi Supervised Learning to Large Number of Labels Using Count-Min Sketch

Graph-based Semi-supervised learning (SSL) algorithms have been successfully used in a large number of applications. These methods classify initially unlabeled nodes by propagating label information over the structure of graph starting from seed nodes. Graph-based SSL algorithms usually scale linearly with the number of distinct labels (m), and require O(m) space on each node. Unfortunately, there exist many applications of practical significance with very large m over large graphs, demanding better space and time complexity. In this paper, we propose MAD-SKETCH, a novel graph-based SSL algorithm which compactly stores label distribution on each node using Count-min Sketch, a randomized data structure. We present theoretical analysis showing that under mild conditions, MAD-SKETCH can reduce space complexity at each node from O(m) to O(log m), and achieve similar savings in time complexity as well. We support our analysis through experiments on multiple real world datasets. We observe that MAD-SKETCH achieves similar performance as existing state-of-the-art graph- based SSL algorithms, while requiring smaller memory footprint and at the same time achieving up to 10x speedup. We find that MAD-SKETCH is able to scale to datasets with one million labels, which is beyond the scope of existing graph- based SSL algorithms.Comment: 9 page

Stein Estimation for Spherically Symmetric Distributions: Recent Developments

This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population is normal or not. Considerable attention is devoted to generalizing the "Stein lemma" which underlies much of the theoretical development of improved minimax estimation for spherically symmetric distributions. A main focus is on distributional robustness results in cases where a residual vector is available to estimate an unknown scale parameter, and, in particular, in finding estimators which are simultaneously generalized Bayes and minimax over large classes of spherically symmetric distributions. Some attention is also given to the problem of estimating a location vector restricted to lie in a polyhedral cone.Comment: Published in at http://dx.doi.org/10.1214/10-STS323 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Trade reform, uncertainty, and export promotion : Mexico 1982-88. BEBR 92-0135

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Religious Participation versus Shopping: What Makes People Happier?

In this paper, we first explore how an exogenous increase in the opportunity cost of religious participation affects individuals' religious participation and reported happiness using data from the General Social Survey. The exogenous shift in the cost of religious participation is a result of repealing of so-called blue laws which restrict retail activity on Sundays. We find that repealing blue laws causes a significant decline in the level of religious participation of white women and in their happiness. We do not observe any significant decline in reported happiness of other groups whose religious participation was not significantly affected by repeal. We also use repeal as an instrumental variable (IV) for church attendance and provide direct evidence that church attendance has a significant positive effect on happiness, especially for women.religious participation, happiness, blue laws