Efficient end-to-end learning for quantizable representations

Embedding representation learning via neural networks is at the core foundation of modern similarity based search. While much effort has been put in developing algorithms for learning binary hamming code representations for search efficiency, this still requires a linear scan of the entire dataset per each query and trades off the search accuracy through binarization. To this end, we consider the problem of directly learning a quantizable embedding representation and the sparse binary hash code end-to-end which can be used to construct an efficient hash table not only providing significant search reduction in the number of data but also achieving the state of the art search accuracy outperforming previous state of the art deep metric learning methods. We also show that finding the optimal sparse binary hash code in a mini-batch can be computed exactly in polynomial time by solving a minimum cost flow problem. Our results on Cifar-100 and on ImageNet datasets show the state of the art search accuracy in precision@k and NMI metrics while providing up to 98X and 478X search speedup respectively over exhaustive linear search. The source code is available at https://github.com/maestrojeong/Deep-Hash-Table-ICML18Comment: Accepted and to appear at ICML 2018. Camera ready versio

Nonparametric Productivity Analysis

How can we measure and compare the relative performance of production units? If input and output variables are one dimensional, then the simplest way is to compute efficiency by calculating and comparing the ratio of output and input for each production unit. This idea is inappropriate though, when multiple inputs or multiple outputs are observed. Consider a bank, for example, with three branches A, B, and C. The branches take the number of staff as the input, and measures outputs such as the number of transactions on personal and business accounts. Assume that the following statistics are observed: Branch A: 60000 personal transactions, 50000 business transactions, 25 people on staff, Branch B: 50000 personal transactions, 25000 business transactions, 15 people on staff, Branch C: 45000 personal transactions, 15000 business transactions, 10 people on staff. We observe that Branch C performed best in terms of personal transactions per staff, whereas Branch A has the highest ratio of business transactions per staff. By contrast Branch B performed better than Branch A in terms of personal transactions per staff, and better than Branch C in terms of business transactions per staff. How can we compare these business units in a fair way? Moreover, can we possibly create a virtual branch that reflects the input/output mechanism and thus creates a scale for the real branches? Productivity analysis provides a systematic approach to these problems. We review the basic concepts of productivity analysis and two popular methods DEA and FDH, which are given in Sections 12.1 and 12.2, respectively. Sections 12.3 and 12.4 contain illustrative examples with real data.relative performance, production units, productivity analysis, Data Envelopment Analysis, DEA, Free Disposal Hull, DFH, insurance agencies, manufacturing industry

Period and toroidal knot mosaics

Knot mosaic theory was introduced by Lomonaco and Kauffman in the paper on `Quantum knots and mosaics' to give a precise and workable definition of quantum knots, intended to represent an actual physical quantum system. A knot (m,n)-mosaic is an $m \! \times \! n$ matrix whose entries are eleven mosaic tiles, representing a knot or a link by adjoining properly. In this paper we introduce two variants of knot mosaics: period knot mosaics and toroidal knot mosaics, which are common features in physics and mathematics. We present an algorithm producing the exact enumeration of period knot (m,n)-mosaics for any positive integers m and n, toroidal knot (m,n)-mosaics for co-prime integers m and n, and furthermore toroidal knot (p,p)-mosaics for a prime number p. We also analyze the asymptotics of the growth rates of their cardinality

Limit Distribution of Convex-Hull Estimators of Boundaries

Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function. --Convex-hull,free disposal hull,frontier function,data envelope analysis,productivity analysis,rate of convergence

Determining Sustainable Development Density using the Urban Carrying Capacity Assessment System

Diverse urban problems in the capital region of Korea occur due to over-development and over-concentration which exceed the region’s carrying capacity. Particularly, environmental problems such as air and water pollution have become more evident and become central issues for urban planners and decision-makers. In achieving sustainable environment through resolving such problems, practical approaches to incorporate the concept of environmental sustainability into managing urban development are needed. This research aims at developing an integrated framework for assessing urban carrying capacity which can determine sustainable development density, and has yielded the following. First, seven determining factors for urban carrying capacity including energy, green areas, roads, subway systems, water supply, sewage treatment, and waste treatment were identified, and the assessment framework was developed by integrating such factors. Second, the UCCAS, a GIS-based carrying capacity assessment system was developed based upon the framework. Finally, through a case study of determining carrying capacity of an urban area, it was revealed that decision support with the UCCAS demonstrated in this research could play a pivotal role in planning and managing urban development more effectively

Asymptotic distribution of conical-hull estimators of directional edges

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of $\mathrm{inputs}\times\mathrm{outputs}$ in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the $\mathrm{inputs}\times\mathrm{outputs}$ space. So far, only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered which corresponds to a situation where the technology presents variable returns-to-scale (VRS). This paper analyzes the case where the most common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is defined as the smallest conical-hull with vertex at the origin enveloping the cloud of observed points. In this paper we determine the asymptotic properties of this estimator, showing that the rate of convergence is better than for the VRS estimator. We derive also its asymptotic sampling distribution with a practical way to simulate it. This allows to define a bias-corrected estimator and to build confidence intervals for the frontier. We compare in a simulated example the bias-corrected estimator with the original conical-hull estimator and show its superiority in terms of median squared error.Comment: Published in at http://dx.doi.org/10.1214/09-AOS746 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Regulation of the Neuron-specific Ras GTPase-activating Protein, synGAP, by Ca2+/Calmodulin-dependent Protein Kinase II

synGAP is a neuron-specific Ras GTPase-activating protein found in high concentration in the postsynaptic density fraction from mammalian forebrain. Proteins in the postsynaptic density, including synGAP, are part of a signaling complex attached to the cytoplasmic tail of the N-methyl-D-aspartate-type glutamate receptor. synGAP can be phosphorylated by a second prominent component of the complex, Ca2+/calmodulin-dependent protein kinase II. Here we show that phosphorylation of synGAP by Ca2+/calmodulin-dependent protein kinase II increases its Ras GTPase-activating activity by 70-95%. We identify four major sites of phosphorylation, serines 1123, 1058, 750/751/756, and 764/765. These sites together with other minor phosphorylation sites in the carboxyl tail of synGAP control stimulation of GTPase-activating activity. When three of these sites and four other serines in the carboxyl tail are mutated, stimulation of GAP activity after phosphorylation is reduced to 21 ± 5% compared with 70-95% for the wild type protein. We used phosphosite-specific antibodies to show that, as predicted, phosphorylation of serines 765 and 1123 is increased in cultured cortical neurons after exposure of the neurons to the agonist N-methyl-D-aspartate