ChoiceRank: Identifying Preferences from Node Traffic in Networks

Understanding how users navigate in a network is of high interest in many applications. We consider a setting where only aggregate node-level traffic is observed and tackle the task of learning edge transition probabilities. We cast it as a preference learning problem, and we study a model where choices follow Luce's axiom. In this case, the $O(n)$ marginal counts of node visits are a sufficient statistic for the $O(n^2)$ transition probabilities. We show how to make the inference problem well-posed regardless of the network's structure, and we present ChoiceRank, an iterative algorithm that scales to networks that contains billions of nodes and edges. We apply the model to two clickstream datasets and show that it successfully recovers the transition probabilities using only the network structure and marginal (node-level) traffic data. Finally, we also consider an application to mobility networks and apply the model to one year of rides on New York City's bicycle-sharing system.Comment: Accepted at ICML 201

Just Sort It! A Simple and Effective Approach to Active Preference Learning

We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking, the optimal solution is to use an efficient sorting algorithm, such as Quicksort. But how do sorting algorithms behave if some comparison outcomes are inconsistent with the ranking? We give favorable guarantees for Quicksort for the popular Bradley-Terry model, under natural assumptions on the parameters. Furthermore, we empirically demonstrate that sorting algorithms lead to a very simple and effective active learning strategy: repeatedly sort the items. This strategy performs as well as state-of-the-art methods (and much better than random sampling) at a minuscule fraction of the computational cost.Comment: Accepted at ICML 201

Analytic Properties of Diffraction Gratings

International audienceThe chapter presents a review of most important general properties of gratings, which a user should not ignore and that are derived directly from the boundary value problem without any use of computer. These analytic properties are valuable at least for two reasons. First, they strongly contribute to a better understanding of an instrument which puzzled and fascinated many specialists of Optics since the beginning of the 20th century. Secondly, they allow a theoretician to check the validity of a new theory or its numerical implementation, although one must be very cautious: a theory can fail while its results satisfy some analytic rules. Specially, this surprising remark apply to properties like energy balance or reciprocity theorem. The first part of this chapter is devoted to the use of the elementary laws of Electromagnetics for stating the boundary value problems of gratings in various cases of materials and polarizations. Then, we deduce from the boundary value problems the most important analytic properties of gratings

Openness, Inequality, and Poverty: Endowments Matter

Using tariffs as a measure of openness, this paper finds consistent evidence that the conditional effects of trade liberalization on inequality are correlated with relative factor endowments. Trade liberalization, measured by changes in tariff revenues, is associated with increases in inequality in countries well-endowed in highly skilled workers and capital or with workers that have very low education levels. Similar, though less robust, results are also obtained when decile data are used instead of the usual Gini coefficients. Taken together, the results are strongly supportive of the factor-proportions theory of trade and suggest that trade liberalization in poor countries where the share of the labor force with little education is high raises inequality. Simulation results also suggest that relatively small changes in inequality as measured by aggregate measures of inequality like the Gini coefficient are magnified when estimates are carried out using decile data.international trade, Income distribution, Poverty

Openness, inequality, and poverty : endowments matter

Using tariffs as a measure of openness, the authors find consistent evidence that the conditional effects of trade liberalization on inequality are correlated with relative factor endowments. Trade liberalization is associated with increases in inequality in countries well-endowed in highly skilled workers and capital or with workers that have very low education levels and in countries relatively well-endowed in mining and fuels. Trade liberalization is associated with decreases in inequality in countries that are well-endowed with primary-educated labor. Similar results are also apparent when decile data are used instead of the usual Gini coefficient. The results are strongly supportive of the factor-proportions theory of trade and suggest that trade liberalization in poor countries where the share of the labor force with very low education levels (likely employed in nontradable activities) is high raises inequality. In the sample, countries with low education levels also have relatively scarce endowments of capital. Quantitatively capital scarcity is the dominating effect so that trade liberalization is accompanied by reduced income inequality in low-income countries. Within-country inequality is also positively correlated with measures of macroeconomic instability. Simulation results suggest that relatively small changes in inequality as measured by aggregate measures of inequality like the Gini coefficient are magnified when estimates are carried out using decile data.Free Trade,Economic Theory&Research,Inequality,Trade Law,Achieving Shared Growth

A Majority Lemma for Randomised Query Complexity

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj?g?) = ?(n?R ?_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f?g?, it suffices to prove a sufficiently strong form of the result only in the special case g = GapOr

Opennes, Inequality, and Poverty: Endowments Matter

Using tariffs as a measure of openness, this paper finds consistent evidence that the conditional effects of trade liberalization on inequality are correlated with relative factor endowments. Trade liberalization, measured by changes in tariff revenues, is associated with increases in inequality in countries well-endowed in highly skilled workers and capital or with workers that have very low education levels. Similar, though less robust, results are also obtained when decile data are used instead of the usual Gini coefficients. Taken together, the results are strongly supportive of the factor-proportions theory of trade and suggest that trade liberalization in poor countries where the share of the labor force with little education is high raises inequality. Simulation results also suggest that relatively small changes in inequality as measured by aggregate measures of inequality like the Gini coefficient are magnified when estimates are carried out using decile data.International Trade, Income Distribution, Poverty

Integral Method for Gratings

International audienceThe chapter containes a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading either to a single integral equation, or to a system of coupled integral equations. Special attention is paid to the singularities of the kernels, and to different techniques to accelerate the convergence of the numerical computations. The theory is applied to gratings having different profiles with or without edges, to real metal and dielectrics, and to perfectly conducting substrates