365,579 research outputs found
Functional Bipartite Ranking: a Wavelet-Based Filtering Approach
It is the main goal of this article to address the bipartite ranking issue
from the perspective of functional data analysis (FDA). Given a training set of
independent realizations of a (possibly sampled) second-order random function
with a (locally) smooth autocorrelation structure and to which a binary label
is randomly assigned, the objective is to learn a scoring function s with
optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it
is shown how to select compact finite dimensional representations of the input
curves adaptively, in order to build accurate ranking rules, using recent
advances in the ranking problem for multivariate data with binary feedback.
Beyond theoretical considerations, the performance of the learning methods for
functional bipartite ranking proposed in this paper are illustrated by
numerical experiments
A Theoretical Analysis of NDCG Type Ranking Measures
A central problem in ranking is to design a ranking measure for evaluation of
ranking functions. In this paper we study, from a theoretical perspective, the
widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures.
Although there are extensive empirical studies of NDCG, little is known about
its theoretical properties. We first show that, whatever the ranking function
is, the standard NDCG which adopts a logarithmic discount, converges to 1 as
the number of items to rank goes to infinity. On the first sight, this result
is very surprising. It seems to imply that NDCG cannot differentiate good and
bad ranking functions, contradicting to the empirical success of NDCG in many
applications. In order to have a deeper understanding of ranking measures in
general, we propose a notion referred to as consistent distinguishability. This
notion captures the intuition that a ranking measure should have such a
property: For every pair of substantially different ranking functions, the
ranking measure can decide which one is better in a consistent manner on almost
all datasets. We show that NDCG with logarithmic discount has consistent
distinguishability although it converges to the same limit for all ranking
functions. We next characterize the set of all feasible discount functions for
NDCG according to the concept of consistent distinguishability. Specifically we
show that whether NDCG has consistent distinguishability depends on how fast
the discount decays, and 1/r is a critical point. We then turn to the cut-off
version of NDCG, i.e., NDCG@k. We analyze the distinguishability of NDCG@k for
various choices of k and the discount functions. Experimental results on real
Web search datasets agree well with the theory.Comment: COLT 201
Divergent mathematical treatments in utility theory
In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper
Channels of transmission of inequality to growth: A survey of the theory and evidence from a Portuguese perspective
We review the theoretical and empirical literature on the relationship between inequality and economic growth from the perspective of the Portuguese economy in order to identify the correct (predicted) sign for the relationship in this particular country and the underlying mechanisms that explain it. Different mechanisms relating inequality and economic growth can be at stake explaining why different countries can experience different outcomes in the same period of time or why the same country experiences different outcomes in different periods of time. It is thus fundamental to correctly identify the channels of transmission of inequality to growth in the Portuguese economy. Ideally, all the mechanisms selected should be tested, but prior judgments should also lead us to produce a ranking of the mechanisms according to its relevance for the economy under analysis. This correct identification and ranking leads to more accurate policy recommendations as far as redistributive policies for the Portuguese economy are concerned.Inequality; Growth; Portugal.
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