34,358 research outputs found
Piecewise linear regularized solution paths
We consider the generic regularized optimization problem
. Efron, Hastie,
Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have shown that for
the LASSO--that is, if is squared error loss and is
the norm of --the optimal coefficient path is piecewise linear,
that is, is piecewise
constant. We derive a general characterization of the properties of (loss ,
penalty ) pairs which give piecewise linear coefficient paths. Such pairs
allow for efficient generation of the full regularized coefficient paths. We
investigate the nature of efficient path following algorithms which arise. We
use our results to suggest robust versions of the LASSO for regression and
classification, and to develop new, efficient algorithms for existing problems
in the literature, including Mammen and van de Geer's locally adaptive
regression splines.Comment: Published at http://dx.doi.org/10.1214/009053606000001370 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Quantifying Information Leakage in Finite Order Deterministic Programs
Information flow analysis is a powerful technique for reasoning about the
sensitive information exposed by a program during its execution. While past
work has proposed information theoretic metrics (e.g., Shannon entropy,
min-entropy, guessing entropy, etc.) to quantify such information leakage, we
argue that some of these measures not only result in counter-intuitive measures
of leakage, but also are inherently prone to conflicts when comparing two
programs P1 and P2 -- say Shannon entropy predicts higher leakage for program
P1, while guessing entropy predicts higher leakage for program P2. This paper
presents the first attempt towards addressing such conflicts and derives
solutions for conflict-free comparison of finite order deterministic programs.Comment: 14 pages, 1 figure. A shorter version of this paper is submitted to
ICC 201
Asymptotics in directed exponential random graph models with an increasing bi-degree sequence
Although asymptotic analyses of undirected network models based on degree
sequences have started to appear in recent literature, it remains an open
problem to study statistical properties of directed network models. In this
paper, we provide for the first time a rigorous analysis of directed
exponential random graph models using the in-degrees and out-degrees as
sufficient statistics with binary as well as continuous weighted edges. We
establish the uniform consistency and the asymptotic normality for the maximum
likelihood estimate, when the number of parameters grows and only one realized
observation of the graph is available. One key technique in the proofs is to
approximate the inverse of the Fisher information matrix using a simple matrix
with high accuracy. Numerical studies confirm our theoretical findings.Comment: Published at http://dx.doi.org/10.1214/15-AOS1343 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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