Nonparametric estimation of the likelihood ratio and divergence functionals

By XuanLong Nguyen, Martin J. Wainwright, Michael I. Jordan. 2007

40 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

On the empirical estimation of integral probability metrics (2012, background): “The empirical estimation of φ-divergences, especially the KL-divergence, has recently been studied in depth [30, 32, 52].”
Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization (2008, methodology): “As a particular case of the Kullback-Leibler divergence, the mutual information specifies capacities in (1)Preliminary versions of this work were presented at the International Symposium on Information Theory (2007) [18] and the Neural Information Processing Systems Conference (2007) [17].”
Kullback-Leibler divergence estimation of continuous distributions (2008, background): “In [18] the authors compute the divergence between p(x) and q(x) using a variational approach, in which convergence is proven ensuring that the estimate for p(x)/q(x) converges to the true measure ratio.”
Estimation of Information Theoretic Measures for Continuous Random Variables (2008, methodology): “The estimation of the divergence and mutual information for continuous random variables has been addressed by many different authors [25, 6, 26, 18, 20, 16], see also the references therein.”
Convex Formulation for Learning from Positive and Unlabeled Data (2015, background): “To cope with this problem, in Keziou (2003) and Nguyen et al. (2007), the following objective function for density ratio estimation was introduced: sup g ∫ g(x)p(x|y = 1)dx− ∫ f∗(g(x))p(x)dx, (10) wheref(t) is a convex function such thatf(1) = 0, and f∗(z) = supt tz − f(t) denotes its Fenchel dual.”
Change-Point Detection in Time-Series Data by Relative Density-Ratio Estimation (2012, background): “This expression can also be obtained based on the fact that the f -divergence D ( P k P ′ ) is lower-bounded via the Legendre-Fenchel convex duality (Rockafellar, 1970) as follows (Keziou, 2003; Nguyen et al., 2007): where f ∗ is the convex conjugate of convex function f deﬁned at (2).”