18,279 research outputs found
Intrinsic Universal Measurements of Non-linear Embeddings
A basic problem in machine learning is to find a mapping from a low
dimensional latent space to a high dimensional observation space. Equipped with
the representation power of non-linearity, a learner can easily find a mapping
which perfectly fits all the observations. However such a mapping is often not
considered as good as it is not simple enough and over-fits. How to define
simplicity? This paper tries to make such a formal definition of the amount of
information imposed by a non-linear mapping. This definition is based on
information geometry and is independent of observations, nor specific
parametrizations. We prove these basic properties and discuss relationships
with parametric and non-parametric embeddings.Comment: work in progres
Guaranteed bounds on the Kullback-Leibler divergence of univariate mixtures using piecewise log-sum-exp inequalities
Information-theoretic measures such as the entropy, cross-entropy and the
Kullback-Leibler divergence between two mixture models is a core primitive in
many signal processing tasks. Since the Kullback-Leibler divergence of mixtures
provably does not admit a closed-form formula, it is in practice either
estimated using costly Monte-Carlo stochastic integration, approximated, or
bounded using various techniques. We present a fast and generic method that
builds algorithmically closed-form lower and upper bounds on the entropy, the
cross-entropy and the Kullback-Leibler divergence of mixtures. We illustrate
the versatile method by reporting on our experiments for approximating the
Kullback-Leibler divergence between univariate exponential mixtures, Gaussian
mixtures, Rayleigh mixtures, and Gamma mixtures.Comment: 20 pages, 3 figure
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