Affine Independent Variational Inference
نویسندگان
چکیده
We consider inference in a broad class of non-conjugate probabilistic models based on minimising the Kullback-Leibler divergence between the given target density and an approximating ‘variational’ density. In particular, for generalised linear models we describe approximating densities formed from an affine transformation of independently distributed latent variables, this class including many well known densities as special cases. We show how all relevant quantities can be efficiently computed using the fast Fourier transform. This extends the known class of tractable variational approximations and enables the fitting for example of skew variational densities to the target density.
منابع مشابه
Affine Independent Variational Inference Supplementary Material
Potential functions g(x) : R→ R that are piecewise smooth with a finite number of discontinuities have expectation 〈 g(wTx) 〉 qw(w|A,b,θ) that is smooth in A,b provided that qv(v) is smooth in v. In this context we say that a function is smooth if it has continuous second order partial derivatives. Specifically, we require that g(x) is piecewise smooth and so can be expressed as a sum of functions
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