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class KL (Operator ):
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"""
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Operator based on Kullback Leibler Divergence
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.. math::
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KL[q(v)||p(v)] = \int q(v)\log\\ frac{q(v)}{p(v)}dv
@@ -41,20 +42,22 @@ class KSD(Operator):
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Operator based on Kernelized Stein Discrepancy
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Input: A target distribution with density function :math:`p(x)`
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- and a set of initial particles :math:`{x^0_i}^n_{i=1}`
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- Output: A set of particles :math:`{x_i}^n_{i=1}` that approximates the target distribution.
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+ and a set of initial particles :math:`\{x^0_i\}^n_{i=1}`
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+ Output: A set of particles :math:`\{x_i\}^n_{i=1}` that approximates the target distribution.
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.. math::
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x_i^{l+1} \leftarrow \epsilon_l \hat{\phi}^{*}(x_i^l)
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\hat{\phi}^{*}(x) = \f rac{1}{n}\sum^{n}_{j=1}[k(x^l_j,x) \n abla_{x^l_j} logp(x^l_j)+ \n abla_{x^l_j} k(x^l_j,x)]
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Parameters
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----------
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- approx : pm.Empirical
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+ approx : :class:`pm.Empirical`
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+ Empirical Approximation used for inference
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References
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----------
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- - Qiang Liu, Dilin Wang (2016)
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+ - Qiang Liu, Dilin Wang (2016)
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Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
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arXiv:1608.04471
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"""
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