title={NIFTy5: Numerical Information Field Theory v5},

title={NIFTy6: Numerical Information Field Theory v5},

author={Arras, Philipp and Baltac, Mihai and Ensslin, Torsten A and Frank, Philipp and Hutschenreuter, Sebastian and Knollmueller, Jakob and Leike, Reimar and Newrzella, Max-Niklas and Platz, Lukas and Reinecke, Martin and others},

author={Arras, Philipp and Baltac, Mihai and Ensslin, Torsten A and Frank, Philipp and Hutschenreuter, Sebastian and Knollmueller, Jakob and Leike, Reimar and Newrzella, Max-Niklas and Platz, Lukas and Reinecke, Martin and others},

journal={Astrophysics Source Code Library},

journal={Astrophysics Source Code Library},

year={2019}

year={2019}

...

@@ -13,7 +13,7 @@ NIFTy-related publications

...

@@ -13,7 +13,7 @@ NIFTy-related publications

author = {{Martin Reinecke, Theo Steininger, Marco Selig}},

author = {{Martin Reinecke, Theo Steininger, Marco Selig}},

title = {NIFTy -- Numerical Information Field TheorY},

title = {NIFTy -- Numerical Information Field TheorY},

NIFTy5 automatically calculates the necessary gradient from a generative model of the signal and the data and uses this to minimize the Hamiltonian.

NIFTy6 automatically calculates the necessary gradient from a generative model of the signal and the data and uses this to minimize the Hamiltonian.

However, MAP often provides unsatisfactory results in cases of deep hirachical Bayesian networks.

However, MAP often provides unsatisfactory results in cases of deep hirachical Bayesian networks.

The reason for this is that MAP ignores the volume factors in parameter space, which are not to be neglected in deciding whether a solution is reasonable or not.

The reason for this is that MAP ignores the volume factors in parameter space, which are not to be neglected in deciding whether a solution is reasonable or not.

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@@ -224,7 +224,7 @@ Thus, only the gradient of the KL is needed with respect to this, which can be e

...

@@ -224,7 +224,7 @@ Thus, only the gradient of the KL is needed with respect to this, which can be e

We stochastically estimate the KL-divergence and gradients with a set of samples drawn from the approximate posterior distribution.

We stochastically estimate the KL-divergence and gradients with a set of samples drawn from the approximate posterior distribution.

The particular structure of the covariance allows us to draw independent samples solving a certain system of equations.

The particular structure of the covariance allows us to draw independent samples solving a certain system of equations.

This KL-divergence for MGVI is implemented in the class :class:`~minimization.metric_gaussian_kl.MetricGaussianKL` within NIFTy5.

This KL-divergence for MGVI is implemented in the class :class:`~minimization.metric_gaussian_kl.MetricGaussianKL` within NIFTy6.

The demo `getting_started_3.py` for example not only infers a field this way, but also the power spectrum of the process that has generated the field.

The demo `getting_started_3.py` for example not only infers a field this way, but also the power spectrum of the process that has generated the field.