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The idea is to construct a neural network (NN) that takes N series of financial returns as input and returns the (approximation of the) inverse of the sample covariance matrix (an N times N matrix). I was wondering if there are any heuristics/rules of thumb for the architecture (depth, width) and type (convolutional, recurrent etc.) of NN suitable for such a task.

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    $\begingroup$ Why do you want do use NN for that? Did you read on covariance matrix estimation, like low rank approximation, iterative approximation (inverting using Woodbury formula)? $\endgroup$ Commented Mar 2, 2020 at 10:17
  • $\begingroup$ In portfolio optimization, the precision matrix is often used to determine optimal portfolio weights. However, since the sample covariance matrix is prone to significant estimation errors, the sample precision matrix is even more problematic. The idea is to use NN to (for N series of financial returns) determine a matrix that is "near" the sample precision matrix but works better (more regularized etc.) via ML. To facilitate the learning process, we believe it would be beneficial to initialize the NN to the precision matrix approximator (hence the question) and subsequently build upon it. $\endgroup$
    – BGa
    Commented Mar 2, 2020 at 12:01
  • $\begingroup$ Yes, generally we are acquainted with such approaches, however, the idea is to abandon such more "classical" approaches and let the learning process find the optimal solution without any additional assumptions. If there are any reasons why you believe this wouldn't work, I'd be glad to hear more. $\endgroup$
    – BGa
    Commented Mar 2, 2020 at 12:04
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    $\begingroup$ There are statistical approaches to this - using methods I mentioned and also robust statistics. What confuses me is that having neural network to learn that seems like it would be even more prone to estimation errors, since NN methods are pretty strong (flexible) regressors and in general more prone to fitting random noise than classical approaches $\endgroup$ Commented Mar 2, 2020 at 19:15

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Related to your question, there are times when you want to use something like inverse covariance estimation to perform link prediction across time series. For this you can include an inverse covariance layer in a neural network that takes as input time series:

https://proceedings.neurips.cc/paper/2014/file/8b16ebc056e613024c057be590b542eb-Paper.pdf

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