MVNPrecisionCholeskyWithUncerts (Part II)

[Angel Berihuete]

Dear TFP users.

I've changed my previous code at

https://colab.research.google.com/drive/1W5W_X9OKnOoA4PymmT32jyTR7BE_3WJh?usp=sharing

with a new version at

https://colab.research.google.com/drive/1TskzNggg3OTSweUkVb75B9CAvdX2jzSg?usp=sharing

I've included all the comments suggested by Dave in the previous discussion, and some recursive functions in order to do the code not dimension dependent.

In the first version I forgot to include a tf.linalg.cholesky function. You can see this "small detail" in the sanity check scatter-plot. The first version has a slight rotation in the data.

Now, when I include the

C3_chol =tf.linalg.cholesky(tf.stack(C3))

in line 61, inside the class MVNPrecisionCholeskyWithUncerts, I get an error

InvalidArgumentError: Cholesky decomposition was not successful. The input might not be valid.

Looking inside de matrices obtained in C3 there are some discrepancies on values outside the main diagonal, i.e., matrix is not "completely" symmetric ... maybe due to floating point errors?

Again is weird ... I can sample from the distribution, but I cannot use it to do inference!

Any clue to resolve this?

[Dave Moore]

The usual hacks to coax a matrix A to be numerically positive definite are:

1) Symmetrization: `A = 0.5 * (A + tf.linalg.matrix_transpose(A))`.

2) Diagonal padding: `A = tf.linalg.set_diag(A, tf.linalg.diag_part(A) + eps) `where eps is some small positive number.

You might also look at our recently-added `simple_robustified_cholesky` method:

https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/linalg/simple_robustified_cholesky

Dave

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[Angel Berihuete]

Dear Dave, so sorry for this huge delay in my response ...too many projects to develop ;)

simple_robustified_cholesky worked perfectly!!

Again, many thanks!!

Ángel