Transformed variables with non-elementwise bijectors

[Paul Welle]

Hi folks -

Trying to understand how 'Transformed Variables' work with bijectors that DON'T operate elementwise. My understanding how how TransformedVariables work comes from the docs, which state `Variable tracking object which applies a bijector upon convert_to_tensor.` Great, that's what I'm looking for.

So for example, with `FillTriangular` I see that this works:

x = [1, 1, 1, 1, 1, 1]
b = tfb.FillTriangular()
b.forward(x)

and returns 3 x 3 matrix with lower diagonal 1's.

however, this breaks:

x = [1, 1, 1, 1, 1, 1]
b = tfb.FillTriangular()
v = tfp.util.TransformedVariable(x, b)

with error `ValueError: Shape (6,) must have rank at least 2`.

It seems like TransformedVariable is looking for a 2 dimensional array, so I tried feeding:

b = tfb.FillTriangular()
new_x = tf.ones((3,3))
v = tfp.util.TransformedVariable(new_x, b)

The result for that code is:

2 0 0

2 2 0

1 1 1

Which I don't see how it's arriving at. Is there something I'm missing here?

Thanks for any help,

Paul

[Pavel Sountsov]

In general, the `initial_value` argument to `TransformedVariable`'s constructor corresponds to the *transformed* output, i.e., if it is valid, then the following equality should hold `initial_value == tf.convert_to_tensor(TransformedVariable(initial_value, bijector))`. Internally, the underlying `tf.Variable` is initialized with `bijector.inverse(initial_value)`.

In your case, your initial value is not valid because it is not a (lower) triangular matrix, so the `FillTriangular.inverse` returns undefined output. If you already have a lower triangular matrix in mind, you can use it as `initial_value`. Otherwise, your first code snippet can be changed to:

```

x = [1, 1, 1, 1, 1, 1]
b = tfb.FillTriangular()

v = tfp.util.TransformedVariable(b(x), b)  # b(x) <=> b.forward(x)

```

We'll improve the documentation to make this clearer, thanks for bringing it up.

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