tf.math.lbeta

Computes \(ln(|Beta(x)|)\), reducing along the last dimension.

tf.math.lbeta(
    x, name=None
)

Given one-dimensional $z = [z_1,...,z_K]$, we define

where $\Gamma$ is the gamma function.

And for $n + 1$ dimensional $x$ with shape $[N_1, ..., N_n, K]$, we define

In other words, the last dimension is treated as the $z$ vector.

Note that if $z = [u, v]$, then

which defines the traditional bivariate beta function.

If the last dimension is empty, we follow the convention that the sum over the empty set is zero, and the product is one.