tf.math.lbeta  |  TensorFlow v2.0.0 (original) (raw)

tf.math.lbeta

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

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tf.compat.v1.lbeta, tf.compat.v1.math.lbeta

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

Given one-dimensional z = [z_0,...,z_{K-1}], we define

Beta(z) = \prod_j Gamma(z_j) / Gamma(\sum_j z_j)Andfor‘n+1‘dimensional‘x‘withshape‘[N1,...,Nn,K]‘,wedefineAnd for n + 1 dimensional x with shape [N1, ..., Nn, K], we defineAndfor‘n+1‘dimensional‘x‘withshape‘[N1,...,Nn,K]‘,wedefinelbeta(x)[i1, ..., in] = Log(|Beta(x[i1, ..., in, :])|)$$

.

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

Note that if z = [u, v], then \(Beta(z) = int_0^1 t^{u-1} (1 - t)^{v-1} dt\), 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.