tf.nn.isotonic_regression

Solves isotonic regression problems along the given axis.

tf.nn.isotonic_regression(
    inputs, decreasing=True, axis=-1
)

For each vector x, the problem solved is

As the solution is component-wise constant, a second tensor is returned that encodes the segments. The problems are solved over the given axis.

Consider the following example, where we solve a batch of two problems. The first input is [3, 1, 2], while the second 1, 3, 4.

>>> x = tf.constant([[3, 1, 2], [1, 3, 4]], dtype=tf.float32)
>>> y, segments = tf.nn.isotonic_regression(x, axis=1)
>>> y  # The solution.
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[3.       , 1.5      , 1.5      ],
       [2.6666667, 2.6666667, 2.6666667]], dtype=float32)>

Note that the first solution has two blocks [2] and [1.5, 1.5]. The second solution is constant, and thus has a single segment. These segments are exactly what the second returned tensor encodes:

segments
<tf.Tensor: shape=(2, 3), dtype=int32, numpy=
array([[0, 1, 1],
       [0, 0, 0]], dtype=int32)>