PartialOrder

class pymc_extras.distributions.transforms.PartialOrder(adj_mat)

Create a PartialOrder transform

A more flexible version of the pymc ordered transform that allows specifying a (strict) partial order on the elements.

Examples

import numpy as np
import pymc as pm
import pymc_extras as pmx

# Define two partial orders on 4 elements
# am[i,j] = 1 means i < j
adj_mats = np.array([
    # 0 < {1, 2} < 3
    [[0, 1, 1, 0],
    [0, 0, 0, 1],
    [0, 0, 0, 1],
    [0, 0, 0, 0]],

    # 1 < 0 < 3 < 2
    [[0, 0, 0, 1],
    [1, 0, 0, 0],
    [0, 0, 0, 0],
    [0, 0, 1, 0]],
])

# Create the partial order from the adjacency matrices
po = pmx.PartialOrder(adj_mats)

with pm.Model() as model:
    # Generate 3 samples from both partial orders
    pm.Normal("po_vals", shape=(3,2,4), transform=po,
                initval=po.initvals((3,2,4)))

    idata = pm.sample()

# Verify that for first po, the zeroth element is always the smallest
assert (idata.posterior['po_vals'][:,:,:,0,0] <
        idata.posterior['po_vals'][:,:,:,0,1:]).all()

# Verify that for second po, the second element is always the largest
assert (idata.posterior['po_vals'][:,:,:,1,2] >=
        idata.posterior['po_vals'][:,:,:,1,:]).all()

Technical notes

Partial order needs to be strict, i.e. without equalities. A DAG defining the partial order is sufficient, as transitive closure is automatically computed. Code works in O(N*D) in runtime, but takes O(N^3) in initialization, where N is the number of nodes in the dag and D is the maximum in-degree of a node in the transitive reduction.

__init__(adj_mat)

Initialize the PartialOrder transform

Parameters:

adj_mat (ndarray) – adjacency matrix for the DAG that generates the partial order, where adj_mat[i][j] = 1 denotes i < j. Note this also accepts multiple DAGs if RV is multidimensional

Methods

__init__(adj_mat)	Initialize the PartialOrder transform
backward(value, *inputs)	Invert the transformation.
forward(value, *inputs)	Apply the transformation.
initvals([shape, lower, upper])	Create a set of appropriate initial values for the variable.
log_jac_det(value, *inputs)	Construct the log of the absolute value of the Jacobian determinant.

Attributes

name
ndim_supp