cpm

Class

class Cpm

A class for conditional probability matrices (CPMs) of MBN.

Parameters:

variables (list) – List of Variables in the scope of the distribution.
no_child (int) – Number of child nodes.
C (2D numpy.ndarray) – Event matrix specifying the state of each instance.
p (1D numpy.ndarray) – Probability vector defining the corresponding probabilities.
Cs (2D numpy.ndarray) – Event matrix of sampled instances.
q (1D numpy.ndarray) – Sampling probability vector of sampled instances.
ps (1D numpy.ndarray) – Current probability vector of sampled instances (q and ps are the same for Monte Carlo simulation, but are not for other sampling techniques e.g. importance sampling).
sample_idx (1D numpy.ndarray) – Index of the sampled instance. When samples are first generated, the index starts from 0 to the number of instances. This vector is necessary since a sample can become two instances during inference and different samples cannot be computed together.

Note

Cs, q, ps, and sample_idx are only necessary when samples are used.

Example Usage

from mbnpy import variable, cpm
import numpy as np

# First define the variables
varis = {}
varis['x1'] = variable.Variable('x1', ['fail', 'surv'])
varis['x2'] = variable.Variable('x2', ['f', 's'])
varis['x3'] = variable.Variable('x3', ['f', 's'])

# Define the CPMs
cpms = {}
cpms['x1'] = cpm.Cpm([varis['x1']], no_child=1, C=np.array([[0], [1]], dtype=int), p = np.array([0.1, 0.9]))
cpms['x2'] = cpm.Cpm([varis['x2']], no_child=1, C=np.array([[0], [1]], dtype=int), p = np.array([0.2, 0.8]))

# 'x3' is a series system of 'x1' and 'x2'
cpms['x3'] = cpm.Cpm([varis['x3'], varis['x1'], varis['x2']], no_child=1,
                    C=np.array([[0, 0, 2], [0, 1, 0], [1, 1, 1]], dtype=int), p = np.array([1.0, 1.0, 1.0]))

Methods

product (1)

Cpm.product(self, M)

Compute the product of the CPM with another CPM.

param M:

Another CPM.

type M:

Cpm

return:

The product of the two CPMs.

rtype:

Cpm

Example: One can perform \(P(X_3|X_1,X_2) \cdot P(X_1)\) as follows:
cpm_x3_x1 = cpms['x3'].product(cpms['x1'])
print(cpm_x3_x1)
Output:
Cpm(variables=['x3', 'x1', 'x2'],
    no_child=2,
    C=[[0 0 2]
    [0 1 0]
    [1 1 1]],
    p=[[0.1]
    [0.9]
    [0.9]],
    )
Notice that no_child is updated to 2 as now Mnew represents \(P(X_3,X_1|X_2)\).

get_subset

Cpm.get_subset(self, row_idx, flag=True, isC=True)

Get a new CPM with a subset of rows from event matrix and probability vector.

param row_idx:

List of row indices to be selected.

type row_idx:

list

param flag:

If True, the subset is selected. If False, the subset is removed.

type flag:

bool

param isC:

If True, the subset is obtained from C and p. If False, the subset is obtained from Cs, q, ps, and sample_idx.

type isC:

bool

return:

A new CPM with the subset of rows.

rtype:

Cpm

Example:
Mnew = cpm_x3_x1.get_subset([0,2])
print(Mnew)
Output:
Cpm(variables=['x3', 'x1', 'x2'],
    no_child=2,
    C=[[0 0 2]
    [1 1 1]],
    p=[[0.1]
    [0.9]],
    )

iscompatible (1)

Cpm.iscompatible(self, M, composite_state=True)

Check if two CPMs are compatible.

param M:

Another CPM. Must include a single row in either C or Cs.

type M:

Cpm

param composite_state:

If True, the function considers compatibility between basic states and composite states. If False, the function considers strict compatibility that two states are compatible when they have the same index.

type composite_state:

bool

return:

For each row of C or Cs, a boolean value indicating whether the row is compatible with the corresponding row in the other CPM.

rtype:

a list of bool

Example:

The code below finds the rows of cpms['x3'] that indicate X3’s failure state:
M1 = cpm.Cpm([varis['x3']], no_child=1, C=np.array([[0]], dtype=int))
is_cmp = cpms['x3'].iscompatible(M1)
print(is_cmp)
Output:
[True, True, False]

sum

Cpm.sum(self, variables, flag=True)

Sum out the variables in the CPM.

param variables:

List of variables to be summed out.

type variables:

list of Variable

param flag:

If True, the variables are summed out. If False, the variables are kept and the other variables are summed out.

type flag:

bool

return:

A new CPM with the variables summed out.

rtype:

Cpm

Example:

The code below sums out X1 from \(P(X_3,X_1|X_2)\), i.e. \(\sum_{X_1} P(X_3,X_1|X_2) = P(X_3|X_2)\):
Mnew = cpm_x3_x1.sum([varis['x1']])
print(Mnew)
Output:
Cpm(variables=['x3', 'x2'],
    no_child=1,
    C=[[0 2]
    [0 0]
    [1 1]],
    p=[[0.1]
    [0.9]
    [0.9]],
)

sort

cpm.sort(self)

Sort the CPM based on C and sample_idx.

return:

A new CPM with the rows sorted.

rtype:

Cpm

Example:

The code below sorts the rows of \(P(X_3|X_2)\) from the result above:
cpm_x3_x2.sort()
print(cpm_x3_x2)
Output:
Cpm(variables=['x3', 'x2'],
    no_child=1,
    C=[[0 0]
    [0 2]
    [1 1]],
    p=[[0.9]
    [0.1]
    [0.9]],
    )

iscompatible (2)

cpm.iscompatible(C, variables, check_vars, check_states, composite_state=True)

Check if a C defined over variables is compatible with check_states of check_vars.

Parameters:

C (2D numpy.ndarray) – Event matrix of the CPM.
variables (list) – List of variables in the scope of C.
check_vars (list) – List of variables to be checked for compatibility.
check_states (list) – List of states to be checked for compatibility.
composite_state (bool) – If True, the function considers compatibility between basic states and composite states. If False, the function considers strict compatibility that two states are compatible when they have the same index.

Returns:

For each row of C, a boolean value indicating whether the row is compatible with the given variables and states.

Return type:

a list of bool

Example:

The code below finds the rows of cpms['x3'] that indicate X3’s failure state:

is_cmp = cpm.iscompatible(cpms['x3'].C, cpms['x3'].variables, [varis['x3']], [0], composite_state=True)

print(is_cmp)

Output:

[True, True, False]

product (2)

cpm.product(cpms):

Mutiply a list or dictionary of CPMs.

Parameters:: cpms (list or dictionary of Cpm) – List of CPMs.
Returns:: The product of the CPMs.
Return type:: Cpm

Example:

Code below multiplies \(P(X_3|X_1,X_2)\), \(P(X_1)\), and \(P(X_2)\), i.e. \(P(X_3,X_1,X_2) = P(X_3|X_1,X_2) \cdot P(X_1) \cdot P(X_2)\):

Mprod = cpm.product(cpms)
print(Mprod)

Output:

Cpm(variables=['x1', 'x2', 'x3'],
    no_child=3,
    C=[[0 0 0]
    [0 1 0]
    [1 0 0]
    [1 1 1]],
    p=[[0.02]
    [0.08]
    [0.18]
    [0.72]],
    )