Skip to content

Quickstart

This page walks through a minimal BRB workflow on the benchmark function \(f(x) = x \sin(x^2)\) from 1. For a fuller walkthrough with plots, see notebooks/01_getting_started.ipynb in the repository.

Define the model

A BRB model is specified by its referential values: discrete anchor points on the input and output spaces.

import numpy as np
from desdeo_brb import BRBModel

# 7 precedent referential values for x in [0, 3]
prv = [np.array([0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0])]

# 5 consequent referential values for f(x)
crv = np.array([-2.5, -1.0, 1.0, 2.0, 3.0])

# Construct the model; initial beliefs computed by evaluating f
# at each precedent referential value
model = BRBModel(prv, crv, initial_rule_fn=lambda x: x[0] * np.sin(x[0] ** 2))

The Cartesian product of precedent referential values defines 7 rules. Each rule has a belief distribution over the 5 consequent referential values.

Inspect the initial rule base

print(model.rule_base.describe_all_rules(
    attribute_names=["x"], consequent_name="f(x)"
))

Output:

Rule 0: IF x is 0 THEN f(x) = {-1: 0.500, 1: 0.500} [w=0.143]
Rule 1: IF x is 0.5 THEN f(x) = {-1: 0.438, 1: 0.562} [w=0.143]
Rule 2: IF x is 1 THEN f(x) = {-1: 0.079, 1: 0.921} [w=0.143]
...

Train the model

BRB training is non-convex, so multiple random restarts are recommended:

X_train = np.linspace(0, 3, 1000).reshape(-1, 1)
y_train = X_train[:, 0] * np.sin(X_train[:, 0] ** 2)

model.fit(X_train, y_train, fix_endpoints=True, n_restarts=10)

See the training guide for details on the available methods.

Predict and explain

# Predict scalar outputs
y_pred = model.predict_values(np.array([[1.5], [2.5]]))
print(y_pred)  # [1.167..., 0.093...]

# Get the full inference trace
result = model.predict(np.array([[1.5]]))
print(result.activation_weights)    # which rules fired
print(result.combined_belief_degrees)  # output belief distribution

# Human-readable explanation
print(model.explain(np.array([[1.5]]), attribute_names=["x"], consequent_name="f(x)"))

Typical explain() output:

Prediction: 1.167

Top activated rules:
  Rule 3 (w=1.0000, x=1.5): {1: 0.833, 2: 0.167}

Combined belief distribution:
  {1: 0.833, 2: 0.167}

Next steps

  1. Yu-Wang Chen, Jian-Bo Yang, Dong-Ling Xu, Zhi-Jie Zhou, and Da-Wei Tang. Inference analysis and adaptive training for belief rule based systems. Expert Systems with Applications, 38(10):12845–12860, 2011. doi:10.1016/j.eswa.2011.04.077. ↩