random

random

RandomBinaryTree(num_variables, *, depth=None, num_repetitions=1, seed=42)

Construct a RG with random binary trees.

See

• Random sum-product networks: A simple but effective approach to probabilistic deep learning. 🔗 Robert Peharz, Antonio Vergari, Karl Stelzner, Alejandro Molina, Xiaoting Shao, Martin Trapp, Kristian Kersting, and Zoubin Ghahramani. In Uncertainty in Artificial Intelligence, pp. 334-344. PMLR, 2020.

Parameters:

Name	Type	Description	Default
num_variables	int	The number of variables in the RG.	required
depth	int	The depth of the binary tree. If None, the maximum possible depth is used.	None
num_repetitions	int	The number of repetitions of binary trees (degree of root).	1
seed	int	The seed to initialize the random state.	42

Returns:

Name	Type	Description
RegionGraph	RegionGraph	A randomized binary tree region graph.

Raises:

Type	Description
ValueError	If either the number of variables or number of reptitions are not positive.
ValueError	If the given depth is either negative or greate than the maximum allowed one.

Source code in cirkit/templates/region_graph/algorithms/random.py

def RandomBinaryTree(
    num_variables: int, *, depth: int | None = None, num_repetitions: int = 1, seed: int = 42
) -> RegionGraph:
    """Construct a RG with random binary trees.

    See:
        - *Random sum-product networks: A simple but effective approach to probabilistic deep learning.*  [🔗](https://proceedings.mlr.press/v115/peharz20a.html)
          Robert Peharz, Antonio Vergari, Karl Stelzner, Alejandro Molina, Xiaoting Shao, Martin Trapp, Kristian Kersting, and Zoubin Ghahramani.
          In Uncertainty in Artificial Intelligence, pp. 334-344. PMLR, 2020.

    Args:
        num_variables (int): The number of variables in the RG.
        depth (int): The depth of the binary tree. If None, the maximum possible depth is used.
        num_repetitions (int): The number of repetitions of binary trees (degree of root).
        seed: The seed to initialize the random state.

    Returns:
        RegionGraph: A randomized binary tree region graph.

    Raises:
        ValueError: If either the number of variables or number of reptitions are not positive.
        ValueError: If the given depth is either negative or greate than the maximum allowed one.
    """
    if num_variables <= 0:
        raise ValueError("The number of variables must be positive")
    if num_repetitions <= 0:
        raise ValueError("The number of repetitions must be positive")
    max_depth = int(np.ceil(np.log2(num_variables)))
    if depth is None:
        depth = max_depth
    elif depth < 0 or depth > max_depth:
        raise ValueError(f"The depth must be between 0 and {max_depth}")
    random_state = np.random.RandomState(seed)
    root = RegionNode(range(num_variables))
    nodes: list[RegionGraphNode] = [root]
    in_nodes: dict[RegionGraphNode, list[RegionGraphNode]] = defaultdict(list)

    def random_scope_partitioning(
        scope: Scope,
        num_parts: int | None = None,
        proportions: Sequence[float] | None = None,
    ) -> list[Scope]:
        # Shuffle the region node scope
        scope_ls = list(scope)
        random_state.shuffle(scope_ls)

        # ANNOTATE: Numpy has typing issues.
        split: np.ndarray  # Unnormalized split points including 0 and 1.
        if proportions is None:
            if num_parts is None:
                raise ValueError("Must provide at least one of num_parts and proportions")
            split = np.arange(num_parts + 1, dtype=np.float64)
        else:
            split = np.array([0.0] + list(proportions), dtype=np.float64).cumsum()

        # ANNOTATE: ndarray.tolist gives Any.
        # CAST: Numpy has typing issues.
        # IGNORE: Numpy has typing issues.
        split_point: list[int] = (
            (split / split[-1] * len(scope_ls)).round().astype(np.int64).tolist()
        )

        # ANNOTATE: Specify content for empty container.
        scopes: list[Scope] = []
        for l, r in itertools.pairwise(split_point):
            if l < r:  # A region must have as least one var, otherwise we skip it.
                scopes.append(Scope(scope_ls[l:r]))

        if len(scopes) == 1:
            # Only one region, meaning cannot partition anymore, and we just keep the original
            # node as the leaf.
            return [Scope(scope_ls)]

        return scopes

    for _ in range(num_repetitions):
        frontier: list[RegionGraphNode] = [root]
        for _ in range(depth):
            next_frontier: list[RegionGraphNode] = []
            for rgn in frontier:
                partition_node = PartitionNode(rgn.scope)
                scopes = random_scope_partitioning(rgn.scope, num_parts=2)
                if len(scopes) == 1:  # No further binary partitionings are possible
                    continue
                region_nodes: list[RegionGraphNode] = [RegionNode(scope) for scope in scopes]
                nodes.append(partition_node)
                nodes.extend(region_nodes)
                in_nodes[rgn].append(partition_node)
                in_nodes[partition_node] = region_nodes
                next_frontier.extend(region_nodes)
            frontier = next_frontier

    return RegionGraph(nodes, in_nodes, outputs=[root])