# Exact Search

## Algorithm Introduction

Search for the optimal graph using Dynamic Programming (DP 1) or A* search 2.

## Usage

    from causal-learn.search.ScoreBased.ExactSearch import bic_exact_search
    dag_est, search_stats = bic_exact_search(X, super_graph, search_method,
                     use_path_extension, use_k_cycle_heuristic,
                     k, verbose, include_graph, max_parents)

## Parameters

X: numpy.ndarray, shape=(n, d). The data to fit the structure too, where each row is a sample and each column corresponds to the associated variable.

super_graph: numpy.ndarray, shape=(d, d). Super-structure to restrict search space (binary matrix). If None, no super-structure is used. Default is None.

search_method: str. Method of of exact search ([‘astar’, ‘dp’]). Default is astar.

use_path_extension: bool. Whether to use optimal path extension for order graph. Note that this trick will not affect the correctness of search procedure. Default is True.

use_k_cycle_heuristic: bool. Whether to use k-cycle conflict heuristic for astar. Default is False.

k: int. Parameter used by k-cycle conflict heuristic for astar. Default is 3.

verbose: bool. Whether to log messages related to search procedure.

max_parents: int. The maximum number of parents a node can have. If used, this means using the k-learn procedure. Can drastically speed up algorithms. If None, no max on parents. Default is None.

## Returns

dag_est: numpy.ndarray, shape=(d, d). Estimated DAG. search_stats: dict. Some statistics related to the seach procedure.

1

  Silander, T., & Myllymäki, P. (2006, July). A simple approach for finding the globally optimal Bayesian network structure. In Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (pp. 445-452).

2

  Yuan, C., & Malone, B. (2013). Learning optimal Bayesian networks: A shortest path perspective. Journal of Artificial Intelligence Research, 48, 23-65.