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use itertools::Itertools;
use rayon::prelude::*;
use crate::{
estimators::{PK, ScoringCriterion},
models::{DiGraph, Graph, Labelled},
set,
types::{Error, Result, Set},
};
/// The hill climbing algorithm for structure learning in CTBNs.
#[derive(Clone, Debug)]
pub struct CTHC<'a, S> {
initial_graph: &'a DiGraph,
score: &'a S,
max_parents: Option<usize>,
prior_knowledge: Option<&'a PK>,
}
impl<'a, S> CTHC<'a, S>
where
S: ScoringCriterion + Labelled,
{
/// Creates a new continuous time hill climbing instance.
///
/// # Arguments
///
/// * `initial_graph` - The initial directed graph.
/// * `score` - The scoring criterion to use.
///
/// # Returns
///
/// A new `ContinuousTimeHillClimbing` instance.
///
#[inline]
pub fn new(initial_graph: &'a DiGraph, score: &'a S) -> Result<Self> {
// Check labels of the initial graph and the estimator are the same.
if initial_graph.labels() != score.labels() {
return Err(Error::LabelMismatch(
&format!("{:?}", initial_graph.labels()),
&format!("{:?}", score.labels()),
));
}
Ok(Self {
initial_graph,
score,
max_parents: None,
prior_knowledge: None,
})
}
/// Sets the maximum number of parents for each vertex.
///
/// # Arguments
///
/// * `max_parents` - The maximum number of parents for each vertex.
///
/// # Returns
///
/// The modified instance.
///
#[inline]
pub const fn with_max_parents(mut self, max_parents: usize) -> Self {
self.max_parents = Some(max_parents);
self
}
/// Sets the prior knowledge for the algorithm.
///
/// # Arguments
///
/// * `prior_knowledge` - The prior knowledge to use.
///
/// # Returns
///
/// The modified instance.
///
#[inline]
pub fn with_prior_knowledge(mut self, prior_knowledge: &'a PK) -> Result<Self> {
// Check labels of prior knowledge and initial graph are the same.
if self.initial_graph.labels() != prior_knowledge.labels() {
return Err(Error::LabelMismatch(
&format!("{:?}", self.initial_graph.labels()),
&format!("{:?}", prior_knowledge.labels()),
));
}
// Check prior knowledge is consistent with initial graph.
for edge in self.initial_graph.vertices().into_iter().permutations(2) {
// Get the edge indices.
let (i, j) = (edge[0], edge[1]);
// Check edge must be either present and not forbidden ...
if self.initial_graph.has_edge(i, j)? {
if prior_knowledge.is_forbidden(i, j) {
return Err(Error::PriorKnowledgeConflict(&format!(
"Initial graph contains forbidden edge ({i}, {j})."
)));
}
// ... or absent and not required.
} else if prior_knowledge.is_required(i, j) {
return Err(Error::PriorKnowledgeConflict(&format!(
"Initial graph does not contain required edge ({i}, {j})."
)));
}
}
// Set prior knowledge.
self.prior_knowledge = Some(prior_knowledge);
Ok(self)
}
/// Execute the CTHC algorithm.
///
/// # Returns
///
/// The fitted graph.
///
pub fn fit(&self) -> Result<DiGraph> {
// Clone the initial graph.
let mut graph = DiGraph::empty(self.initial_graph.labels())?;
// For each vertex in the graph ...
for i in self.initial_graph.vertices() {
// Initialize the previous score to negative infinity.
let mut prev_score = f64::NEG_INFINITY;
// Set the initial parent set as the current parent set.
let mut curr_pa = self.initial_graph.parents(&set![i])?;
// Compute the score of the current parent set.
let mut curr_score = self.score.call(&set![i], &curr_pa)?;
// While the score of the current parent set is higher than the previous score ...
while prev_score < curr_score {
// Set the previous score to the score of the current parent set.
prev_score = curr_score;
// Get the candidate parent sets by adding ...
let poss_pa = {
// Clone the current parent set.
[curr_pa.clone()].into_iter().filter(|curr_pa|
// Check if maximum parents has been reached.
if let Some(max_parents) = self.max_parents {
curr_pa.len() < max_parents
} else {
true
}
).flat_map(|curr_pa| {
// Get the vertices that are not in the current parent set.
self.initial_graph
.vertices()
.into_iter()
.filter_map(move |j| {
if i != j {
// If the vertex is not in the current parent set ...
if let Err(p_j) = curr_pa.binary_search(&j) {
// Clone the current parent set.
let mut curr_pa = curr_pa.clone();
// Insert the vertex in order.
curr_pa.shift_insert(p_j, j);
// Return it as a candidate for addition.
return Some(curr_pa);
}
}
// Otherwise, the vertex is already present.
None
})
})
}
// ... or removing vertices.
.chain({
// Clone the current parent set.
let curr_pa = curr_pa.clone();
// Get the size of the candidate subset, avoid underflow.
let k = curr_pa.len().saturating_sub(1);
// Generate all the k-sized subsets.
curr_pa.into_iter().combinations(k).map(Set::from_iter)
});
// For each candidate parent sets ...
for next_pa in poss_pa {
// Compute the score of the candidate parent set.
let next_score = self.score.call(&set![i], &next_pa)?;
// If the score of the candidate parent set is higher ...
if curr_score < next_score {
// Update the current parent set to the candidate parent set.
curr_pa = next_pa;
// Update the score of the current parent set.
curr_score = next_score;
}
}
}
// Set the current parent set.
for j in curr_pa {
// Add an edge from vertex `j` to vertex `i`.
graph.add_edge(j, i)?;
}
}
// Return the final graph.
Ok(graph)
}
}
impl<'a, S> CTHC<'a, S>
where
S: ScoringCriterion + Sync,
{
/// Execute the CTHC algorithm in parallel.
///
/// # Returns
///
/// The fitted graph.
///
pub fn par_fit(&self) -> Result<DiGraph> {
// For each vertex in the graph ...
let parents: Vec<_> = self
.initial_graph
.vertices()
.into_par_iter()
.map(|i| {
// Initialize the previous score to negative infinity.
let mut prev_score = f64::NEG_INFINITY;
// Set the initial parent set as the current parent set.
let mut curr_pa = self.initial_graph.parents(&set![i])?;
// Compute the score of the current parent set.
let mut curr_score = self.score.call(&set![i], &curr_pa)?;
// While the score of the current parent set is higher than the previous score ...
while prev_score < curr_score {
// Set the previous score to the score of the current parent set.
prev_score = curr_score;
// Get the candidate parent sets by adding ...
let poss_pa: Vec<_> = {
// Clone the current parent set.
[curr_pa.clone()].into_iter().filter(|curr_pa|
// Check if maximum parents has been reached.
if let Some(max_parents) = self.max_parents {
curr_pa.len() < max_parents
} else {
true
}
).flat_map(|curr_pa| {
// Get the vertices that are not in the current parent set.
self.initial_graph
.vertices()
.into_iter()
.filter_map(move |j| {
if i != j {
// If the vertex is not in the current parent set ...
if let Err(p_j) = curr_pa.binary_search(&j) {
// Clone the current parent set.
let mut curr_pa = curr_pa.clone();
// Insert the vertex in order.
curr_pa.shift_insert(p_j, j);
// Return it as a candidate for addition.
return Some(curr_pa);
}
}
// Otherwise, the vertex is already present.
None
})
})
}
// ... or removing vertices.
.chain({
// Clone the current parent set.
let curr_pa = curr_pa.clone();
// Get the size of the candidate subset, avoid underflow.
let k = curr_pa.len().saturating_sub(1);
// Generate all the k-sized subsets.
curr_pa.into_iter().combinations(k).map(Set::from_iter)
})
// Collect to allow for parallel iteration.
.collect();
// For each candidate parent sets ...
let scores = poss_pa
.into_par_iter()
// Compute the score of the candidate parent set in parallel.
.map(|next_pa| self.score.call(&set![i], &next_pa).map(|s| (s, next_pa)))
.collect::<Result<Vec<_>>>()?;
if scores.iter().any(|(s, _)| s.is_nan()) {
return Err(Error::NanValue());
}
if let Some((next_score, next_pa)) = scores
.into_iter()
// Get the one with the highest score in parallel.
.max_by(|(a, _), (b, _)| {
a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal)
})
{
// If the score of the candidate parent set is higher ...
if curr_score < next_score {
// Update the current parent set to the candidate parent set.
curr_pa = next_pa;
// Update the score of the current parent set.
curr_score = next_score;
}
}
}
// Return the current parent set.
Ok(curr_pa)
})
.collect::<Result<_>>()?;
// Clone the initial graph.
let mut graph = DiGraph::empty(self.initial_graph.labels())?;
// Set the current parent set.
for (i, curr_pa) in parents.into_iter().enumerate() {
for j in curr_pa {
// Add an edge from vertex `j` to vertex `i`.
graph.add_edge(j, i)?;
}
}
// Return the final graph.
Ok(graph)
}
}