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//! Online Bayesian Change Point Detection
//!
//! This code is derived from
//! "Bayesian Online Changepoint Detection"; Ryan Adams, David `MacKay`; arXiv:0710.3742
//! Which can be found [here](https://arxiv.org/pdf/0710.3742.pdf).
use crate::traits::BocpdLike;
use rand::{rngs::SmallRng, SeedableRng};
use rv::prelude::*;
use std::collections::VecDeque;
#[cfg(feature = "serde1")]
use serde::{Deserialize, Serialize};
/// Online Bayesian Change Point Detection with a truncated tail
///
/// The truncation takes place after run length probabilites are computed.
/// The truncation point is chosen based on the most recent point from which
/// all successive mass is below the given threshold.
#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
#[derive(Clone, Debug)]
pub struct BocpdTruncated<X, Fx, Pr>
where
Fx: Rv<X> + HasSuffStat<X>,
Pr: ConjugatePrior<X, Fx>,
Fx::Stat: Clone,
{
/// Geometric distribution timescale used as the Hazard Function.
/// \[
/// H(\tao) = 1/\lambda
/// \] where `hazard` is $\lambda$.
hazard: f64,
/// Probability of observing data type `X` i.e. $\pi^{(r)}_t = P(x_t | suff_stat)$.
predictive_prior: Pr,
/// Sequence of sufficient statistics representing cumulative states.
suff_stats: VecDeque<Fx::Stat>,
/// Initial suff_stat
initial_suffstat: Option<Fx::Stat>,
/// Run-length probabilities.
r: Vec<f64>,
empty_suffstat: Fx::Stat,
/// Cumulative CDF values are dropped after this threshold.
cdf_threshold: f64,
/// Point at which to stop storing runlength probabilities (prevents storing probabilities ~ 0)
cutoff_threadhold: f64,
}
impl<X, Fx, Pr> BocpdTruncated<X, Fx, Pr>
where
Fx: Rv<X> + HasSuffStat<X>,
Pr: ConjugatePrior<X, Fx, Posterior = Pr> + Clone,
Fx::Stat: Clone,
{
/// Create a new Bocpd analyzer
///
/// # Parameters
/// * `hazard` - The hazard function for `P_{gap} = 1/hazard`.
/// * `predictive_prior` - Prior for the predictive distribution.
///
/// # Example
/// ```rust
/// use changepoint::BocpdTruncated;
/// use rv::prelude::*;
///
/// let cpd = BocpdTruncated::new(
/// 250.0,
/// NormalGamma::new_unchecked(0.0, 1.0, 1.0, 1.0),
/// );
/// ```
pub fn new(hazard_lambda: f64, predictive_prior: Pr) -> Self {
let mut rng = SmallRng::seed_from_u64(0xABCD);
let fx: Fx = predictive_prior.draw(&mut rng);
let empty_suffstat = fx.empty_suffstat();
Self {
hazard: hazard_lambda.recip(),
predictive_prior,
suff_stats: VecDeque::new(),
r: Vec::new(),
empty_suffstat,
cdf_threshold: 1E-3,
cutoff_threadhold: 1E-6,
initial_suffstat: None,
}
}
/// Change the cutoff for mass to be discarded on the tail end of run-lengths
#[must_use]
pub fn with_cutoff(self, cutoff_threadhold: f64) -> Self {
Self {
cutoff_threadhold,
..self
}
}
/// Reset the introspector and replace the predictive prior
pub fn reset_with_prior(&mut self, predictive_prior: Pr) {
self.predictive_prior = predictive_prior;
self.reset();
}
}
impl<X, Fx, Pr> BocpdTruncated<X, Fx, Pr>
where
Fx: Rv<X> + HasSuffStat<X>,
Pr: ConjugatePrior<X, Fx, Posterior = Pr> + Clone,
Fx::Stat: Clone,
{
/// Reduce the observed values into a new BOCPD with those observed values integrated into the
/// prior.
#[must_use]
pub fn collapse_stats(self) -> Self {
let new_prior: Pr = self.suff_stats.back().map_or(
self.predictive_prior.clone(),
|suff_stat| {
self.predictive_prior
.posterior(&DataOrSuffStat::SuffStat(suff_stat))
},
);
Self {
suff_stats: VecDeque::new(),
r: vec![],
predictive_prior: new_prior,
..self
}
}
}
impl<X, Fx, Pr> BocpdLike<X> for BocpdTruncated<X, Fx, Pr>
where
Fx: Rv<X> + HasSuffStat<X>,
Pr: ConjugatePrior<X, Fx, Posterior = Pr> + Clone,
Fx::Stat: Clone,
{
type Fx = Fx;
type PosteriorPredictive = Mixture<Pr>;
/// Update the model with a new datum and return the distribution of run lengths.
fn step(&mut self, data: &X) -> &[f64] {
if self.r.is_empty() {
self.suff_stats.push_front(
self.initial_suffstat
.clone()
.unwrap_or_else(|| self.empty_suffstat.clone()),
);
// The initial point is, by definition, a change point
self.r.push(1.0);
} else {
self.suff_stats.push_front(self.empty_suffstat.clone());
self.r.push(0.0);
let mut r0 = 0.0;
let mut r_sum = 0.0;
let mut r_seen = 0.0;
for i in (0..(self.r.len() - 1)).rev() {
if self.r[i] == 0.0 {
self.r[i + 1] = 0.0;
} else {
// Evaluate growth probabilites and shift probabilities down
// scaling by the hazard function and the predprobs
let pp = self
.predictive_prior
.ln_pp(
data,
&DataOrSuffStat::SuffStat(&self.suff_stats[i]),
)
.exp();
r_seen += self.r[i];
let h = self.hazard;
self.r[i + 1] = self.r[i] * pp * (1.0 - h);
r0 += self.r[i] * pp * h;
r_sum += self.r[i + 1];
if 1.0 - r_seen < self.cdf_threshold {
break;
}
}
}
r_sum += r0;
// Accumulate mass back down to r[0], the probability there was a
// change point at this location.
self.r[0] = r0;
// Normalize R
for i in 0..self.r.len() {
self.r[i] /= r_sum;
}
// Truncate
let cutoff = self
.r
.iter()
.rev()
.scan(0.0, |acc, p| {
*acc += p;
Some(*acc)
})
.enumerate()
.find(|(_, cdf)| *cdf > self.cutoff_threadhold)
.map(|x| self.r.len() - x.0 + 1);
if let Some(trunc_index) = cutoff {
self.r.truncate(trunc_index);
self.suff_stats.truncate(trunc_index);
// Renormalize r
let this_r_sum: f64 = self.r.iter().sum();
for i in 0..self.r.len() {
self.r[i] /= this_r_sum;
}
}
}
// Update the SuffStat with the new data
self.suff_stats
.iter_mut()
.for_each(|stat| stat.observe(data));
debug_assert!(
!self.r.iter().any(|x| x.is_nan()),
"Resulting run-length probabilities cannot contain NaNs"
);
&self.r
}
fn reset(&mut self) {
self.suff_stats.clear();
self.r.clear();
}
fn pp(&self) -> Self::PosteriorPredictive {
if self.suff_stats.is_empty() {
let post = self.initial_suffstat.clone().map_or_else(
|| self.predictive_prior.clone(),
|ss| {
self.predictive_prior
.posterior(&DataOrSuffStat::SuffStat(&ss))
},
);
Mixture::uniform(vec![post])
.expect("The mixture could not be constructed")
} else {
let dists: Vec<Pr::Posterior> = self
.suff_stats
.iter()
.take(self.r.len())
.map(|ss| {
self.predictive_prior
.posterior(&DataOrSuffStat::SuffStat(ss))
})
.collect();
Mixture::new(self.r.clone(), dists)
.expect("The mixture could not be constructed")
}
}
fn preload(&mut self, data: &[X]) {
let mut stat = self.empty_suffstat.clone();
stat.observe_many(data);
self.initial_suffstat = Some(stat);
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::generators;
use crate::utils::{map_changepoints, max_error};
use rand::rngs::StdRng;
use rand::SeedableRng;
#[test]
fn each_vec_is_a_probability_dist() {
let mut rng: StdRng = StdRng::seed_from_u64(0xABCD);
let data = generators::discontinuous_jump(
&mut rng, 0.0, 1.0, 10.0, 5.0, 500, 1000,
);
let mut cpd = BocpdTruncated::new(
250.0,
NormalGamma::new(0.0, 1.0, 1.0, 1.0).unwrap(),
);
let res: Vec<Vec<f64>> =
data.iter().map(|d| cpd.step(d).to_vec()).collect();
for row in &res {
let sum: f64 = row.iter().sum();
assert::close(sum, 1.0, 1E-6);
}
}
#[test]
fn detect_obvious_switch() {
let mut rng: StdRng = StdRng::seed_from_u64(0xABCD);
let data = generators::discontinuous_jump(
&mut rng, 0.0, 1.0, 10.0, 5.0, 500, 700,
);
let mut cpd = BocpdTruncated::new(
250.0,
NormalGamma::new_unchecked(0.0, 1.0, 1.0, 1.0),
);
let rs: Vec<Vec<f64>> =
data.iter().map(|d| (*cpd.step(d)).into()).collect();
let change_points = map_changepoints(&rs);
let error = max_error(&change_points, &[0, 499]);
assert!(error <= 1);
}
#[test]
fn coal_mining_data() {
let data = generators::coal_mining_incidents();
let mut cpd =
BocpdTruncated::new(100.0, Gamma::new_unchecked(1.0, 1.0));
let rs: Vec<Vec<f64>> =
data.iter().map(|d| cpd.step(d).into()).collect();
let change_points = map_changepoints(&rs);
let error = max_error(&change_points, &[0, 40, 95]);
assert!(error <= 1);
}
/// This test checks for change points with 3-month treasury bill market data
///
/// # Data Source
/// > Board of Governors of the Federal Reserve System (US), 3-Month Treasury Bill: Secondary
/// > Market Rate [TB3MS], retrieved from FRED, Federal Reserve Bank of St. Louis;
/// > <https://fred.stlouisfed.org/series/TB3MS>, March 24, 2020.
#[test]
fn treasury_changes() -> Result<(), Box<dyn std::error::Error + 'static>> {
let raw_data: &str = include_str!("../../resources/TB3MS.csv");
let data: Vec<f64> = raw_data
.lines()
.skip(1)
.map(|line| {
let (_, line) = line.split_at(11);
line.parse().unwrap()
})
.collect();
let mut cpd =
BocpdTruncated::new(250.0, NormalGamma::new(0.0, 1.0, 1.0, 1.0)?);
let rs: Vec<Vec<f64>> = data
.iter()
.zip(data.iter().skip(1))
.map(|(a, b)| (b - a) / a)
.map(|d| cpd.step(&d).to_vec())
.collect();
let change_points = map_changepoints(&rs);
let error = max_error(
&change_points,
&[0, 66, 93, 293, 295, 887, 898, 900, 931, 936, 977, 982],
);
assert!(error <= 1);
Ok(())
}
}