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// Copyright 2018 Manuel Holtgrewe, Berlin Institute of Health.
// Licensed under the MIT license (http://opensource.org/licenses/MIT)
// This file may not be copied, modified, or distributed
// except according to those terms.
//! An implementation of Hidden Markov Models in Rust.
//!
//! ## Examples
//!
//! ### Discrete Emission Distribution
//!
//! We construct the example from Borodovsky & Ekisheva (2006), pp. 80 (also see
//! [these slides](http://cecas.clemson.edu/~ahoover/ece854/refs/Gonze-ViterbiAlgorithm.pdf).
//!
//! ```rust
//! use approx::assert_relative_eq;
//! use bio::stats::hmm::discrete_emission::Model as DiscreteEmissionHMM;
//! use bio::stats::hmm::viterbi;
//! use bio::stats::Prob;
//! use ndarray::array;
//!
//! let transition = array![[0.5, 0.5], [0.4, 0.6]];
//! let observation = array![[0.2, 0.3, 0.3, 0.2], [0.3, 0.2, 0.2, 0.3]];
//! let initial = array![0.5, 0.5];
//!
//! let hmm = DiscreteEmissionHMM::with_float(&transition, &observation, &initial)
//! .expect("Dimensions should be consistent");
//! let (path, log_prob) = viterbi(&hmm, &vec![2, 2, 1, 0, 1, 3, 2, 0, 0]);
//! let prob = Prob::from(log_prob);
//! assert_relative_eq!(4.25e-8_f64, *prob, epsilon = 1e-9_f64);
//! ```
//!
//! ### Continuous (Gaussian) Emission Distribution
//!
//! ```rust
//! use approx::assert_relative_eq;
//! use bio::stats::hmm::univariate_continuous_emission::GaussianModel as GaussianHMM;
//! use bio::stats::hmm::viterbi;
//! use bio::stats::Prob;
//! use ndarray::array;
//! use statrs::distribution::Normal;
//!
//! let transition = array![[0.5, 0.5], [0.4, 0.6]];
//! let observation = vec![
//! Normal::new(0.0, 1.0).unwrap(),
//! Normal::new(2.0, 1.0).unwrap(),
//! ];
//! let initial = array![0.5, 0.5];
//!
//! let hmm = GaussianHMM::with_float(&transition, observation, &initial)
//! .expect("Dimensions should be consistent");
//! let (path, log_prob) = viterbi(
//! &hmm,
//! &vec![-0.1, 0.1, -0.2, 0.5, 0.8, 1.1, 1.2, 1.5, 0.5, 0.2],
//! );
//! let prob = Prob::from(log_prob);
//! assert_relative_eq!(2.64e-8_f64, *prob, epsilon = 1e-9_f64);
//! ```
//!
//! ### Trainning a Discrete Emission Model with Baum-Welch algorithm
//!
//! We construct the example from Jason Eisner lecture which can be followed along
//! with his spreadsheet ([link](http://www.cs.jhu.edu/~jason/papers/#eisner-2002-tnlp)).
//! Take a look at tests in source file.
//!
//! ## Numeric Stability
//!
//! The implementation uses log-scale probabilities for numeric stability.
//!
//! ## Limitations
//!
//! Currently, only discrete and single-variate Gaussian continuous HMMs are implemented.
//! Also, only dense transition matrices and trainning of discrete models are supported.
//!
//! ## References
//!
//! - Rabiner, Lawrence R. "A tutorial on hidden Markov models and selected applications
//! in speech recognition." Proceedings of the IEEE 77, no. 2 (1989): 257-286.
//! - Eisner, Jason "An interactive spreadsheet for teaching the forward-backward algorithm.
//! in speech recognition." In ACL Workshop on Teaching NLP and CL (2002).
pub mod errors;
use std::cmp::Ordering;
use ndarray::prelude::*;
use num_traits::Zero;
use ordered_float::OrderedFloat;
use statrs::distribution::Continuous;
pub use self::errors::{Error, Result};
use super::LogProb;
use std::cmp::Eq;
use std::fmt::Debug;
use std::hash::Hash;
use super::Prob;
use std::cell::RefCell;
use std::collections::BTreeMap;
custom_derive! {
/// A newtype for HMM states.
// #[derive(
// NewtypeFrom,
// NewtypeDeref,
// Default,
// Copy,
// Clone,
// Eq,
// PartialEq,
// Ord,
// PartialOrd,
// Hash,
// Debug,
// )]
// #[derive(Serialize, Deserialize)]
#[derive(
NewtypeFrom,
NewtypeDeref,
Default,
Copy,
Clone,
Eq,
PartialEq,
Ord,
PartialOrd,
Hash,
Debug,
)]
#[derive(serde::Serialize, serde::Deserialize)]
pub struct State(pub usize);
}
/// Iterate over the states of a `Model`.
#[derive(
Default, Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug, Serialize, Deserialize,
)]
pub struct StateIter {
nxt: usize,
max: usize,
}
impl StateIter {
/// Constructor.
pub fn new(num_states: usize) -> Self {
Self {
nxt: 0,
max: num_states,
}
}
}
impl Iterator for StateIter {
type Item = State;
fn next(&mut self) -> Option<State> {
if self.nxt < self.max {
let cur = self.nxt;
self.nxt += 1;
Some(State(cur))
} else {
None
}
}
}
/// Transition between two states in a `Model`.
#[derive(
Default, Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug, Serialize, Deserialize,
)]
pub struct StateTransition {
/// Source of the transition.
pub src: State,
/// Destination of the transition.
pub dst: State,
}
impl StateTransition {
/// Constructor.
pub fn new(src: State, dst: State) -> Self {
Self { src, dst }
}
}
/// Iterate over all state transitions of a `Model`.
#[derive(
Default, Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug, Serialize, Deserialize,
)]
pub struct StateTransitionIter {
nxt_a: usize,
nxt_b: usize,
max: usize,
}
impl StateTransitionIter {
/// Constructor.
pub fn new(num_states: usize) -> Self {
Self {
nxt_a: 0,
nxt_b: 0,
max: num_states,
}
}
}
impl Iterator for StateTransitionIter {
type Item = StateTransition;
fn next(&mut self) -> Option<StateTransition> {
let cur_b = self.nxt_b;
let cur_a = self.nxt_a;
if self.nxt_b < self.max {
self.nxt_b += 1;
Some(StateTransition::new(State(cur_a), State(cur_b)))
} else if self.nxt_a < self.max {
self.nxt_b = 0;
self.nxt_a += 1;
Some(StateTransition::new(State(cur_a), State(cur_b)))
} else {
None
}
}
}
/// A trait for Hidden Markov Models (HMM) with generic `Observation` type.
///
/// Rabiner (1989) defines a Hidden Markov Model λ as the tiple (*A*, *B*, π) of transition matrix
/// *A*, emission probabilities *B*, and initial state distribution π. This has been generalized
/// in `Model` such that you implement `transition_prob()`, `observation_prob()`, and
/// `initial_prob()` (and the other methods; implementation of `transition_prob_idx()` can
/// optionally be implemented and your implementation of `transition_prob()` can then panic).
///
/// The inference algorithm implementations `viterbi()`, `forward()`, and `backward()` will work
/// with any implementation.
///
/// Consequently, this allows for the implementation of HMMs with both discrete and continuous
/// emission distributions.
#[allow(unconditional_recursion)]
pub trait Model<Observation> {
/// The number of states in the model.
fn num_states(&self) -> usize;
/// Return iterator over the states of an HMM.
fn states(&self) -> StateIter;
/// Returns an iterator of all transitions.
fn transitions(&self) -> StateTransitionIter;
/// Transition probability between two states `from` and `to`.
fn transition_prob(&self, from: State, to: State) -> LogProb;
/// Transition probability between two states `from` and `to` for observation with index
/// `_to_idx` (index of `to`).
///
/// This feature comes in handy in several applications of HMMs to biological sequences.
/// One prominent one is how XHMM by Fromer et al. (2014) uses the distance between target
/// regions for adjusting the transition probabilities.
///
/// The default implementation return the result of the position-independent
/// `transition_prob()`.
fn transition_prob_idx(&self, from: State, to: State, _to_idx: usize) -> LogProb {
self.transition_prob(from, to)
}
/// Initial probability given the HMM `state`.
fn initial_prob(&self, state: State) -> LogProb;
/// Probability for the given observation in the given state.
fn observation_prob(&self, state: State, observation: &Observation) -> LogProb;
/// End probability given the HMM `state`.
fn end_prob(&self, _state: State) -> LogProb {
self.end_prob(_state)
}
fn has_end_state(&self) -> bool {
false
}
}
/// Compute the probability Viterbi matrix and the pointers to the origin.
fn viterbi_matrices<O, M: Model<O>>(
hmm: &M,
observations: &[O],
) -> (Array2<LogProb>, Array2<usize>) {
// The matrix with probabilities.
let mut vals = Array2::<LogProb>::zeros((observations.len(), hmm.num_states()));
// For each cell in `vals`, a pointer to the row in the previous column (for the traceback).
let mut from = Array2::<usize>::zeros((observations.len(), hmm.num_states()));
// Compute matrix.
for (i, o) in observations.iter().enumerate() {
if i == 0 {
// Initial column.
for s in hmm.states() {
vals[[0, *s]] = hmm.initial_prob(s) + hmm.observation_prob(s, o);
from[[0, *s]] = *s;
}
} else {
// Subsequent columns.
for j in hmm.states() {
let x = vals
.index_axis(Axis(0), i - 1)
.iter()
.enumerate()
.map(|(a, p)| (State(a), p))
.max_by(|(a, &x), (b, &y)| {
if x.is_zero() && y.is_zero() {
Ordering::Equal
} else if x.is_zero() {
Ordering::Less
} else if y.is_zero() {
Ordering::Greater
} else {
(x + hmm.transition_prob_idx(*a, j, i))
.partial_cmp(&(y + hmm.transition_prob_idx(*b, j, i)))
.unwrap()
}
})
.map(|(x, y)| (x, *y))
.unwrap();
vals[[i, *j]] =
x.1 + hmm.transition_prob_idx(x.0, j, i) + hmm.observation_prob(j, o);
from[[i, *j]] = *x.0;
}
}
}
(vals, from)
}
fn viterbi_traceback(vals: Array2<LogProb>, from: Array2<usize>) -> (Vec<State>, LogProb) {
// Traceback through matrix.
let n = vals.len_of(Axis(0));
let mut result: Vec<State> = Vec::new();
let mut curr = 0;
let mut res_prob = LogProb::ln_zero();
for (i, col) in vals.axis_iter(Axis(0)).rev().enumerate() {
if i == 0 {
let tmp = col
.iter()
.enumerate()
.max_by_key(|&(_, item)| OrderedFloat(**item))
.unwrap();
curr = tmp.0;
res_prob = *tmp.1;
} else {
curr = from[[n - i, curr]];
}
result.push(State(curr));
}
result.reverse();
(result, res_prob)
}
/// Execute Viterbi algorithm on the given slice of `Observation` values to get the maximum a
/// posteriori (MAP) probability.
///
/// ## Arguments
///
/// - `hmm` - the `Model` to run the Viterbi algorithm on
/// - `observations` - a slice of observation values to use in the algorithm
///
/// ## Result
///
/// The resulting pair *(s, p)* is the `Vec<State>` of most probable states given `hmm`
/// and `observations` as well as the probability (as `LogProb`) of path `s`.
///
/// ## Type Parameters
///
/// - `O` - the observation type
/// - `M` - type `Model` type
pub fn viterbi<O, M: Model<O>>(hmm: &M, observations: &[O]) -> (Vec<State>, LogProb) {
let (vals, from) = viterbi_matrices(hmm, observations);
viterbi_traceback(vals, from)
}
/// Execute the forward algorithm and return the forward probabilites as `LogProb` values
/// and the resulting forward probability.
///
/// ## Arguments
///
/// - `hmm` - the `Model` to run the forward algorithm on
/// - `observations` - a slice of observation values to use in the algorithm
///
/// ## Result
///
/// The resulting pair (*P*, *p*) is the forward probability table (`P[[s, o]]` is the entry
/// for state `s` and observation `o`) and the overall probability for `observations` (as
/// `LogProb`).
///
/// ## Type Parameters
///
/// - `O` - the observation type
/// - `M` - type `Model` type
pub fn forward<O, M: Model<O>>(hmm: &M, observations: &[O]) -> (Array2<LogProb>, LogProb) {
// The matrix with probabilities.
let mut vals = Array2::<LogProb>::zeros((observations.len(), hmm.num_states()));
// Compute matrix.
for (i, o) in observations.iter().enumerate() {
if i == 0 {
// Initial column.
for s in hmm.states() {
vals[[0, *s]] = hmm.initial_prob(s) + hmm.observation_prob(s, o);
}
} else {
// Subsequent columns.
for j in hmm.states() {
let xs = hmm
.states()
.map(|k| {
vals[[i - 1, *k]]
+ hmm.transition_prob_idx(k, j, i)
+ hmm.observation_prob(j, o)
// + maybe_initial
})
.collect::<Vec<LogProb>>();
vals[[i, *j]] = LogProb::ln_sum_exp(&xs);
}
}
}
// Compute final probability.
let prob_vec_final = hmm
.states()
.map(|k| vals[[observations.len() - 1, *k]] + hmm.end_prob(k))
.collect::<Vec<LogProb>>();
let prob = LogProb::ln_sum_exp(&prob_vec_final);
// let prob = LogProb::ln_sum_exp(vals.row(observations.len() - 1).to_slice().unwrap());
(vals, prob)
}
pub fn backward<O, M: Model<O>>(hmm: &M, observations: &[O]) -> (Array2<LogProb>, LogProb) {
// The matrix with probabilities.
let mut vals = Array2::<LogProb>::zeros((observations.len(), hmm.num_states()));
let mut prob_vec_final = vec![];
// Compute matrix.
let n = observations.len();
for (i, o) in observations.iter().rev().enumerate() {
if i == 0 {
for j in hmm.states() {
vals[[0, *j]] = hmm.end_prob(j);
}
for j in hmm.states() {
let xs = hmm
.states()
.map(|k| {
vals[[i, *k]]
+ hmm.transition_prob_idx(j, k, n - i)
+ hmm.observation_prob(k, o)
})
.collect::<Vec<LogProb>>();
if observations.len() > 1 {
vals[[i + 1, *j]] = LogProb::ln_sum_exp(&xs);
} else {
prob_vec_final = hmm
.states()
.map(|k| vals[[i, *k]] + hmm.initial_prob(k) + hmm.observation_prob(k, o))
.collect::<Vec<LogProb>>();
}
}
} else if i == (observations.len() - 1) {
prob_vec_final = hmm
.states()
.map(|k| vals[[i, *k]] + hmm.initial_prob(k) + hmm.observation_prob(k, o))
.collect::<Vec<LogProb>>();
} else {
// Previous columns.
for j in hmm.states() {
let xs = hmm
.states()
.map(|k| {
vals[[i, *k]]
+ hmm.transition_prob_idx(j, k, n - i)
+ hmm.observation_prob(k, o)
})
.collect::<Vec<LogProb>>();
vals[[i + 1, *j]] = LogProb::ln_sum_exp(&xs);
}
}
}
let prob = LogProb::ln_sum_exp(&prob_vec_final);
(vals, prob)
}
/// Execute **one step** of Baum-Welch algorithm to find the maximum likelihood estimate of the parameters of a HMM given a set of observed
/// feature vector and return the estimated initial state distribution (*π**), estimated transition matrix (*A**),
/// estimated emission probabilities matrix (*B**) and end probabilities vector (if the model has declared an end state beforehand).
/// This function doesn't update the HMM parameters in the model and has been implemented for Discrete Emissions Models only.
/// It return values as `LogProb`.
///
/// ## Arguments
///
/// - `hmm` - the `Model` to run the baum-welch or expected maximization algorithm on. It has to be a Discrete Model with a `Trainable` trait implemented.
/// - `observations` - a slice of observation values to use in the algorithm
///
/// ## Result
///
/// The resulting tuple (*π**, *A**, B*, E*) is the estimated initial probability table (`P[s]`),
/// the estimated transitions probability table (`P[[s, o]]` is the entry
/// for state `s1` and other state `s2`), the estimated emission probability table (`P[[s, s]]` is the entry
/// for state `s` and observation class `o`) and if we specify an end probability when building the model,
/// E* is the estimated end probabilities. Otherwise, E* is a vector with size equal to initial probability
/// and all values set to LogProb(1.0). The values in all outputs are shown as `LogProb`.
///
/// ## Type Parameters
///
/// - `O` - the observation type (only discrete emissions)
/// - `M` - type `Model` type
pub fn baum_welch<O: Debug + Eq + Hash + Ord, M: Model<O>>(
hmm: &M,
observations: &[O],
) -> (
Array1<LogProb>,
Array2<LogProb>,
Array2<LogProb>,
Array1<LogProb>,
) {
// Execute forward algorithm to calculate the alpha probabilities for each time-step.
// Ignore P(x)
let (prob_table_f, _) = forward(hmm, observations);
// Execute backward algorithm to calculate the beta probabilities for each time-step.
let (prob_table_b_cor, _) = backward(hmm, observations);
// The time-step in forward matrix goes from t=0 to t=N. Coversely, the backward matrix
// entries are in reverse order, i.e., from t=N to t=0.
// The following code puts the backward matrix in the same order as forward matrix.
// This is usefull when computing the alfa times beta probabilities.
let n = observations.len() - 1;
let mut prob_table_b = Array2::<LogProb>::zeros((observations.len(), hmm.num_states()));
for (j, el) in prob_table_b_cor.axis_iter(Axis(0)).enumerate() {
prob_table_b.row_mut(n - j).assign(&el);
}
// Product of the forward probability and backward probability which is translated
// into a sum in log space. Results in gamma array which is an array of size = len(Observation) x N_states representing
// the probability of being in state t at time j for this observations.
let alpha_betas = &prob_table_f + &prob_table_b;
// Log-likelihood of the observation given the model.
// This probability must be the same as probabilities calculated by forward or backward functions
let probx = LogProb::ln_sum_exp(alpha_betas.row(observations.len() - 1).to_slice().unwrap());
// Dictionary-like vec_hashs_prob_obs stores b_{i}^{*}(v_{k}) which is the expected number of times the output observations
// have been equal to observation v_{k} while in state i over the expected
// total number of times in state i.
let mut vec_hashs_prob_obs: Vec<BTreeMap<&O, LogProb>> = Vec::new();
let mut distinct_obs = 0;
for h in hmm.states() {
let mut probs_observations: BTreeMap<&O, LogProb> = BTreeMap::new();
// First, for the numerator of b_{i}^{^}(v_{k}) we sum gamma for all time steps t in which the observation o_{t}
// is the symbol v_{k}
for (t, o) in observations.iter().enumerate() {
// For example, in einsner example, it calculates the probabilities P(->state, observation), for example p(->C,1) or p(->C,2) or p(->C,3)
let p = probs_observations.entry(o).or_insert_with(LogProb::ln_zero);
*p = (*p).ln_add_exp(alpha_betas[[t, *h]] - probx);
}
distinct_obs = probs_observations.len();
vec_hashs_prob_obs.push(probs_observations);
}
let mut vals_xi =
Array2::<LogProb>::zeros((observations.len(), hmm.num_states() * hmm.num_states()));
// Calculate the arc probabilities.
// It's the xi equation which it's entries represent the probability of being in state i and j,
// in times t and t+1, respectively, given the observed sequence and parameters.
// The vals_xi matrix is of size (time-steps, N_states^2) to store for each observation (or time-step)
// the probability of being at state i and j in times t and t+1. The element vals_xi[t, k] indicates
// the probability in time t and k is the index encoding of the pair of states (i,j).
for (t, o) in observations.iter().enumerate() {
if t == 0 {
continue;
} else {
for (idxstate, j) in hmm.states().enumerate() {
let numerador = hmm
.states()
.map(|i| {
prob_table_f[[t - 1, *j]]
+ hmm.transition_prob_idx(j, i, t)
+ prob_table_b[[t, *i]]
+ hmm.observation_prob(i, o)
- probx
})
.collect::<Vec<LogProb>>();
vals_xi
.slice_mut(s![
t,
idxstate * hmm.num_states()..(idxstate + 1) * hmm.num_states()
])
.assign(&Array1::from(numerador));
}
}
}
let mut sum_p_states = Vec::new();
for k in hmm.states() {
let sum_prob_states =
LogProb::ln_sum_exp(&alpha_betas.column(*k).map(|x| x - probx).to_vec());
sum_p_states.push(sum_prob_states);
}
let mut observations_hat = Array2::<LogProb>::zeros((hmm.num_states(), distinct_obs));
let mut transitions_hat = Array2::<LogProb>::zeros((hmm.num_states(), hmm.num_states()));
for (idxstate, i) in hmm.states().enumerate() {
let gamma_i = LogProb::ln_sum_exp(
&alpha_betas
.column(*i)
.to_vec()
.iter()
.map(|x| *x - probx)
.collect::<Vec<LogProb>>(),
);
let end_i = if hmm.has_end_state() {
LogProb::ln_zero()
} else {
alpha_betas[[observations.len() - 1, *i]] - probx
};
let q = vals_xi.slice(s![
..,
idxstate * hmm.num_states()..(idxstate + 1) * hmm.num_states()
]);
for k in hmm.states() {
let sa = LogProb::ln_sum_exp(&q.column(*k).to_vec());
transitions_hat[[*i, *k]] = sa - gamma_i.ln_sub_exp(end_i);
}
let mut ind_probs = vec![];
for v in vec_hashs_prob_obs[*i].values() {
ind_probs.push(*v - gamma_i);
}
observations_hat
.row_mut(*i)
.assign(&Array1::from(ind_probs));
}
let pi_hat = Array1::from(
alpha_betas
.row(0)
.to_vec()
.iter()
.map(|x| *x - probx)
.collect::<Vec<LogProb>>(),
);
let end_hat = if hmm.has_end_state() {
Array1::from(
sum_p_states
.iter()
.zip(alpha_betas.row(observations.len() - 1).to_vec().iter())
.map(|(sg, g)| (*g - probx) - *sg)
.collect::<Vec<LogProb>>(),
)
} else {
Array1::from(
pi_hat
.iter()
.map(|_x| LogProb::from(Prob(1.0)))
.collect::<Vec<LogProb>>(),
)
};
(pi_hat, transitions_hat, observations_hat, end_hat)
}
/// A trait for trainning Hidden Markov Models (HMM) with generic `Observation` type using Baum-Welch algorithm.
pub trait Trainable<Observation> {
/// Iterative procedure to train the model using Baum-Welch algorithm given the training sequences.
///
/// As arguments, a set of sequences (observations) and two optional argumets: maximum number of iterations (`n_iter`) and tolerance (`tol`).
/// The baum-welch iterative training procedure will stop either if it reaches the tolerance of the relative log-likelihood augmentation (default `1e-6`) or
/// exceed the maximum number of iterations (default `500`).
fn train_baum_welch(
&self,
observations: &[Vec<Observation>],
n_iter: Option<usize>,
tol: Option<f64>,
) -> (
Array1<LogProb>,
Array2<LogProb>,
Array2<LogProb>,
Array1<LogProb>,
);
/// This feature comes in handy in Bam-Welch algorithm when doing an update of HMM parameters.
///
/// After receiving the estimated parameters found after trainning, this method updates the values in the
/// HMM model.
fn update_matrices(
&self,
transition_hat: Array2<LogProb>,
observation_hat: Array2<LogProb>,
initial_hat: Array1<LogProb>,
end_hat: Array1<LogProb>,
);
}
/// Implementation of Hidden Markov Model with emission values from discrete distributions.
pub mod discrete_emission {
use super::super::{LogProb, Prob};
use super::*;
/// Implementation of a `hmm::Model` with emission values from discrete distributions.
///
/// Log-scale probabilities are used for numeric stability.
///
/// In Rabiner's tutorial, a discrete emission value HMM has `N` states and `M` output symbols.
/// The state transition matrix with dimensions `NxN` is `A`, the observation probability
/// distribution is the matrix `B` with dimensions `NxM` and the initial state distribution `pi`
/// has length `N`.
#[derive(Default, Clone, PartialEq, Debug)]
pub struct Model {
/// The state transition matrix (size `NxN`), `A` in Rabiner's tutorial.
transition: Array2<LogProb>,
/// The observation symbol probability distribution (size `NxM`), `B` in Rabiner's tutorial.
observation: Array2<LogProb>,
/// The initial state distribution (size `N`), `pi` in Rabiner's tutorial.
initial: Array1<LogProb>,
}
impl Model {
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors already in log-probability space.
pub fn new(
transition: Array2<LogProb>,
observation: Array2<LogProb>,
initial: Array1<LogProb>,
) -> Result<Self> {
let (an0, an1) = transition.dim();
let (bn, bm) = observation.dim();
let pin = initial.dim();
if an0 != an1 || an0 != bn || an0 != pin {
Err(Error::InvalidDimension {
an0,
an1,
bn,
bm,
pin,
})
} else {
Ok(Self {
transition,
observation,
initial,
})
}
}
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors already as `Prob` values.
pub fn with_prob(
transition: &Array2<Prob>,
observation: &Array2<Prob>,
initial: &Array1<Prob>,
) -> Result<Self> {
Self::new(
transition.map(|x| LogProb::from(*x)),
observation.map(|x| LogProb::from(*x)),
initial.map(|x| LogProb::from(*x)),
)
}
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors with probabilities as `f64` values.
pub fn with_float(
transition: &Array2<f64>,
observation: &Array2<f64>,
initial: &Array1<f64>,
) -> Result<Self> {
Self::new(
transition.map(|x| LogProb::from(Prob(*x))),
observation.map(|x| LogProb::from(Prob(*x))),
initial.map(|x| LogProb::from(Prob(*x))),
)
}
}
impl super::Model<usize> for Model {
fn num_states(&self) -> usize {
self.transition.dim().0
}
fn states(&self) -> StateIter {
StateIter {
nxt: 0,
max: self.num_states(),
}
}
fn transitions(&self) -> StateTransitionIter {
StateTransitionIter {
nxt_a: 0,
nxt_b: 0,
max: self.num_states(),
}
}
fn transition_prob(&self, from: State, to: State) -> LogProb {
self.transition[[*from, *to]]
}
fn initial_prob(&self, state: State) -> LogProb {
self.initial[[*state]]
}
fn observation_prob(&self, state: State, observation: &usize) -> LogProb {
self.observation[[*state, *observation]]
}
fn end_prob(&self, _state: State) -> LogProb {
LogProb::ln_one()
}
}
}
/// Implementation of Hidden Markov Model with emission values from discrete distributions and an optional explicity end state.
/// This module also implements the `Trainable` trait allowing to be trainned by Baum-Welch algorithm.
pub mod discrete_emission_opt_end {
use super::super::{LogProb, Prob};
use super::*;
/// Implementation of a `hmm::Model` with emission values from discrete distributions and an optional declared end state.
///
/// Log-scale probabilities are used for numeric stability.
///
/// In Rabiner's tutorial, a discrete emission value HMM has `N` states and `M` output symbols.
/// The state transition matrix with dimensions `NxN` is `A`, the observation probability
/// distribution is the matrix `B` with dimensions `NxM` and the initial state distribution `pi`
/// has length `N`. We also included a silent end state `ε` with vector length `N` that do not emit symbols for
/// modelling the end of sequences. It's optional to supply the end probabilities at the creation of the model.
/// If this happens, we'll create a dummy end state to simulate as if the end state has not been included.
#[derive(Default, Clone, PartialEq, Debug)]
pub struct Model {
/// The state transition matrix (size `NxN`), `A` in Rabiner's tutorial.
transition: RefCell<Array2<LogProb>>,
/// The observation symbol probability distribution (size `NxM`), `B` in Rabiner's tutorial.
observation: RefCell<Array2<LogProb>>,
/// The initial state distribution (size `N`), `pi` in Rabiner's tutorial.
initial: RefCell<Array1<LogProb>>,
end: RefCell<Array1<LogProb>>,
has_end_state: bool,
}
impl Model {
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors already in log-probability space.
pub fn new(
transition: RefCell<Array2<LogProb>>,
observation: RefCell<Array2<LogProb>>,
initial: RefCell<Array1<LogProb>>,
end: RefCell<Array1<LogProb>>,
has_end_state: bool,
) -> Result<Self> {
let (an0, an1) = transition.borrow().dim();
let (bn, bm) = observation.borrow().dim();
let pin = initial.borrow().dim();
if an0 != an1 || an0 != bn || an0 != pin {
Err(Error::InvalidDimension {
an0,
an1,
bn,
bm,
pin,
})
} else {
Ok(Self {
transition,
observation,
initial,
end,
has_end_state,
})
}
}
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors already as `Prob` values.
pub fn with_prob(
transition: &Array2<Prob>,
observation: &Array2<Prob>,
initial: &Array1<Prob>,
end: Option<&Array1<Prob>>,
) -> Result<Self> {
let initial_dim = initial.dim();
let end_possible = (0..initial_dim)
.map(|_x| Prob(1.0))
.collect::<Array1<Prob>>();
let has_end_state = end.is_some();
let end_un = end.unwrap_or(&end_possible);
Self::new(
RefCell::new(transition.map(|x| LogProb::from(*x))),
RefCell::new(observation.map(|x| LogProb::from(*x))),
RefCell::new(initial.map(|x| LogProb::from(*x))),
RefCell::new(end_un.map(|x| LogProb::from(*x))),
has_end_state,
)
}
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors with probabilities as `f64` values.
pub fn with_float(
transition: &Array2<f64>,
observation: &Array2<f64>,
initial: &Array1<f64>,
end: Option<&Array1<f64>>,
) -> Result<Self> {
let initial_dim = initial.dim();
let end_possible = (0..initial_dim).map(|_x| 1.0).collect::<Array1<f64>>();
let end_un = end.unwrap_or(&end_possible);
let has_end_state = end.is_some();
Self::new(
RefCell::new(transition.map(|x| LogProb::from(Prob(*x)))),
RefCell::new(observation.map(|x| LogProb::from(Prob(*x)))),
RefCell::new(initial.map(|x| LogProb::from(Prob(*x)))),
RefCell::new(end_un.map(|x| LogProb::from(Prob(*x)))),
has_end_state,
)
}
}
impl super::Model<usize> for Model {
fn num_states(&self) -> usize {
let transition = self.transition.borrow();
transition.dim().0
}
fn states(&self) -> StateIter {
StateIter {
nxt: 0,
max: self.num_states(),
}
}
fn transitions(&self) -> StateTransitionIter {
StateTransitionIter {
nxt_a: 0,
nxt_b: 0,
max: self.num_states(),
}
}
fn transition_prob(&self, from: State, to: State) -> LogProb {
let transition_prob = self.transition.borrow();
transition_prob[[*from, *to]]
}
fn initial_prob(&self, state: State) -> LogProb {
let initial_prob = self.initial.borrow();
initial_prob[[*state]]
}
fn end_prob(&self, _state: State) -> LogProb {
let end_prob = self.end.borrow();
end_prob[[*_state]]
}
fn observation_prob(&self, state: State, observation: &usize) -> LogProb {
let observation_prob = self.observation.borrow();
observation_prob[[*state, *observation]]
}
fn has_end_state(&self) -> bool {
self.has_end_state
}
}
impl super::Trainable<usize> for Model {
fn update_matrices(
&self,
transition_hat: Array2<LogProb>,
observation_hat: Array2<LogProb>,
initial_hat: Array1<LogProb>,
end_hat: Array1<LogProb>,
) {
let mut end_prob = self.end.borrow_mut();
*end_prob = end_hat;
let mut transition_prob = self.transition.borrow_mut();
*transition_prob = transition_hat;
let mut observation_prob = self.observation.borrow_mut();
*observation_prob = observation_hat;
let mut initial_prob = self.initial.borrow_mut();
*initial_prob = initial_hat;
}
fn train_baum_welch(
&self,
observations: &[Vec<usize>],
n_iter: Option<usize>,
tol: Option<f64>,
) -> (
Array1<LogProb>,
Array2<LogProb>,
Array2<LogProb>,
Array1<LogProb>,
) {
let hmm = self;
let tol = tol.unwrap_or(1e-6_f64);
let n_iter = n_iter.unwrap_or(500);
let (pi_hat, transitions_hat, observations_hat, end_hat) =
super::baum_welch(hmm, &observations[0]);
let (
mut pi_hat_ref,
mut transitions_hat_ref,
mut observations_hat_ref,
mut end_hat_ref,
) = (pi_hat, transitions_hat, observations_hat, end_hat);
let (_, mut prob_fwd_new) = super::forward(hmm, &observations[0]);
// initialize var llh to store the log likelihood of trainned model
let mut llh: LogProb = LogProb::ln_one();
// Get the number of observations in first "sample"
let mut obs_n = observations[0].len() as f64;
// Normalize the previous log likelihood computed by number of observations
let mut nllh_o = LogProb::from(Prob((*prob_fwd_new / obs_n).exp()));
println!(
"Iter num {:?} - LLH: {:?} - Normalized LLH: {:?}",
0, prob_fwd_new, nllh_o
);
for iteration in 0..(n_iter - 1) {
for obs in observations.iter() {
let (pi_hat, transitions_hat, observations_hat, end_hat) = baum_welch(hmm, obs);
pi_hat_ref = pi_hat.to_owned();
transitions_hat_ref = transitions_hat.to_owned();
observations_hat_ref = observations_hat.to_owned();
end_hat_ref = end_hat.to_owned();
hmm.update_matrices(transitions_hat, observations_hat, pi_hat, end_hat);
let (_, prob_fwd_new_ii) = super::forward(hmm, obs);
llh = prob_fwd_new_ii;
// Get the number of observations
obs_n = obs.len() as f64;
}
// Normalize the new log likelihood computed in this iteration by number of observations
let nllh = LogProb::from(Prob((*llh / obs_n).exp()));
println!(
"Iter num {:?} - LLH: {:?} - Normalized LLH: {:?}",
iteration + 1,
llh,
nllh
);
if nllh_o >= nllh {
prob_fwd_new = llh;
// Normalize the previous log likelihood computed by number of observations
nllh_o = LogProb::from(Prob((*prob_fwd_new / obs_n).exp()));
// Skip to next iteration
continue;
}
if nllh.ln_sub_exp(nllh_o) < LogProb::from(Prob(tol)) {
// Stop trainning if the difference between the new log like and the old is less than a threshold
break;
} else {
// Otherwise, set the old log like as the new log like
prob_fwd_new = llh;
// Normalize the previous log likelihood computed by number of observations
nllh_o = LogProb::from(Prob((*prob_fwd_new / obs_n).exp()));
}
}
(
pi_hat_ref,
transitions_hat_ref,
observations_hat_ref,
end_hat_ref,
)
}
}
}
/// Implementation of Hidden Markov Models with emission values from univariate continuous
/// distributions.
pub mod univariate_continuous_emission {
use super::super::{LogProb, Prob};
use super::*;
/// Implementation of a `hmm::Model` with emission values from univariate continuous distributions.
///
/// Log-scale probabilities are used for numeric stability.
#[derive(Default, Clone, PartialEq, Debug)]
pub struct Model<Dist: Continuous<f64, f64>> {
/// The state transition matrix (size `NxN`), `A` in Rabiner's tutorial.
transition: Array2<LogProb>,
/// The emission probability distributions.
observation: Vec<Dist>,
/// The initial state distribution (size `N`), `pi` in Rabiner's tutorial.
initial: Array1<LogProb>,
}
impl<Dist: Continuous<f64, f64>> Model<Dist> {
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors already in log-probability space.
pub fn new(
transition: Array2<LogProb>,
observation: Vec<Dist>,
initial: Array1<LogProb>,
) -> Result<Self> {
let (an0, an1) = transition.dim();
let bn = observation.len();
let pin = initial.dim();
if an0 != an1 || an0 != bn || an0 != pin {
Err(Error::InvalidDimension {
an0,
an1,
bn,
bm: bn,
pin,
})
} else {
Ok(Self {
transition,
observation,
initial,
})
}
}
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors already as `Prob` values.
pub fn with_prob(
transition: &Array2<Prob>,
observation: Vec<Dist>,
initial: &Array1<Prob>,
) -> Result<Self> {
Self::new(
transition.map(|x| LogProb::from(*x)),
observation,
initial.map(|x| LogProb::from(*x)),
)
}
/// Construct new Hidden MarkovModel with the given transition, observation, and initial
/// state matrices and vectors with probabilities as `f64` values.
pub fn with_float(
transition: &Array2<f64>,
observation: Vec<Dist>,
initial: &Array1<f64>,
) -> Result<Self> {
Self::new(
transition.map(|x| LogProb::from(Prob(*x))),
observation,
initial.map(|x| LogProb::from(Prob(*x))),
)
}
}
impl<Dist: Continuous<f64, f64>> super::Model<f64> for Model<Dist> {
fn num_states(&self) -> usize {
self.transition.dim().0
}
fn states(&self) -> StateIter {
StateIter {
nxt: 0,
max: self.num_states(),
}
}
fn transitions(&self) -> StateTransitionIter {
StateTransitionIter {
nxt_a: 0,
nxt_b: 0,
max: self.num_states(),
}
}
fn transition_prob(&self, from: State, to: State) -> LogProb {
self.transition[[*from, *to]]
}
fn initial_prob(&self, state: State) -> LogProb {
self.initial[[*state]]
}
fn observation_prob(&self, state: State, observation: &f64) -> LogProb {
LogProb::from(Prob::from(self.observation[*state].pdf(*observation)))
}
fn end_prob(&self, _state: State) -> LogProb {
LogProb::ln_one()
}
}
/// Shortcut for HMM with emission values from a Gaussian distribution.
pub type GaussianModel = Model<statrs::distribution::Normal>;
}
#[cfg(test)]
mod tests {
use super::super::Prob;
use ndarray::array;
use statrs::distribution::Normal;
use super::discrete_emission::Model as DiscreteEmissionHMM;
use super::discrete_emission_opt_end::Model as DiscreteEmissionHMMoptEND;
use super::univariate_continuous_emission::GaussianModel as GaussianHMM;
use super::*;
#[test]
fn test_discrete_viterbi_toy_example() {
// We construct the toy example from Borodovsky & Ekisheva (2006), pp. 80.
//
// http://cecas.clemson.edu/~ahoover/ece854/refs/Gonze-ViterbiAlgorithm.pdf
//
// States: 0=High GC content, 1=Low GC content
// Symbols: 0=A, 1=C, 2=G, 3=T
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = array![[0.2, 0.3, 0.3, 0.2], [0.3, 0.2, 0.2, 0.3]];
let initial = array![0.5, 0.5];
let hmm = DiscreteEmissionHMM::with_float(&transition, &observation, &initial)
.expect("Dimensions should be consistent");
let (path, log_prob) = viterbi(&hmm, &[2, 2, 1, 0, 1, 3, 2, 0, 0]);
let prob = Prob::from(log_prob);
let expected = vec![0, 0, 0, 1, 1, 1, 1, 1, 1]
.iter()
.map(|i| State(*i))
.collect::<Vec<State>>();
assert_eq!(expected, path);
assert_relative_eq!(4.25e-8_f64, *prob, epsilon = 1e-9_f64);
}
#[test]
fn test_discrete_forward_toy_example() {
// Same toy example as above.
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = array![[0.2, 0.3, 0.3, 0.2], [0.3, 0.2, 0.2, 0.3]];
let initial = array![0.5, 0.5];
let hmm = DiscreteEmissionHMM::with_float(&transition, &observation, &initial)
.expect("Dimensions should be consistent");
let log_prob = forward(&hmm, &[2, 2, 1, 0]).1;
let prob = Prob::from(log_prob);
assert_relative_eq!(0.0038432_f64, *prob, epsilon = 0.0001);
}
#[test]
fn test_discrete_backward_toy_example() {
// Same toy example as above.
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = array![[0.2, 0.3, 0.3, 0.2], [0.3, 0.2, 0.2, 0.3]];
let initial = array![0.5, 0.5];
let hmm = DiscreteEmissionHMM::with_float(&transition, &observation, &initial)
.expect("Dimensions should be consistent");
let (_, log_prob) = backward(&hmm, &[2, 2, 1, 0]);
let prob = Prob::from(log_prob);
assert_relative_eq!(0.0038432_f64, *prob, epsilon = 0.0001);
}
#[test]
fn test_discrete_forward_equals_backward_toy_example() {
// Same toy example as above.
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = array![[0.2, 0.3, 0.3, 0.2], [0.3, 0.2, 0.2, 0.3]];
let initial = array![0.5, 0.5];
let hmm = DiscreteEmissionHMM::with_float(&transition, &observation, &initial)
.expect("Dimensions should be consistent");
for len in 1..10 {
let mut seq: Vec<usize> = vec![0; len];
while seq.iter().sum::<usize>() != len {
for i in 0..len {
if seq[i] == 0 {
seq[i] = 1;
break;
} else {
seq[i] = 0;
}
}
let prob_fwd = *Prob::from(forward(&hmm, &seq).1);
let prob_bck = *Prob::from(backward(&hmm, &seq).1);
assert_relative_eq!(prob_fwd, prob_bck, epsilon = 0.00001);
}
}
}
#[test]
fn test_gaussian_viterbi_simple_example() {
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = vec![
Normal::new(0.0, 1.0).unwrap(),
Normal::new(2.0, 1.0).unwrap(),
];
let initial = array![0.5, 0.5];
let hmm = GaussianHMM::with_float(&transition, observation, &initial)
.expect("Dimensions should be consistent");
let (path, log_prob) = viterbi(&hmm, &[-0.1, 0.1, -0.2, 0.5, 0.8, 1.1, 1.2, 1.5, 0.5, 0.2]);
let prob = Prob::from(log_prob);
let expected = vec![0, 0, 0, 0, 0, 1, 1, 1, 0, 0]
.iter()
.map(|i| State(*i))
.collect::<Vec<State>>();
assert_eq!(expected, path);
assert_relative_eq!(2.64e-8_f64, *prob, epsilon = 1e-9_f64);
}
#[test]
fn test_gaussian_forward_simple_example() {
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = vec![
Normal::new(0.0, 1.0).unwrap(),
Normal::new(2.0, 1.0).unwrap(),
];
let initial = array![0.5, 0.5];
let hmm = GaussianHMM::with_float(&transition, observation, &initial)
.expect("Dimensions should be consistent");
let log_prob = forward(&hmm, &[0.1, 1.5, 1.8, 2.2, 0.5]).1;
let prob = Prob::from(log_prob);
assert_relative_eq!(7.820e-4_f64, *prob, epsilon = 1e-5_f64);
}
#[test]
fn test_gaussian_backward_simple_example() {
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = vec![
Normal::new(0.0, 1.0).unwrap(),
Normal::new(2.0, 1.0).unwrap(),
];
let initial = array![0.5, 0.5];
let hmm = GaussianHMM::with_float(&transition, observation, &initial)
.expect("Dimensions should be consistent");
let log_prob = backward(&hmm, &[0.1, 1.5, 1.8, 2.2, 0.5]).1;
let prob = Prob::from(log_prob);
assert_relative_eq!(7.820e-4_f64, *prob, epsilon = 1e-5_f64);
}
#[test]
fn test_gaussian_forward_equals_backward_simple_example() {
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = vec![
Normal::new(0.0, 1.0).unwrap(),
Normal::new(2.0, 1.0).unwrap(),
];
let initial = array![0.5, 0.5];
let hmm = GaussianHMM::with_float(&transition, observation, &initial)
.expect("Dimensions should be consistent");
let seqs = vec![vec![0.1, 0.5, 1.0, 1.5, 1.8, 2.1]];
for seq in &seqs {
let prob_fwd = *Prob::from(forward(&hmm, &seq).1);
let prob_bck = *Prob::from(backward(&hmm, &seq).1);
assert_relative_eq!(prob_fwd, prob_bck, epsilon = 0.00001);
}
}
#[test]
fn test_recriate_discrete_backward_toy_example() {
// Same toy example as above.
let transition = array![[0.5, 0.5], [0.4, 0.6]];
let observation = array![[0.2, 0.3, 0.3, 0.2], [0.3, 0.2, 0.2, 0.3]];
let initial = array![0.5, 0.5];
let hmm = DiscreteEmissionHMMoptEND::with_float(&transition, &observation, &initial, None)
.expect("Dimensions should be consistent");
let (_, log_prob) = backward(&hmm, &[2, 2, 1, 0]);
let prob = Prob::from(log_prob);
assert_relative_eq!(0.0038432_f64, *prob, epsilon = 0.0001);
}
#[test]
fn test_discrete_with_end_backward_toy_example() {
// We construct Jason Eisner's dairy ice-cream consumption example.
//
// http://www.cs.jhu.edu/~jason/papers/#eisner-2002-tnlp
//
// States: 0=Hot day, 1=Cold day
// Symbols: 0=one ice creams, 1=two ice creams, 2=three ice creams
let transition = array![[0.8, 0.1], [0.1, 0.8]];
let observation = array![[0.7, 0.2, 0.1], [0.1, 0.2, 0.7]];
let initial = array![0.5, 0.5];
let end = array![0.1, 0.1];
let ices = vec![
1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 2, 2,
1, 2, 1, 1,
];
let hmm =
DiscreteEmissionHMMoptEND::with_float(&transition, &observation, &initial, Some(&end))
.expect("Dimensions should be consistent");
let (_, log_backward_probok) = backward(&hmm, &ices);
let prob = Prob::from(log_backward_probok);
assert_relative_eq!(0.912e-18_f64, *prob, epsilon = 0.1e-20_f64);
}
#[test]
fn test_baum_welch_one_iter_example() {
// Same Jason Eisner's ice cream example as above with little bias
// towards initial day being a hot day (p=0.7)
let transition = array![[0.8, 0.1], [0.1, 0.8]];
let observation = array![[0.7, 0.2, 0.1], [0.1, 0.2, 0.7]];
let initial = array![0.3, 0.7];
let end = array![0.1, 0.1];
let ices = vec![
1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 2, 2,
1, 2, 1, 1,
];
let hmm =
DiscreteEmissionHMMoptEND::with_float(&transition, &observation, &initial, Some(&end))
.expect("Dimensions should be consistent");
// Apply one iteration of baum-welch algorithm and return estimated parameters without
// updating the model in loco.
let (pi_hat, transitions_hat, observations_hat, end_hat) = baum_welch(&hmm, &ices);
// Transform estimated log prob values into prob
let pi_hat_vec = pi_hat.iter().map(|x| Prob::from(*x)).collect::<Vec<Prob>>();
let transitions_hat_vec = transitions_hat
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let observations_hat_vec = observations_hat
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let end_hat_vec = end_hat
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
// Compare with the example given in Jason Eisner's spreadsheet (http://www.cs.jhu.edu/~jason/papers/#eisner-2002-tnlp)
let pi_hat_vec_ori = vec![0.0597, 0.9403]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let transitions_hat_vec_ori = vec![0.8797, 0.1049, 0.0921, 0.8658]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let observations_hat_vec_ori = vec![0.6765, 0.2188, 0.1047, 0.0584, 0.4251, 0.5165]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let end_hat_vec_ori = vec![0.0153, 0.0423]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
assert!(pi_hat_vec
.iter()
.zip(pi_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.001) <= *a) && (*a <= *b + Prob::from(0.001))));
assert!(transitions_hat_vec
.iter()
.zip(transitions_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.001) <= *a) && (*a <= *b + Prob::from(0.001))));
assert!(observations_hat_vec
.iter()
.zip(observations_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.01) <= *a) && (*a <= *b + Prob::from(0.01))));
assert!(end_hat_vec
.iter()
.zip(end_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.01) <= *a) && (*a <= *b + Prob::from(0.01))));
}
#[test]
fn test_baum_welch_train_example() {
// Same Jason Eisner's ice cream example as above with little bias
// towards initial day being a hot day (p=0.7)
let transition = array![[0.8, 0.1], [0.1, 0.8]];
let observation = array![[0.7, 0.2, 0.1], [0.1, 0.2, 0.7]];
let initial = array![0.3, 0.7];
let end = array![0.1, 0.1];
let observations = [vec![
1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 2, 2,
1, 2, 1, 1,
]];
let hmm =
DiscreteEmissionHMMoptEND::with_float(&transition, &observation, &initial, Some(&end))
.expect("Dimensions should be consistent");
// Run 10 iterations of Baum-Welch algorithm
let (pi_hat, transitions_hat, observations_hat, end_hat) =
hmm.train_baum_welch(&observations, Some(10), None);
// Transform the obtained LogProb values into Prob.
let pi_hat_vec = pi_hat.iter().map(|x| Prob::from(*x)).collect::<Vec<Prob>>();
let transitions_hat_vec = transitions_hat
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let observations_hat_vec = observations_hat
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let end_hat_vec = end_hat
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
// Example based on Jason Eisner spreadsheet (http://www.cs.jhu.edu/~jason/papers/#eisner-2002-tnlp)
let pi_hat_vec_ori = vec![0.0, 1.0]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let transitions_hat_vec_ori = vec![0.9337, 0.0663, 0.0718, 0.865]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let observations_hat_vec_ori = vec![0.6407, 0.1481, 0.2112, 1.5e-4, 0.5341, 0.4657]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
let end_hat_vec_ori = vec![0.0, 0.0632]
.iter()
.map(|x| Prob::from(*x))
.collect::<Vec<Prob>>();
assert!(pi_hat_vec
.iter()
.zip(pi_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.001) <= *a) && (*a <= *b + Prob::from(0.001))));
assert!(transitions_hat_vec
.iter()
.zip(transitions_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.001) <= *a) && (*a <= *b + Prob::from(0.001))));
assert!(observations_hat_vec
.iter()
.zip(observations_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.01) <= *a) && (*a <= *b + Prob::from(0.01))));
assert!(end_hat_vec
.iter()
.zip(end_hat_vec_ori.iter())
.all(|(a, b)| (*b - Prob::from(0.01) <= *a) && (*a <= *b + Prob::from(0.01))));
}
}