turnbull: Pre-compute survival probabilities
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250cfd8798
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7234E476BF21C61A
@ -287,8 +287,11 @@ fn get_turnbull_intervals(data_times: &MatrixXx2<f64>) -> Vec<(f64, f64)> {
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}
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fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, max_iterations: u32, ll_tolerance: f64, mut p: Vec<f64>) -> (Vec<f64>, f64) {
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// Pre-compute S, the survival probability at the start of each interval
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let mut s = p_to_s(&p);
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// Get likelihood for each observation
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let mut likelihood_obs = get_likelihood_obs(data, &p);
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let mut likelihood_obs = get_likelihood_obs(data, &s);
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let mut ll_model: f64 = likelihood_obs.iter().map(|l| l.ln()).sum();
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let mut iteration = 1;
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@ -296,55 +299,41 @@ fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, ma
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// -------
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// EM step
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// Pre-compute S, the survival probability at the start of each interval
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let mut s = Vec::with_capacity(data.num_intervals() + 1);
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let mut survival = 1.0;
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s.push(1.0);
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for p_j in p.iter() {
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survival -= p_j;
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s.push(survival);
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}
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// Update p
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let mut p_new = Vec::with_capacity(data.num_intervals());
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for j in 0..data.num_intervals() {
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let tmp: f64 = data.data_time_interval_indexes.iter()
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.filter(|(idx_left, idx_right)| j >= *idx_left && j <= *idx_right)
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//.map(|(idx_left, idx_right)| 1.0 / p[*idx_left..(*idx_right + 1)].iter().sum::<f64>())
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.map(|(idx_left, idx_right)| 1.0 / (s[*idx_left] - s[*idx_right + 1]))
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.sum();
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p_new.push(p[j] * tmp / (data.num_obs() as f64));
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}
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let likelihood_obs_after_em = get_likelihood_obs(data, &p_new);
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let mut s_new = p_to_s(&p_new);
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let likelihood_obs_after_em = get_likelihood_obs(data, &s_new);
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let ll_model_after_em: f64 = likelihood_obs_after_em.iter().map(|l| l.ln()).sum();
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p = p_new;
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s = s_new;
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// --------
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// ICM step
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// Compute Λ
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// S = 1 means Λ = -inf and S = 0 means Λ = inf so skip these
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let mut lambda = Vec::with_capacity(data.num_intervals() - 1);
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let mut survival: f64 = 1.0;
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for j in 0..(data.num_intervals() - 1) {
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survival -= p[j];
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lambda.push((-survival.ln()).ln());
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}
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// Compute Λ, the cumulative hazard
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let lambda = s_to_lambda(&s);
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// Compute gradient
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let mut gradient = DVector::zeros(data.num_intervals() - 1);
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for j in 0..(data.num_intervals() - 1) {
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let sum_right: f64 = data.data_time_interval_indexes.iter()
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.filter(|(idx_left, idx_right)| j + 1 == *idx_right + 1)
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.map(|(idx_left, idx_right)| (-lambda[j].exp() + lambda[j]).exp() / p[*idx_left..(*idx_right + 1)].iter().sum::<f64>())
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.map(|(idx_left, idx_right)| (-lambda[j].exp() + lambda[j]).exp() / (s[*idx_left] - s[*idx_right + 1]))
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.sum();
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let sum_left: f64 = data.data_time_interval_indexes.iter()
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.filter(|(idx_left, idx_right)| j + 1 == *idx_left)
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.map(|(idx_left, idx_right)| (-lambda[j].exp() + lambda[j]).exp() / p[*idx_left..(*idx_right + 1)].iter().sum::<f64>())
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.map(|(idx_left, idx_right)| (-lambda[j].exp() + lambda[j]).exp() / (s[*idx_left] - s[*idx_right + 1]))
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.sum();
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gradient[j] = sum_right - sum_left;
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@ -356,7 +345,7 @@ fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, ma
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let sum_left: f64 = data.data_time_interval_indexes.iter()
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.filter(|(idx_left, idx_right)| j + 1 == *idx_left)
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.map(|(idx_left, idx_right)| {
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let denom: f64 = p[*idx_left..(*idx_right + 1)].iter().sum();
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let denom = s[*idx_left] - s[*idx_right + 1];
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let a = ((lambda[j] - lambda[j].exp()).exp() * (1.0 - lambda[j].exp())) / denom;
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let b = (2.0 * lambda[j] - 2.0 * lambda[j].exp()).exp() / denom.powi(2);
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-a - b
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@ -366,7 +355,7 @@ fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, ma
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let sum_right: f64 = data.data_time_interval_indexes.iter()
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.filter(|(idx_left, idx_right)| j + 1 == *idx_right + 1)
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.map(|(idx_left, idx_right)| {
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let denom: f64 = p[*idx_left..(*idx_right + 1)].iter().sum();
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let denom = s[*idx_left] - s[*idx_right + 1];
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let a = ((lambda[j] - lambda[j].exp()).exp() * (1.0 - lambda[j].exp())) / denom;
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let b = (2.0 * lambda[j] - 2.0 * lambda[j].exp()).exp() / denom.powi(2);
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a - b
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@ -395,17 +384,21 @@ fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, ma
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let lambda_new = monotonic_regression_pava(lambda_target, weights.clone());
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// Convert Λ to S to p
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s_new = Vec::with_capacity(data.num_intervals() + 1);
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p_new = Vec::with_capacity(data.num_intervals());
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let mut survival = 1.0;
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s_new.push(1.0);
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for lambda_j in lambda_new.iter() {
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let next_survival = (-lambda_j.exp()).exp();
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s_new.push(next_survival);
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p_new.push(survival - next_survival);
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survival = next_survival;
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}
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s_new.push(0.0);
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p_new.push(survival);
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let likelihood_obs_new = get_likelihood_obs(data, &p_new);
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let likelihood_obs_new = get_likelihood_obs(data, &s_new);
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ll_model_new = likelihood_obs_new.iter().map(|l| l.ln()).sum();
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if ll_model_new > ll_model_after_em {
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@ -423,7 +416,7 @@ fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, ma
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let converged = ll_change <= ll_tolerance;
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p = p_new;
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//likelihood_obs = likelihood_obs_new;
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s = s_new;
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ll_model = ll_model_new;
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// Estimate progress bar according to either the order of magnitude of the ll_change relative to tolerance, or iteration/max_iterations
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@ -448,11 +441,31 @@ fn fit_turnbull_estimator(data: &mut TurnbullData, progress_bar: ProgressBar, ma
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return (p, ll_model);
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}
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fn p_to_s(p: &Vec<f64>) -> Vec<f64> {
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let mut s = Vec::with_capacity(p.len() + 1); // Survival probabilities
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let mut survival = 1.0;
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s.push(1.0);
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for p_j in p.iter() {
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survival -= p_j;
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s.push(survival);
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}
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return s;
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}
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fn s_to_lambda(s: &Vec<f64>) -> Vec<f64> {
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// S = 1 means Λ = -inf and S = 0 means Λ = inf so skip these
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let mut lambda = Vec::with_capacity(s.len() - 2); // Cumulative hazard
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for s_j in &s[1..(s.len() - 1)] {
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lambda.push((-s_j.ln()).ln());
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}
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return lambda;
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}
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fn get_likelihood_obs(data: &TurnbullData, s: &Vec<f64>) -> Vec<f64> {
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return data.data_time_interval_indexes
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.par_iter()
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.map(|(idx_left, idx_right)| s[*idx_left..(*idx_right + 1)].iter().sum())
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.collect();
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.map(|(idx_left, idx_right)| s[*idx_left] - s[*idx_right + 1])
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.collect(); // TODO: Return iterator directly
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}
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fn compute_hessian(data: &TurnbullData, s: &Vec<f64>) -> DMatrix<f64> {
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