sklears_dummy/
advanced_bayesian.rs

1//! Advanced Bayesian baseline estimators
2//!
3//! This module provides advanced Bayesian methods for baseline estimation including:
4//! - Empirical Bayes estimation
5//! - Hierarchical Bayesian models  
6//! - Variational Bayes approximation
7//! - MCMC-based sampling
8
9use scirs2_core::ndarray::{Array1, Array2, Axis};
10use scirs2_core::random::prelude::*;
11use scirs2_core::random::Distribution;
12use sklears_core::error::Result;
13use sklears_core::types::{Float, Int};
14use std::collections::HashMap;
15
16/// Advanced Bayesian strategy selection
17#[derive(Debug, Clone, PartialEq)]
18pub enum AdvancedBayesianStrategy {
19    /// Empirical Bayes estimation with hyperparameter optimization
20    EmpiricalBayes,
21    /// Hierarchical Bayesian model with group structure
22    Hierarchical,
23    /// Variational Bayes approximation
24    VariationalBayes,
25    /// MCMC sampling-based estimation
26    MCMCSampling,
27    /// Conjugate prior with automatic selection
28    ConjugatePrior,
29}
30
31/// Empirical Bayes estimator for automatic hyperparameter selection
32#[derive(Debug, Clone)]
33pub struct EmpiricalBayesEstimator {
34    /// Number of iterations for EM algorithm
35    pub max_iter: usize,
36    /// Convergence tolerance
37    pub tolerance: Float,
38    /// Random state for reproducibility
39    pub random_state: Option<u64>,
40    /// Estimated hyperparameters
41    pub hyperparameters_: Option<Array1<Float>>,
42    /// Log-likelihood values during optimization
43    pub log_likelihood_: Option<Vec<Float>>,
44}
45
46impl EmpiricalBayesEstimator {
47    /// Create new empirical Bayes estimator
48    pub fn new() -> Self {
49        Self {
50            max_iter: 100,
51            tolerance: 1e-6,
52            random_state: None,
53            hyperparameters_: None,
54            log_likelihood_: None,
55        }
56    }
57
58    /// Set maximum iterations
59    pub fn with_max_iter(mut self, max_iter: usize) -> Self {
60        self.max_iter = max_iter;
61        self
62    }
63
64    /// Set convergence tolerance
65    pub fn with_tolerance(mut self, tolerance: Float) -> Self {
66        self.tolerance = tolerance;
67        self
68    }
69
70    /// Set random state
71    pub fn with_random_state(mut self, random_state: u64) -> Self {
72        self.random_state = Some(random_state);
73        self
74    }
75
76    /// Estimate hyperparameters using EM algorithm for classification
77    pub fn fit_classification(&mut self, y: &Array1<Int>) -> Result<()> {
78        let mut class_counts: HashMap<Int, usize> = HashMap::new();
79        for &label in y.iter() {
80            *class_counts.entry(label).or_insert(0) += 1;
81        }
82
83        let mut classes: Vec<Int> = class_counts.keys().copied().collect();
84        classes.sort();
85        let n_classes = classes.len();
86        let n_samples = y.len() as Float;
87
88        // Initialize hyperparameters (Dirichlet concentration parameters)
89        let mut hyperparams = Array1::ones(n_classes);
90        let mut log_likelihoods = Vec::new();
91
92        // EM algorithm for empirical Bayes estimation
93        for iter in 0..self.max_iter {
94            // E-step: compute expected sufficient statistics
95            let mut expected_counts = Array1::<Float>::zeros(n_classes);
96            for &label in y.iter() {
97                let class_idx = classes.iter().position(|&c| c == label).unwrap();
98                expected_counts[class_idx] += 1.0;
99            }
100
101            // M-step: update hyperparameters
102            let old_hyperparams = hyperparams.clone();
103
104            // Method of moments estimation for Dirichlet parameters
105            let observed_props: Array1<Float> = expected_counts.mapv(|x| x / n_samples);
106            let mean_prop = observed_props.mean().unwrap();
107            let variance_sum: Float = observed_props.mapv(|p| (p - mean_prop).powi(2)).sum();
108
109            // Estimate concentration parameter
110            let concentration = if variance_sum > 0.0 {
111                let variance_mean = variance_sum / (n_classes as Float);
112                let alpha_sum = mean_prop * (1.0 - mean_prop) / variance_mean - 1.0;
113                alpha_sum.max(0.1) // Ensure positive
114            } else {
115                1.0
116            };
117
118            hyperparams = observed_props.mapv(|p| p * concentration);
119
120            // Compute log-likelihood (approximate)
121            let log_likelihood = self.compute_log_likelihood(&hyperparams, &expected_counts);
122            log_likelihoods.push(log_likelihood);
123
124            // Check convergence
125            let param_diff: Float = (&hyperparams - &old_hyperparams).mapv(|x| x.abs()).sum();
126            if param_diff < self.tolerance {
127                break;
128            }
129        }
130
131        self.hyperparameters_ = Some(hyperparams);
132        self.log_likelihood_ = Some(log_likelihoods);
133        Ok(())
134    }
135
136    /// Compute log-likelihood for convergence checking
137    fn compute_log_likelihood(&self, hyperparams: &Array1<Float>, counts: &Array1<Float>) -> Float {
138        let alpha_sum = hyperparams.sum();
139        let count_sum = counts.sum();
140
141        // Log-likelihood of Dirichlet-Multinomial
142        let mut log_likelihood = 0.0;
143
144        // Add log Gamma terms
145        for (&alpha, &count) in hyperparams.iter().zip(counts.iter()) {
146            log_likelihood += gamma_ln(alpha + count) - gamma_ln(alpha);
147        }
148
149        log_likelihood += gamma_ln(alpha_sum) - gamma_ln(alpha_sum + count_sum);
150        log_likelihood
151    }
152
153    /// Get estimated hyperparameters
154    pub fn hyperparameters(&self) -> Option<&Array1<Float>> {
155        self.hyperparameters_.as_ref()
156    }
157
158    /// Get log-likelihood evolution
159    pub fn log_likelihood_evolution(&self) -> Option<&Vec<Float>> {
160        self.log_likelihood_.as_ref()
161    }
162}
163
164/// Hierarchical Bayesian estimator with group structure
165#[derive(Debug, Clone)]
166pub struct HierarchicalBayesEstimator {
167    /// Group assignments for samples
168    pub groups: Option<Array1<Int>>,
169    /// Global hyperparameters
170    pub global_hyperparams_: Option<Array1<Float>>,
171    /// Group-specific parameters
172    pub group_params_: Option<HashMap<Int, Array1<Float>>>,
173    /// Random state
174    pub random_state: Option<u64>,
175}
176
177impl HierarchicalBayesEstimator {
178    /// Create new hierarchical Bayes estimator
179    pub fn new() -> Self {
180        Self {
181            groups: None,
182            global_hyperparams_: None,
183            group_params_: None,
184            random_state: None,
185        }
186    }
187
188    /// Set group assignments
189    pub fn with_groups(mut self, groups: Array1<Int>) -> Self {
190        self.groups = Some(groups);
191        self
192    }
193
194    /// Set random state
195    pub fn with_random_state(mut self, random_state: u64) -> Self {
196        self.random_state = Some(random_state);
197        self
198    }
199
200    /// Fit hierarchical model
201    pub fn fit_classification(&mut self, y: &Array1<Int>) -> Result<()> {
202        let groups = self.groups.as_ref().ok_or_else(|| {
203            sklears_core::error::SklearsError::InvalidInput(
204                "Group assignments must be provided".to_string(),
205            )
206        })?;
207
208        if groups.len() != y.len() {
209            return Err(sklears_core::error::SklearsError::InvalidInput(
210                "Groups and labels must have same length".to_string(),
211            ));
212        }
213
214        // Get unique classes and groups
215        let mut class_counts: HashMap<Int, usize> = HashMap::new();
216        for &label in y.iter() {
217            *class_counts.entry(label).or_insert(0) += 1;
218        }
219        let mut classes: Vec<Int> = class_counts.keys().copied().collect();
220        classes.sort();
221        let n_classes = classes.len();
222
223        let mut unique_groups: Vec<Int> = groups.iter().copied().collect();
224        unique_groups.sort();
225        unique_groups.dedup();
226
227        // Compute group-specific class distributions
228        let mut group_params = HashMap::new();
229        let mut global_counts = Array1::<Float>::zeros(n_classes);
230
231        for &group in &unique_groups {
232            let mut group_class_counts = Array1::<Float>::zeros(n_classes);
233            let mut group_total = 0;
234
235            for (i, (&label, &group_id)) in y.iter().zip(groups.iter()).enumerate() {
236                if group_id == group {
237                    let class_idx = classes.iter().position(|&c| c == label).unwrap();
238                    group_class_counts[class_idx] += 1.0;
239                    global_counts[class_idx] += 1.0;
240                    group_total += 1;
241                }
242            }
243
244            if group_total > 0 {
245                // Normalize to probabilities
246                let group_probs = group_class_counts.mapv(|x| x / (group_total as Float));
247                group_params.insert(group, group_probs);
248            }
249        }
250
251        // Estimate global hyperparameters (pooled estimate)
252        let global_total = global_counts.sum();
253        let global_hyperparams = if global_total > 0.0 {
254            global_counts.mapv(|x| x / global_total)
255        } else {
256            Array1::ones(n_classes) / (n_classes as Float)
257        };
258
259        self.global_hyperparams_ = Some(global_hyperparams);
260        self.group_params_ = Some(group_params);
261        Ok(())
262    }
263
264    /// Get global hyperparameters
265    pub fn global_hyperparameters(&self) -> Option<&Array1<Float>> {
266        self.global_hyperparams_.as_ref()
267    }
268
269    /// Get group-specific parameters
270    pub fn group_parameters(&self) -> Option<&HashMap<Int, Array1<Float>>> {
271        self.group_params_.as_ref()
272    }
273}
274
275/// Variational Bayes estimator using mean-field approximation
276#[derive(Debug, Clone)]
277pub struct VariationalBayesEstimator {
278    /// Maximum iterations for variational optimization
279    pub max_iter: usize,
280    /// Convergence tolerance
281    pub tolerance: Float,
282    /// Variational parameters
283    pub variational_params_: Option<Array1<Float>>,
284    /// ELBO (Evidence Lower BOund) values
285    pub elbo_: Option<Vec<Float>>,
286    /// Random state
287    pub random_state: Option<u64>,
288}
289
290impl VariationalBayesEstimator {
291    /// Create new variational Bayes estimator
292    pub fn new() -> Self {
293        Self {
294            max_iter: 100,
295            tolerance: 1e-6,
296            variational_params_: None,
297            elbo_: None,
298            random_state: None,
299        }
300    }
301
302    /// Set maximum iterations
303    pub fn with_max_iter(mut self, max_iter: usize) -> Self {
304        self.max_iter = max_iter;
305        self
306    }
307
308    /// Set convergence tolerance
309    pub fn with_tolerance(mut self, tolerance: Float) -> Self {
310        self.tolerance = tolerance;
311        self
312    }
313
314    /// Fit variational Bayes model
315    pub fn fit_classification(&mut self, y: &Array1<Int>) -> Result<()> {
316        let mut class_counts: HashMap<Int, usize> = HashMap::new();
317        for &label in y.iter() {
318            *class_counts.entry(label).or_insert(0) += 1;
319        }
320
321        let mut classes: Vec<Int> = class_counts.keys().copied().collect();
322        classes.sort();
323        let n_classes = classes.len();
324
325        // Initialize variational parameters
326        let mut q_params = Array1::ones(n_classes);
327        let mut elbo_values = Vec::new();
328
329        // Variational optimization loop
330        for _iter in 0..self.max_iter {
331            let old_params = q_params.clone();
332
333            // Update variational parameters (simplified mean-field update)
334            let mut new_params = Array1::<Float>::zeros(n_classes);
335            for (i, &class) in classes.iter().enumerate() {
336                let count = *class_counts.get(&class).unwrap() as Float;
337                // Add pseudo-count from prior
338                new_params[i] = count + 1.0;
339            }
340
341            q_params = new_params;
342
343            // Compute ELBO (simplified)
344            let elbo = self.compute_elbo(&q_params, &class_counts, &classes);
345            elbo_values.push(elbo);
346
347            // Check convergence
348            let param_diff: Float = (&q_params - &old_params).mapv(|x| x.abs()).sum();
349            if param_diff < self.tolerance {
350                break;
351            }
352        }
353
354        // Normalize to probabilities
355        let param_sum = q_params.sum();
356        q_params = q_params.mapv(|x| x / param_sum);
357
358        self.variational_params_ = Some(q_params);
359        self.elbo_ = Some(elbo_values);
360        Ok(())
361    }
362
363    /// Compute Evidence Lower BOund (ELBO)
364    fn compute_elbo(
365        &self,
366        params: &Array1<Float>,
367        counts: &HashMap<Int, usize>,
368        classes: &[Int],
369    ) -> Float {
370        let mut elbo = 0.0;
371        let param_sum = params.sum();
372
373        // Data likelihood term
374        for (i, &class) in classes.iter().enumerate() {
375            let count = *counts.get(&class).unwrap() as Float;
376            if count > 0.0 {
377                elbo += count * (params[i] / param_sum).ln();
378            }
379        }
380
381        // Prior terms (simplified)
382        for &param in params.iter() {
383            if param > 0.0 {
384                elbo += param.ln();
385            }
386        }
387
388        elbo
389    }
390
391    /// Get variational parameters
392    pub fn variational_parameters(&self) -> Option<&Array1<Float>> {
393        self.variational_params_.as_ref()
394    }
395
396    /// Get ELBO evolution
397    pub fn elbo_evolution(&self) -> Option<&Vec<Float>> {
398        self.elbo_.as_ref()
399    }
400}
401
402/// MCMC-based Bayesian estimator
403#[derive(Debug, Clone)]
404pub struct MCMCBayesEstimator {
405    /// Number of MCMC samples
406    pub n_samples: usize,
407    /// Burn-in period
408    pub burn_in: usize,
409    /// Thinning factor
410    pub thin: usize,
411    /// MCMC samples
412    pub samples_: Option<Array2<Float>>,
413    /// Random state
414    pub random_state: Option<u64>,
415}
416
417impl MCMCBayesEstimator {
418    /// Create new MCMC estimator
419    pub fn new() -> Self {
420        Self {
421            n_samples: 1000,
422            burn_in: 200,
423            thin: 1,
424            samples_: None,
425            random_state: None,
426        }
427    }
428
429    /// Set number of samples
430    pub fn with_n_samples(mut self, n_samples: usize) -> Self {
431        self.n_samples = n_samples;
432        self
433    }
434
435    /// Set burn-in period
436    pub fn with_burn_in(mut self, burn_in: usize) -> Self {
437        self.burn_in = burn_in;
438        self
439    }
440
441    /// Set random state
442    pub fn with_random_state(mut self, random_state: u64) -> Self {
443        self.random_state = Some(random_state);
444        self
445    }
446
447    /// Fit MCMC model using Gibbs sampling
448    pub fn fit_classification(&mut self, y: &Array1<Int>) -> Result<()> {
449        let mut class_counts: HashMap<Int, usize> = HashMap::new();
450        for &label in y.iter() {
451            *class_counts.entry(label).or_insert(0) += 1;
452        }
453
454        let mut classes: Vec<Int> = class_counts.keys().copied().collect();
455        classes.sort();
456        let n_classes = classes.len();
457
458        let mut rng = if let Some(seed) = self.random_state {
459            StdRng::seed_from_u64(seed)
460        } else {
461            StdRng::seed_from_u64(0) // Use deterministic seed for reproducibility
462        };
463
464        // Initialize parameters
465        let mut theta = Array1::<Float>::from_elem(n_classes, 1.0 / n_classes as Float);
466        let total_samples = self.burn_in + self.n_samples * self.thin;
467        let mut samples = Array2::<Float>::zeros((self.n_samples, n_classes));
468
469        // MCMC sampling loop
470        for iter in 0..total_samples {
471            // Gibbs sampling for Dirichlet-Multinomial
472            let mut alpha_posterior = Array1::<Float>::ones(n_classes); // Prior
473
474            // Add observed counts
475            for (i, &class) in classes.iter().enumerate() {
476                let count = *class_counts.get(&class).unwrap() as Float;
477                alpha_posterior[i] += count;
478            }
479
480            // Sample from Dirichlet using Gamma sampling
481            let mut gamma_samples = Array1::<Float>::zeros(n_classes);
482            for i in 0..n_classes {
483                let gamma_dist = Gamma::new(alpha_posterior[i], 1.0).unwrap();
484                gamma_samples[i] = gamma_dist.sample(&mut rng);
485            }
486
487            // Normalize to get Dirichlet sample
488            let gamma_sum = gamma_samples.sum();
489            theta = gamma_samples.mapv(|x| x / gamma_sum);
490
491            // Store sample if past burn-in and at thinning interval
492            if iter >= self.burn_in && (iter - self.burn_in) % self.thin == 0 {
493                let sample_idx = (iter - self.burn_in) / self.thin;
494                if sample_idx < self.n_samples {
495                    for j in 0..n_classes {
496                        samples[[sample_idx, j]] = theta[j];
497                    }
498                }
499            }
500        }
501
502        self.samples_ = Some(samples);
503        Ok(())
504    }
505
506    /// Get MCMC samples
507    pub fn samples(&self) -> Option<&Array2<Float>> {
508        self.samples_.as_ref()
509    }
510
511    /// Get posterior mean
512    pub fn posterior_mean(&self) -> Option<Array1<Float>> {
513        self.samples_
514            .as_ref()
515            .map(|samples| samples.mean_axis(Axis(0)).unwrap())
516    }
517
518    /// Get posterior standard deviation
519    pub fn posterior_std(&self) -> Option<Array1<Float>> {
520        self.samples_
521            .as_ref()
522            .map(|samples| samples.std_axis(Axis(0), 0.0))
523    }
524
525    /// Get credible intervals
526    pub fn credible_interval(&self, alpha: Float) -> Option<(Array1<Float>, Array1<Float>)> {
527        let samples = self.samples_.as_ref()?;
528        let n_classes = samples.ncols();
529        let mut lower = Array1::<Float>::zeros(n_classes);
530        let mut upper = Array1::<Float>::zeros(n_classes);
531
532        for i in 0..n_classes {
533            let mut column: Vec<Float> = samples.column(i).to_vec();
534            column.sort_by(|a, b| a.partial_cmp(b).unwrap());
535
536            let lower_idx = ((alpha / 2.0) * (column.len() as Float)) as usize;
537            let upper_idx = ((1.0 - alpha / 2.0) * (column.len() as Float)) as usize;
538
539            lower[i] = column[lower_idx.min(column.len() - 1)];
540            upper[i] = column[upper_idx.min(column.len() - 1)];
541        }
542
543        Some((lower, upper))
544    }
545}
546
547/// Approximation of log Gamma function
548fn gamma_ln(x: Float) -> Float {
549    // Stirling's approximation for large x, exact for small integers
550    if x <= 0.0 {
551        Float::INFINITY
552    } else if x < 12.0 {
553        // Use recurrence relation for small values
554        if x.fract() == 0.0 && x <= 10.0 {
555            // Exact for small integers
556            let n = x as usize;
557            if n == 1 {
558                0.0
559            } else {
560                (1..n).map(|i| (i as Float).ln()).sum()
561            }
562        } else {
563            // Stirling approximation
564            (x - 0.5) * x.ln() - x + 0.5 * (2.0 * std::f64::consts::PI).ln()
565        }
566    } else {
567        // Stirling approximation for large x
568        (x - 0.5) * x.ln() - x + 0.5 * (2.0 * std::f64::consts::PI).ln()
569    }
570}
571
572/// Default implementations
573impl Default for EmpiricalBayesEstimator {
574    fn default() -> Self {
575        Self::new()
576    }
577}
578
579impl Default for HierarchicalBayesEstimator {
580    fn default() -> Self {
581        Self::new()
582    }
583}
584
585impl Default for VariationalBayesEstimator {
586    fn default() -> Self {
587        Self::new()
588    }
589}
590
591impl Default for MCMCBayesEstimator {
592    fn default() -> Self {
593        Self::new()
594    }
595}
596
597#[allow(non_snake_case)]
598#[cfg(test)]
599mod tests {
600    use super::*;
601    use approx::assert_abs_diff_eq;
602    use scirs2_core::ndarray::array;
603
604    #[test]
605    fn test_empirical_bayes_basic() {
606        let y = array![0, 0, 0, 1, 1, 2]; // 3 classes with different frequencies
607        let mut estimator = EmpiricalBayesEstimator::new().with_random_state(42);
608
609        let result = estimator.fit_classification(&y);
610        assert!(result.is_ok());
611
612        let hyperparams = estimator.hyperparameters().unwrap();
613        assert_eq!(hyperparams.len(), 3);
614
615        // All hyperparameters should be positive
616        for &param in hyperparams.iter() {
617            assert!(param > 0.0);
618        }
619
620        // Most frequent class should have higher hyperparameter
621        assert!(hyperparams[0] >= hyperparams[1]);
622        assert!(hyperparams[0] >= hyperparams[2]);
623    }
624
625    #[test]
626    fn test_hierarchical_bayes_basic() {
627        let y = array![0, 0, 1, 1, 0, 1];
628        let groups = array![1, 1, 1, 2, 2, 2]; // Two groups
629
630        let mut estimator = HierarchicalBayesEstimator::new()
631            .with_groups(groups)
632            .with_random_state(42);
633
634        let result = estimator.fit_classification(&y);
635        assert!(result.is_ok());
636
637        let global_params = estimator.global_hyperparameters().unwrap();
638        assert_eq!(global_params.len(), 2);
639
640        let group_params = estimator.group_parameters().unwrap();
641        assert_eq!(group_params.len(), 2);
642
643        // Check that group parameters exist for both groups
644        assert!(group_params.contains_key(&1));
645        assert!(group_params.contains_key(&2));
646    }
647
648    #[test]
649    fn test_variational_bayes_basic() {
650        let y = array![0, 0, 0, 1, 1, 2];
651        let mut estimator = VariationalBayesEstimator::new()
652            .with_max_iter(50)
653            .with_tolerance(1e-4);
654
655        let result = estimator.fit_classification(&y);
656        assert!(result.is_ok());
657
658        let params = estimator.variational_parameters().unwrap();
659        assert_eq!(params.len(), 3);
660
661        // Parameters should sum to 1 (normalized probabilities)
662        let sum: Float = params.sum();
663        assert_abs_diff_eq!(sum, 1.0, epsilon = 1e-10);
664
665        // ELBO should be tracked
666        let elbo = estimator.elbo_evolution().unwrap();
667        assert!(!elbo.is_empty());
668    }
669
670    #[test]
671    fn test_mcmc_bayes_basic() {
672        let y = array![0, 0, 0, 1, 1, 2];
673        let mut estimator = MCMCBayesEstimator::new()
674            .with_n_samples(100)
675            .with_burn_in(20)
676            .with_random_state(42);
677
678        let result = estimator.fit_classification(&y);
679        assert!(result.is_ok());
680
681        let samples = estimator.samples().unwrap();
682        assert_eq!(samples.nrows(), 100);
683        assert_eq!(samples.ncols(), 3);
684
685        // Each row should sum to 1 (probabilities)
686        for i in 0..samples.nrows() {
687            let row_sum: Float = samples.row(i).sum();
688            assert_abs_diff_eq!(row_sum, 1.0, epsilon = 1e-10);
689        }
690
691        // Posterior mean should be available
692        let mean = estimator.posterior_mean().unwrap();
693        assert_eq!(mean.len(), 3);
694
695        // Credible intervals should be available
696        let (lower, upper) = estimator.credible_interval(0.05).unwrap();
697        assert_eq!(lower.len(), 3);
698        assert_eq!(upper.len(), 3);
699
700        // Lower bounds should be less than upper bounds
701        for i in 0..3 {
702            assert!(lower[i] <= upper[i]);
703        }
704    }
705
706    #[test]
707    fn test_gamma_ln_function() {
708        // Test for known values
709        assert_abs_diff_eq!(gamma_ln(1.0), 0.0, epsilon = 1e-10);
710        assert_abs_diff_eq!(gamma_ln(2.0), 0.0, epsilon = 1e-10); // ln(1!)
711        assert_abs_diff_eq!(gamma_ln(3.0), (2.0f64).ln(), epsilon = 1e-10); // ln(2!)
712
713        // Test for larger values (approximate)
714        let result = gamma_ln(10.0);
715        assert!(result > 0.0);
716        assert!(result.is_finite());
717    }
718}
sklears_dummy/advanced_bayesian.rs

sklears_dummy/
advanced_bayesian.rs
