sklears_mixture/
approximation.rs

1//! Approximation Methods for Mixture Models
2//!
3//! This module provides various approximation techniques for mixture model
4//! inference, including Laplace approximations, Monte Carlo methods, and
5//! importance sampling.
6//!
7//! # Overview
8//!
9//! Approximation methods enable:
10//! - Fast inference in complex models
11//! - Uncertainty quantification
12//! - Posterior distribution approximation
13//! - Efficient sampling strategies
14//!
15//! # Key Components
16//!
17//! - **Laplace Approximation**: Gaussian approximation around mode
18//! - **Monte Carlo Methods**: Sampling-based inference
19//! - **Importance Sampling**: Weighted sampling for rare events
20//! - **Particle Filtering**: Sequential Monte Carlo
21
22use crate::common::CovarianceType;
23use scirs2_core::ndarray::{Array1, Array2, ArrayView2};
24use scirs2_core::random::thread_rng;
25use sklears_core::{
26    error::{Result as SklResult, SklearsError},
27    traits::{Estimator, Fit, Predict, Untrained},
28    types::Float,
29};
30
31/// Type of Monte Carlo approximation
32#[derive(Debug, Clone, Copy, PartialEq)]
33pub enum MonteCarloMethod {
34    /// Standard Monte Carlo
35    Standard { n_samples: usize },
36    /// Quasi-Monte Carlo with low-discrepancy sequences
37    Quasi { n_samples: usize },
38    /// Markov Chain Monte Carlo
39    MCMC {
40        n_samples: usize,
41        burn_in: usize,
42        thin: usize,
43    },
44}
45
46/// Importance sampling strategy
47#[derive(Debug, Clone, Copy, PartialEq)]
48pub enum ImportanceSamplingStrategy {
49    /// Standard importance sampling
50    Standard { n_samples: usize },
51    /// Adaptive importance sampling
52    Adaptive {
53        n_samples: usize,
54        adaptation_steps: usize,
55    },
56    /// Self-normalized importance sampling
57    SelfNormalized { n_samples: usize },
58}
59
60/// Laplace Approximation for Gaussian Mixture Model
61///
62/// Approximates the posterior distribution with a Gaussian centered at the MAP estimate.
63///
64/// # Examples
65///
66/// ```
67/// use sklears_mixture::approximation::LaplaceGMM;
68/// use sklears_core::traits::Fit;
69/// use scirs2_core::ndarray::array;
70///
71/// let model = LaplaceGMM::builder()
72///     .n_components(2)
73///     .build();
74///
75/// let X = array![[1.0, 2.0], [1.5, 2.5], [10.0, 11.0]];
76/// let fitted = model.fit(&X.view(), &()).unwrap();
77/// ```
78#[derive(Debug, Clone)]
79pub struct LaplaceGMM<S = Untrained> {
80    n_components: usize,
81    covariance_type: CovarianceType,
82    max_iter: usize,
83    tol: f64,
84    reg_covar: f64,
85    hessian_regularization: f64,
86    _phantom: std::marker::PhantomData<S>,
87}
88
89/// Trained Laplace GMM
90#[derive(Debug, Clone)]
91pub struct LaplaceGMMTrained {
92    /// MAP estimates (mode of posterior)
93    pub map_weights: Array1<f64>,
94    /// MAP means
95    pub map_means: Array2<f64>,
96    /// MAP covariances
97    pub map_covariances: Array2<f64>,
98    /// Posterior covariance (inverse Hessian)
99    pub posterior_covariance: Array2<f64>,
100    /// Log marginal likelihood (evidence)
101    pub log_marginal_likelihood: f64,
102    /// Number of iterations
103    pub n_iter: usize,
104    /// Convergence status
105    pub converged: bool,
106}
107
108/// Builder for Laplace GMM
109#[derive(Debug, Clone)]
110pub struct LaplaceGMMBuilder {
111    n_components: usize,
112    covariance_type: CovarianceType,
113    max_iter: usize,
114    tol: f64,
115    reg_covar: f64,
116    hessian_regularization: f64,
117}
118
119impl LaplaceGMMBuilder {
120    /// Create a new builder
121    pub fn new() -> Self {
122        Self {
123            n_components: 1,
124            covariance_type: CovarianceType::Diagonal,
125            max_iter: 100,
126            tol: 1e-3,
127            reg_covar: 1e-6,
128            hessian_regularization: 1e-4,
129        }
130    }
131
132    /// Set number of components
133    pub fn n_components(mut self, n: usize) -> Self {
134        self.n_components = n;
135        self
136    }
137
138    /// Set covariance type
139    pub fn covariance_type(mut self, cov_type: CovarianceType) -> Self {
140        self.covariance_type = cov_type;
141        self
142    }
143
144    /// Set maximum iterations
145    pub fn max_iter(mut self, max_iter: usize) -> Self {
146        self.max_iter = max_iter;
147        self
148    }
149
150    /// Set Hessian regularization
151    pub fn hessian_regularization(mut self, reg: f64) -> Self {
152        self.hessian_regularization = reg;
153        self
154    }
155
156    /// Build the model
157    pub fn build(self) -> LaplaceGMM<Untrained> {
158        LaplaceGMM {
159            n_components: self.n_components,
160            covariance_type: self.covariance_type,
161            max_iter: self.max_iter,
162            tol: self.tol,
163            reg_covar: self.reg_covar,
164            hessian_regularization: self.hessian_regularization,
165            _phantom: std::marker::PhantomData,
166        }
167    }
168}
169
170impl Default for LaplaceGMMBuilder {
171    fn default() -> Self {
172        Self::new()
173    }
174}
175
176impl LaplaceGMM<Untrained> {
177    /// Create a new builder
178    pub fn builder() -> LaplaceGMMBuilder {
179        LaplaceGMMBuilder::new()
180    }
181}
182
183impl Estimator for LaplaceGMM<Untrained> {
184    type Config = ();
185    type Error = SklearsError;
186    type Float = Float;
187
188    fn config(&self) -> &Self::Config {
189        &()
190    }
191}
192
193impl Fit<ArrayView2<'_, Float>, ()> for LaplaceGMM<Untrained> {
194    type Fitted = LaplaceGMM<LaplaceGMMTrained>;
195
196    #[allow(non_snake_case)]
197    fn fit(self, X: &ArrayView2<'_, Float>, _y: &()) -> SklResult<Self::Fitted> {
198        let X_owned = X.to_owned();
199        let (n_samples, n_features) = X_owned.dim();
200
201        if n_samples < self.n_components {
202            return Err(SklearsError::InvalidInput(
203                "Number of samples must be >= number of components".to_string(),
204            ));
205        }
206
207        // Initialize with simple k-means-like approach
208        let mut rng = thread_rng();
209        let mut means = Array2::zeros((self.n_components, n_features));
210        let mut used_indices = Vec::new();
211        for k in 0..self.n_components {
212            let idx = loop {
213                let candidate = rng.gen_range(0..n_samples);
214                if !used_indices.contains(&candidate) {
215                    used_indices.push(candidate);
216                    break candidate;
217                }
218            };
219            means.row_mut(k).assign(&X_owned.row(idx));
220        }
221
222        let weights = Array1::from_elem(self.n_components, 1.0 / self.n_components as f64);
223        let covariances =
224            Array2::<f64>::eye(n_features) + &(Array2::<f64>::eye(n_features) * self.reg_covar);
225
226        // Compute posterior covariance (simplified - would need proper Hessian)
227        let n_params = self.n_components * (n_features + 1);
228        let posterior_covariance = Array2::<f64>::eye(n_params) * self.hessian_regularization;
229
230        // Compute log marginal likelihood (approximate)
231        let log_marginal_likelihood = 0.0; // Placeholder
232
233        let trained_state = LaplaceGMMTrained {
234            map_weights: weights,
235            map_means: means,
236            map_covariances: covariances,
237            posterior_covariance,
238            log_marginal_likelihood,
239            n_iter: 1,
240            converged: true,
241        };
242
243        Ok(LaplaceGMM {
244            n_components: self.n_components,
245            covariance_type: self.covariance_type,
246            max_iter: self.max_iter,
247            tol: self.tol,
248            reg_covar: self.reg_covar,
249            hessian_regularization: self.hessian_regularization,
250            _phantom: std::marker::PhantomData,
251        }
252        .with_state(trained_state))
253    }
254}
255
256impl LaplaceGMM<Untrained> {
257    fn with_state(self, _state: LaplaceGMMTrained) -> LaplaceGMM<LaplaceGMMTrained> {
258        LaplaceGMM {
259            n_components: self.n_components,
260            covariance_type: self.covariance_type,
261            max_iter: self.max_iter,
262            tol: self.tol,
263            reg_covar: self.reg_covar,
264            hessian_regularization: self.hessian_regularization,
265            _phantom: std::marker::PhantomData,
266        }
267    }
268}
269
270impl Predict<ArrayView2<'_, Float>, Array1<usize>> for LaplaceGMM<LaplaceGMMTrained> {
271    #[allow(non_snake_case)]
272    fn predict(&self, X: &ArrayView2<'_, Float>) -> SklResult<Array1<usize>> {
273        let (n_samples, _) = X.dim();
274        Ok(Array1::zeros(n_samples))
275    }
276}
277
278// Monte Carlo GMM
279#[derive(Debug, Clone)]
280pub struct MonteCarloGMM<S = Untrained> {
281    n_components: usize,
282    mc_method: MonteCarloMethod,
283    _phantom: std::marker::PhantomData<S>,
284}
285
286#[derive(Debug, Clone)]
287pub struct MonteCarloGMMTrained {
288    pub samples_weights: Vec<Array1<f64>>,
289    pub samples_means: Vec<Array2<f64>>,
290    pub n_samples: usize,
291}
292
293#[derive(Debug, Clone)]
294pub struct MonteCarloGMMBuilder {
295    n_components: usize,
296    mc_method: MonteCarloMethod,
297}
298
299impl MonteCarloGMMBuilder {
300    pub fn new() -> Self {
301        Self {
302            n_components: 1,
303            mc_method: MonteCarloMethod::Standard { n_samples: 1000 },
304        }
305    }
306
307    pub fn n_components(mut self, n: usize) -> Self {
308        self.n_components = n;
309        self
310    }
311
312    pub fn mc_method(mut self, method: MonteCarloMethod) -> Self {
313        self.mc_method = method;
314        self
315    }
316
317    pub fn build(self) -> MonteCarloGMM<Untrained> {
318        MonteCarloGMM {
319            n_components: self.n_components,
320            mc_method: self.mc_method,
321            _phantom: std::marker::PhantomData,
322        }
323    }
324}
325
326impl Default for MonteCarloGMMBuilder {
327    fn default() -> Self {
328        Self::new()
329    }
330}
331
332impl MonteCarloGMM<Untrained> {
333    pub fn builder() -> MonteCarloGMMBuilder {
334        MonteCarloGMMBuilder::new()
335    }
336}
337
338// Importance Sampling GMM
339#[derive(Debug, Clone)]
340pub struct ImportanceSamplingGMM<S = Untrained> {
341    n_components: usize,
342    is_strategy: ImportanceSamplingStrategy,
343    _phantom: std::marker::PhantomData<S>,
344}
345
346#[derive(Debug, Clone)]
347pub struct ImportanceSamplingGMMTrained {
348    pub weights_samples: Vec<Array1<f64>>,
349    pub importance_weights: Array1<f64>,
350    pub effective_sample_size: f64,
351}
352
353#[derive(Debug, Clone)]
354pub struct ImportanceSamplingGMMBuilder {
355    n_components: usize,
356    is_strategy: ImportanceSamplingStrategy,
357}
358
359impl ImportanceSamplingGMMBuilder {
360    pub fn new() -> Self {
361        Self {
362            n_components: 1,
363            is_strategy: ImportanceSamplingStrategy::Standard { n_samples: 1000 },
364        }
365    }
366
367    pub fn n_components(mut self, n: usize) -> Self {
368        self.n_components = n;
369        self
370    }
371
372    pub fn is_strategy(mut self, strategy: ImportanceSamplingStrategy) -> Self {
373        self.is_strategy = strategy;
374        self
375    }
376
377    pub fn build(self) -> ImportanceSamplingGMM<Untrained> {
378        ImportanceSamplingGMM {
379            n_components: self.n_components,
380            is_strategy: self.is_strategy,
381            _phantom: std::marker::PhantomData,
382        }
383    }
384}
385
386impl Default for ImportanceSamplingGMMBuilder {
387    fn default() -> Self {
388        Self::new()
389    }
390}
391
392impl ImportanceSamplingGMM<Untrained> {
393    pub fn builder() -> ImportanceSamplingGMMBuilder {
394        ImportanceSamplingGMMBuilder::new()
395    }
396}
397
398#[cfg(test)]
399mod tests {
400    use super::*;
401    use scirs2_core::ndarray::array;
402
403    #[test]
404    fn test_laplace_gmm_builder() {
405        let model = LaplaceGMM::builder()
406            .n_components(3)
407            .hessian_regularization(1e-3)
408            .build();
409
410        assert_eq!(model.n_components, 3);
411        assert_eq!(model.hessian_regularization, 1e-3);
412    }
413
414    #[test]
415    fn test_monte_carlo_methods() {
416        let methods = vec![
417            MonteCarloMethod::Standard { n_samples: 500 },
418            MonteCarloMethod::Quasi { n_samples: 1000 },
419            MonteCarloMethod::MCMC {
420                n_samples: 2000,
421                burn_in: 100,
422                thin: 5,
423            },
424        ];
425
426        for method in methods {
427            let model = MonteCarloGMM::builder().mc_method(method).build();
428            assert_eq!(model.mc_method, method);
429        }
430    }
431
432    #[test]
433    fn test_importance_sampling_strategies() {
434        let strategies = vec![
435            ImportanceSamplingStrategy::Standard { n_samples: 500 },
436            ImportanceSamplingStrategy::Adaptive {
437                n_samples: 1000,
438                adaptation_steps: 10,
439            },
440            ImportanceSamplingStrategy::SelfNormalized { n_samples: 750 },
441        ];
442
443        for strategy in strategies {
444            let model = ImportanceSamplingGMM::builder()
445                .is_strategy(strategy)
446                .build();
447            assert_eq!(model.is_strategy, strategy);
448        }
449    }
450
451    #[test]
452    fn test_laplace_gmm_fit() {
453        let X = array![[1.0, 2.0], [1.5, 2.5], [10.0, 11.0]];
454
455        let model = LaplaceGMM::builder().n_components(2).build();
456
457        let result = model.fit(&X.view(), &());
458        assert!(result.is_ok());
459    }
460
461    #[test]
462    fn test_monte_carlo_gmm_builder() {
463        let model = MonteCarloGMM::builder()
464            .n_components(4)
465            .mc_method(MonteCarloMethod::Quasi { n_samples: 2000 })
466            .build();
467
468        assert_eq!(model.n_components, 4);
469    }
470
471    #[test]
472    fn test_importance_sampling_gmm_builder() {
473        let model = ImportanceSamplingGMM::builder()
474            .n_components(3)
475            .is_strategy(ImportanceSamplingStrategy::Adaptive {
476                n_samples: 1500,
477                adaptation_steps: 20,
478            })
479            .build();
480
481        assert_eq!(model.n_components, 3);
482    }
483
484    #[test]
485    fn test_builder_defaults() {
486        let laplace = LaplaceGMM::builder().build();
487        assert_eq!(laplace.n_components, 1);
488
489        let mc = MonteCarloGMM::builder().build();
490        assert_eq!(mc.n_components, 1);
491
492        let is = ImportanceSamplingGMM::builder().build();
493        assert_eq!(is.n_components, 1);
494    }
495}
sklears_mixture/approximation.rs

sklears_mixture/
approximation.rs
