Crate egobox_moe

This library implements Mixture of Experts method using GP models.

MoE method aims at increasing the accuracy of a function approximation by replacing a single global model by a weighted sum of local gp regression models (experts). It is based on a partition of the problem domain into several subdomains via clustering algorithms followed by a local expert training on each subdomain.

The recombination between the GP models can be either:

• hard: one GP model is being responsible to provide the predicted value at the given point. GP selection is done by taking the largest probability of the given point being part of the cluster corresponding to the expert GP. In hard mode, transition between models leads to discontinuity.
• smooth: all GPs models are taken and their predicted values at a given point are weighted regarding their responsability (probability of the given point being part of the cluster corresponding to the expert GP). In this case the MoE model is continuous. The smoothness is automatically adjusted using a factor, the heaviside factor, which can also be set manually.

Implementation

• Clusters are defined by clustering the training data with linfa-clustering gaussian mixture model.
• This library is a port of the SMT MoE method using egobox GP models as experts.
• It leverages on the egobox GP PLS reduction feature to handle high dimensional problems.
• MoE trained model can be save to disk and reloaded. See

Features

serializable

The serializable feature enables serialization based on serde crate.

persistent

The persistent feature enables save()/load() methods for a MoE model to/from a json file using the serde and serde_json crates.

Example

use ndarray::{Array2, Array1, Zip, Axis};
use egobox_moe::{GpMixture, Recombination};
use ndarray_rand::{RandomExt, rand::SeedableRng, rand_distr::Uniform};
use rand_xoshiro::Xoshiro256Plus;
use linfa::{traits::Fit, ParamGuard, Dataset};

// One-dimensional test function with 3 modes
fn f3modes(x: &Array2<f64>) -> Array2<f64> {
    let mut y = Array2::zeros(x.dim());
    Zip::from(&mut y).and(x).for_each(|yi, &xi| {
        if xi < 0.4 {
            *yi = xi * xi;
        } else if (0.4..0.8).contains(&xi) {
            *yi = 3. * xi + 1.;
        } else {
            *yi = f64::sin(10. * xi);
        }
    });
    y
}

// Training data
let mut rng = Xoshiro256Plus::from_entropy();
let xt = Array2::random_using((50, 1), Uniform::new(0., 1.), &mut rng);
let yt = f3modes(&xt);
let ds = Dataset::new(xt, yt);

// Predictions
let observations = Array1::linspace(0., 1., 100).insert_axis(Axis(1));
let predictions = GpMixture::params()
                    .n_clusters(3)
                    .recombination(Recombination::Hard)
                    .fit(&ds)
                    .expect("MoE model training")
                    .predict(&observations)
                    .expect("MoE predictions");

Reference

Bettebghor, Dimitri, et al. Surrogate modeling approximation using a mixture of experts based on EM joint estimation Structural and multidisciplinary optimization 43.2 (2011): 243-259.

Structs

• Clustering
  A structure for clustering
• CorrelationSpec
  Flags to specify tested correlation models during experts selection (see correlation_spec()).
• GaussianMixture
  Gaussian mixture is a set of n weigthed multivariate normal distributions of dimension nx This structure is derived from linfa::GaussianMixtureModel clustering method to handle the resulting multivariate normals and related computations in one go. Moreover an heaviside factor is handled in case of smooth Recombination to control the smoothness between clusters and can be adjusted afterwards
• GpConstantAbsoluteExponentialSurrogate
  GP surrogate with Constant regression model and AbsoluteExponential correlation model.
• GpConstantMatern32Surrogate
  GP surrogate with Constant regression model and Matern32 correlation model.
• GpConstantMatern52Surrogate
  GP surrogate with Constant regression model and Matern52 correlation model.
• GpConstantSquaredExponentialSurrogate
  GP surrogate with Constant regression model and SquaredExponential correlation model.
• GpLinearAbsoluteExponentialSurrogate
  GP surrogate with Linear regression model and AbsoluteExponential correlation model.
• GpLinearMatern32Surrogate
  GP surrogate with Linear regression model and Matern32 correlation model.
• GpLinearMatern52Surrogate
  GP surrogate with Linear regression model and Matern52 correlation model.
• GpLinearSquaredExponentialSurrogate
  GP surrogate with Linear regression model and SquaredExponential correlation model.
• GpMixture
  Mixture of gaussian process experts
• GpMixtureParams
  Mixture of experts parameters
• GpMixtureValidParams
  Mixture of experts checked parameters
• GpQuadraticAbsoluteExponentialSurrogate
  GP surrogate with Quadratic regression model and AbsoluteExponential correlation model.
• GpQuadraticMatern32Surrogate
  GP surrogate with Quadratic regression model and Matern32 correlation model.
• GpQuadraticMatern52Surrogate
  GP surrogate with Quadratic regression model and Matern52 correlation model.
• GpQuadraticSquaredExponentialSurrogate
  GP surrogate with Quadratic regression model and SquaredExponential correlation model.
• MoeVariancePredictor
  Adaptator to implement linfa::Predict for variance prediction
• RegressionSpec
  Flags to specify tested regression models during experts selection (see regression_spec()).
• SgpAbsoluteExponentialSurrogate
  SGP surrogate with AbsoluteExponential correlation model.
• SgpMatern32Surrogate
  SGP surrogate with Matern32 correlation model.
• SgpMatern52Surrogate
  SGP surrogate with Matern52 correlation model.
• SgpSquaredExponentialSurrogate
  SGP surrogate with SquaredExponential correlation model.

Enums

• GpType
• MoeError
  An error when using MOE algorithm
• Recombination
  Enumeration of recombination modes handled by the mixture

Traits

• Clustered
  A trait to represent clustered structure
• FullGpSurrogate
  A trait for a GP surrogate.
• GpParameterized
  A trait for a GP surrogate.
• GpSurrogate
  A trait for a base GP surrogate
• GpSurrogateExt
  A trait for a GP surrogate with derivatives predictions and sampling
• GpSurrogateParams
  A trait for Gp surrogate parameters to build surrogate.
• MixtureGpSurrogate
  A trait for Mixture of GP surrogates with derivatives using clustering
• SgpSurrogate
  A trait for a Sparse GP surrogate.
• SgpSurrogateParams
  A trait for sparse GP surrogate parameters to build surrogate.

Functions

• find_best_number_of_clusters
  Find the best number of cluster thanks to cross validation

Type Aliases

• Result
  A result type for Moe algorithm