Crate egobox_moe
source ·Expand description
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::{Moe, 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 = Moe::params()
.n_clusters(3)
.recombination(Recombination::Hard)
.fit(&ds)
.expect("MoE model training")
.predict_values(&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
Flags to specify tested correlation models during experts selection (see MoeParams).
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 afterwardsGP surrogate with
Constant regression model and AbsoluteExponential correlation model. GP surrogate parameters with
Constant regression model and AbsoluteExponential correlation model. GP surrogate with
Constant regression model and Matern32 correlation model. GP surrogate parameters with
Constant regression model and Matern32 correlation model. GP surrogate with
Constant regression model and Matern52 correlation model. GP surrogate parameters with
Constant regression model and Matern52 correlation model. GP surrogate with
Constant regression model and SquaredExponential correlation model. GP surrogate parameters with
Constant regression model and SquaredExponential correlation model. GP surrogate with
Linear regression model and AbsoluteExponential correlation model. GP surrogate parameters with
Linear regression model and AbsoluteExponential correlation model. GP surrogate with
Linear regression model and Matern32 correlation model. GP surrogate parameters with
Linear regression model and Matern32 correlation model. GP surrogate with
Linear regression model and Matern52 correlation model. GP surrogate parameters with
Linear regression model and Matern52 correlation model. GP surrogate with
Linear regression model and SquaredExponential correlation model. GP surrogate parameters with
Linear regression model and SquaredExponential correlation model. GP surrogate with
Quadratic regression model and AbsoluteExponential correlation model. GP surrogate parameters with
Quadratic regression model and AbsoluteExponential correlation model. GP surrogate with
Quadratic regression model and Matern32 correlation model. GP surrogate parameters with
Quadratic regression model and Matern32 correlation model. GP surrogate with
Quadratic regression model and Matern52 correlation model. GP surrogate parameters with
Quadratic regression model and Matern52 correlation model. GP surrogate with
Quadratic regression model and SquaredExponential correlation model. GP surrogate parameters with
Quadratic regression model and SquaredExponential correlation model. Mixture of gaussian process experts
Mixture of experts parameters
Mixture of experts checked parameters
Flags to specify tested regression models during experts selection (see MoeParams::regression_spec).
Enums
An error when using MOE algorithm
Enumeration of recombination modes handled by the mixture
Traits
A trait for surrogates using clustering
A trait for a surrogate used as expert in the mixture.
A trait for surrogate parameters to build surrogate once fitted.
Functions
Find the best number of cluster thanks to cross validation
Type Definitions
A result type for Moe algorithm