lucid::MedianHeuristicTuner Class Reference

Tuner that adjusts the kernel parameters using the median heuristic method. More...

#include <MedianHeuristicTuner.h>

Inheritance diagram for lucid::MedianHeuristicTuner:

Public Member Functions
std::string	to_string () const override
	Obtain the string representation of this object.
Public Member Functions inherited from lucid::Tuner
void	tune (Estimator &estimator, ConstMatrixRef training_inputs, ConstMatrixRef training_outputs) const
	Optimise the kernel hyperparameters.
void	tune_online (Estimator &estimator, ConstMatrixRef training_inputs, const OutputComputer &training_outputs) const
	Optimise the kernel hyperparameters.

Private Member Functions
void	tune_impl (Estimator &estimator, ConstMatrixRef training_inputs, const OutputComputer &training_outputs) const override
	Optimise the kernel hyperparameters.

Detailed Description

Tuner that adjusts the kernel parameters using the median heuristic method.

It computes the median of pairwise distances between input data points for each dimension. These computed medians are used to update the \( \sigma_l \) parameters of the kernel in the given estimator. More specifically, given a set of training inputs \( \{x_1, x_2, \ldots, x_n\} \) from \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),

\[\sigma_l = \sqrt{\text{median}\{\|x_i - x_j\|^2 : 1 \le i < j \le n\}} \]

Once the kernel parameters are updated, the estimator is consolidated using the training data.

Note

Based on the paper Large sample analysis of the median heuristic.

Member Function Documentation

to_string()

std::string lucid::MedianHeuristicTuner::to_string ( ) const

nodiscardoverridevirtual

Obtain the string representation of this object.

Returns

string representation of this object

Reimplemented from lucid::Tuner.

tune_impl()

void lucid::MedianHeuristicTuner::tune_impl ( Estimator & estimator, ConstMatrixRef training_inputs, const OutputComputer & training_outputs ) const

overrideprivatevirtual

Optimise the kernel hyperparameters.

Starting from the initial guess, the optimiser finds the best hyperparameters for the kernel. It is up to the subclass to determine the optimisation algorithm used.

Note

The method must call the consolidate method of the estimator to ensure that the kernel is ready to be used.

Precondition

The number of rows in the training inputs should be equal to the number of rows in the training outputs.

Todo

If the OutputComputer becomes a bottleneck, consider having a separate method for when the outputs are available from the get-go.

Parameters

estimator	estimator to optimise
training_inputs	training input data
training_outputs	training output data. It uses an OutputComputer to compute the outputs when needed

Implements lucid::Tuner.

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The documentation for this class was generated from the following files:

• lucid/model/MedianHeuristicTuner.h
• lucid/model/MedianHeuristicTuner.cpp