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refit

Class:FeatureSelectionNCARegression

Refit neighborhood component analysis (NCA) model for regression

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Syntax

mdlrefit =refit(mdl,Name,Value)

Description

mdlrefit= refit(mdl,Name,Value)refits the modelmdl, with modified parameters specified by one or moreName,Valuepair arguments.

Input Arguments

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Neighborhood component analysis model or classification, specified as aFeatureSelectionNCARegressionobject.

Name-Value Arguments

Specify optional pairs of arguments asName1=Value1,...,NameN=ValueN, whereNameis the argument name andValueis the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and encloseNamein quotes.

Fitting Options

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Method for fitting the model, specified as the comma-separated pair consisting of'FitMethod'and one of the following.

  • 'exact'— Performs fitting using all of the data.

  • 'none'— No fitting. Use this option to evaluate the generalization error of the NCA model using the initial feature weights supplied in the call tofsrnca.

  • 'average'— The function divides the data into partitions (subsets), fits each partition using theexactmethod, and returns the average of the feature weights. You can specify the number of partitions using theNumPartitionsname-value pair argument.

Example:'FitMethod','none'

Regularization parameter, specified as the comma-separated pair consisting of'Lambda'and a non-negative scalar value.

Fornobservations, the bestLambdavalue that minimizes the generalization error of the NCA model is expected to be a multiple of 1/n

Example:'Lambda',0.01

Data Types:double|single

Solver type for estimating feature weights, specified as the comma-separated pair consisting of'Solver'and one of the following.

  • 'lbfgs'— Limited memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm (LBFGS algorithm)

  • 'sgd'— Stochastic gradient descent

  • 'minibatch-lbfgs'——与LBFGS随机梯度下降算法applied to mini-batches

Example:'solver','minibatch-lbfgs'

Initial feature weights, specified as the comma-separated pair consisting of'InitialFeatureWeights'and ap-by-1 vector of real positive scalar values.

Data Types:double|single

Indicator for verbosity level for the convergence summary display, specified as the comma-separated pair consisting of'Verbose'and one of the following.

  • 0 — No convergence summary

  • 1 — Convergence summary including iteration number, norm of the gradient, and objective function value.

  • >1 — More convergence information depending on the fitting algorithm

    When using solver'minibatch-lbfgs'and verbosity level >1, the convergence information includes iteration log from intermediate mini-batch LBFGS fits.

Example:'Verbose',2

Data Types:double|single

LBFGS or Mini-Batch LBFGS Options

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Relative convergence tolerance on the gradient norm for solverlbfgs, specified as the comma-separated pair consisting of'GradientTolerance'and a positive real scalar value.

Example:'GradientTolerance',0.00001

Data Types:double|single

SGD or Mini-Batch LBFGS Options

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Initial learning rate for solversgd, specified as the comma-separated pair consisting of'InitialLearningRate'and a positive scalar value.

When using solver type'sgd', the learning rate decays over iterations starting with the value specified for'InitialLearningRate'.

Example:'InitialLearningRate',0.8

Data Types:double|single

Maximum number of passes for solver'sgd'(stochastic gradient descent), specified as the comma-separated pair consisting of'PassLimit'and a positive integer. Every pass processessize(mdl.X,1)observations.

Example:'PassLimit',10

Data Types:double|single

SGD or LBFGS or Mini-Batch LBFGS Options

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Maximum number of iterations, specified as the comma-separated pair consisting of'IterationLimit'and a positive integer.

Example:'IterationLimit',250

Data Types:double|single

Output Arguments

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Neighborhood component analysis model or classification, returned as aFeatureSelectionNCARegressionobject. You can either save the results as a new model or update the existing model asmdl = refit(mdl,Name,Value).

Examples

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Open Live Script

Load the sample data.

load('robotarm.mat')

Therobotarm(pumadyn32nm) dataset is created using a robot arm simulator with 7168 training and 1024 test observations with 32 features [1], [2]. This is a preprocessed version of the original data set. Data are preprocessed by subtracting off a linear regression fit followed by normalization of all features to unit variance.

Compute the generalization error without feature selection.

nca = fsrnca(Xtrain,ytrain,'FitMethod','none','Standardize',1); L = loss(nca,Xtest,ytest)
L = 0.9017

Now, refit the model and compute the prediction loss with feature selection, with λ = 0 (no regularization term) and compare to the previous loss value, to determine feature selection seems necessary for this problem. For the settings that you do not change,refituses the settings of the initial modelnca. For example, it uses the feature weights found inncaas the initial feature weights.

nca2 = refit(nca,'FitMethod','exact','Lambda',0); L2 = loss(nca2,Xtest,ytest)
L2 = 0.1088

The decrease in the loss suggests that feature selection is necessary.

Plot the feature weights.

figure() plot(nca2.FeatureWeights,'ro')

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

Tuning the regularization parameter usually improves the results. Suppose that, after tuning λ using cross-validation as inTune Regularization Parameter in NCA for Regression, the best λ value found is 0.0035. Refit thencamodel using this λ value and stochastic gradient descent as the solver. Compute the prediction loss.

nca3 = refit(nca2,'FitMethod','exact','Lambda',0.0035,...'Solver','sgd'); L3 = loss(nca3,Xtest,ytest)
L3 = 0.0573

Plot the feature weights.

figure() plot(nca3.FeatureWeights,'ro')

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

After tuning the regularization parameter, the loss decreased even more and the software identified four of the features as relevant.

References

[1] Rasmussen, C. E., R. M. Neal, G. E. Hinton, D. van Camp, M. Revow, Z. Ghahramani, R. Kustra, and R. Tibshirani. The DELVE Manual, 1996,https://mlg.eng.cam.ac.uk/pub/pdf/RasNeaHinetal96.pdf

[2]https://www.cs.toronto.edu/~delve/data/datasets.html

Version History

Introduced in R2016b

See Also

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