How to Implement Time-Series Cross-Validation in MATLAB Lasso?

I am trying to apply rolling cross-validation (or expanding window cross-validation) in MATLAB using the lasso function for time series data. I found the tspartition function, which seems suited for time series partitioning, but I am encountering an error when trying to use it with lasso.

Here's the code I am currently using:

rng('default')

X = rand(10,5);
y = 2 + X * [2 * rand(5,1) - 2 * rand(5,1)] + randn(10,1);

LambdaValues = logspace(-4, 1, 100);

CV = tspartition(size(X,1), 'ExpandingWindow', 5);

[B, FitInfo] = lasso(X, y, 'CV', CV, 'Lambda', LambdaValues, 'Standardize', false, 'Intercept', true);

However, this gives me the following error:

Error using classreg.learning.generator.Partitioner.processArgs (line 126)
'CVPartition' value must be a cvpartition object.

Error in lasso (line 513)
The parameter 'CV' must be a positive integer or a partition created with CVPARTITION. It may not be a
'Leaveout' partition.

It seems that tspartition is not compatible with lasso since the latter requires a cvpartition object. Is there a way to implement rolling or expanding window cross-validation for time series data with lasso in MATLAB? How can I achieve this without getting the error?

Answer 1

[Abhishek Kumar Singh]

Hi @Barbab,

To perform rolling or expanding window cross-validation with the lasso function in MATLAB, you need to manually handle the cross-validation process because lasso requires a cvpartition object, which does not directly support time series partitioning like tspartition.

To manually implement expanding window cross-validation, start by initializing your parameters, specifically defining the size of your initial training set and the increment for each subsequent step. Then, loop over the data, expanding the training window and moving the validation window forward with each iteration. Within this loop, use the lasso function to train your model on the current training set and evaluate its performance on the validation set. This approach allows you to simulate a time series cross-validation process, which is particularly useful for handling sequential data.

Here's a sample code to demonstrate this approach:

% Sample data
rng('default')
X = rand(10, 5);
y = 2 + X * [2 * rand(5, 1) - 2 * rand(5, 1)] + randn(10, 1);

% Parameters
initialTrainSize = 5;  % Initial size of the training set
n = size(X, 1);        % Total number of observations
LambdaValues = logspace(-4, 1, 100);

% Preallocate storage for coefficients
numFeatures = size(X, 2);
numLambdas = length(LambdaValues);
B_all = zeros(numFeatures, n - initialTrainSize, numLambdas);

% Expanding window cross-validation
for i = initialTrainSize:(n-1)
    % Define train and validation indices
    trainIdx = 1:i;
    valIdx = i+1;
    
    % Training data
    X_train = X(trainIdx, :);
    y_train = y(trainIdx);
    
    % Fit the lasso model on the training data
    [B, FitInfo] = lasso(X_train, y_train, 'Lambda', LambdaValues, 'Standardize', false, 'Intercept', true);
    
    % Store results
    B_all(:, i - initialTrainSize + 1, :) = B;
end

% Ensure B_all has the correct dimensions
assert(size(B_all, 2) == (n - initialTrainSize), 'Dimension mismatch in B_all');

% Plot coefficients for a specific lambda index
lambdaIdx = 50;  % Choose a valid lambda index

if lambdaIdx > numLambdas
    error('lambdaIdx exceeds the number of lambda values.');
end

figure;
for featureIdx = 1:numFeatures
    plot(squeeze(B_all(featureIdx, :, lambdaIdx)), '-o', 'DisplayName', ['Feature ' num2str(featureIdx)]);
    hold on;
end
xlabel('Expanding Window Iteration');
ylabel('Coefficient Value');
title(['Lasso Coefficients for Lambda Index ' num2str(lambdaIdx)]);
legend show;
grid on;

By adjusting parameters like initialTrainSize and the loop range, you can adapt the approach to fit your dataset and strategy, ensuring proper sequential data handling. Within the loop, you can evaluate model performance using metrics like RMSE or MAE on the validation set.

Hope this helps!