Scaling Gaussian Processes for Learning Curve Prediction via Latent Kronecker Structure

• URL: http://arxiv.org/abs/2410.09239v1
• Date: Fri, 11 Oct 2024 20:24:33 GMT
• Title: Scaling Gaussian Processes for Learning Curve Prediction via Latent Kronecker Structure
• Authors: Jihao Andreas Lin, Sebastian Ament, Maximilian Balandat, Eytan Bakshy,
• Abstract summary: We show that our GP model can match the performance of a Transformer on a learning curve prediction task. Our method only requires $mathcalO(n3 + m3)$ time and $mathcalO(n2 + m2)$ space.
• Score: 16.319561844942886
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A key task in AutoML is to model learning curves of machine learning models jointly as a function of model hyper-parameters and training progression. While Gaussian processes (GPs) are suitable for this task, na\"ive GPs require $\mathcal{O}(n^3m^3)$ time and $\mathcal{O}(n^2 m^2)$ space for $n$ hyper-parameter configurations and $\mathcal{O}(m)$ learning curve observations per hyper-parameter. Efficient inference via Kronecker structure is typically incompatible with early-stopping due to missing learning curve values. We impose $\textit{latent Kronecker structure}$ to leverage efficient product kernels while handling missing values. In particular, we interpret the joint covariance matrix of observed values as the projection of a latent Kronecker product. Combined with iterative linear solvers and structured matrix-vector multiplication, our method only requires $\mathcal{O}(n^3 + m^3)$ time and $\mathcal{O}(n^2 + m^2)$ space. We show that our GP model can match the performance of a Transformer on a learning curve prediction task.

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