LMC Multitask Gaussian Process Model: Exact Decoupled Solutions
Core Concepts
The LMC model can be efficiently computed with a decoupled structure under specific noise conditions, offering a simpler alternative to state-of-the-art models.
Abstract
The Linear Model of Co-regionalization (LMC) for multitask Gaussian processes is explored. Recent work has shown that under certain conditions, the latent processes of the model can be decoupled, leading to more efficient computations. The study introduces a full parametrization of the resulting projected LMC model and demonstrates its effectiveness on real and synthetic data. Various simplifications and approximations are discussed, highlighting the benefits of the proposed approach.
Abstract:
LMC is a general model for multitask GP.
Naive implementations have cubic complexity.
Decoupling latent processes reduces complexity.
Efficient computation with mild noise assumptions.
Introduction:
Multi-Outputs Gaussian Processes are popular.
Models fall into two main categories: convolutional GPs and linearly correlated GPs.
The Linear Model of Co-regionalization (LMC) is a natural idea for modeling outputs as linear combinations of common unobserved processes.
Data Extraction:
"Naive implementations have cubic complexity in the number of datapoints and number of tasks."
"We demonstrate the validity of our approach by comparing the resulting projected LMC to concurrent simplifications."
Exact and general decoupled solutions of the LMC Multitask Gaussian Process model
Stats
"Naive implementations have cubic complexity in the number of datapoints and number of tasks."
"We demonstrate the validity of our approach by comparing the resulting projected LMC to concurrent simplifications."
Quotes
"We here extend these results, showing from the most general assumptions that the only condition necessary to an efficient exact computation of the LMC is a mild hypothesis on the noise model."