Kernel multi-task latent analysis.

摘要

In this thesis, we develop a Multi-task Latent Analysis (MLA) approach and its nonlinear version Kernel Multi-task Latent Analysis (KMLA) for modelling many-to-many relationships between inputs and responses. KMLA performs dimensionality reduction targeted towards a multi-task loss function like (Kernel) Partial Least Squares (KPLS). KMLA is a more general approach that can utilize the widely-used convex loss functions for inference tasks and it still keeps a lot of good properties of KPLS. KMLA achieves inductive transfer between tasks by forcing the tasks to share same latent variables (LV).;KMLA is an efficient multi-task method. For a given dataset and loss function, KMLA produces linear or nonlinear features for all the tasks that are suitable for data visualization, dimensionality reduction, and generalization. KMLA has finite convergence to the optimal solution of the original problem. Stopping with a small number of LV yields models with good generalization. The KMLA framework can be used to achieve inductive transfer between tasks, allowing more accurate models to be produced with less data.;We apply KMLA to chromatography problems and perform experiments on two datasets; one is protein cation-exchange chromatography, and the other is displacer anion-exchange chromatography. In linear MLA, we model all the tasks simultaneously in order to improve the overall generalization. We compare predicting task one-by-one and predicting all tasks for different regression losses. When the responses are highly correlated, predicting all is better than one-by-one. We extend nonlinear KMLA to semi-supervised learning. The target is one response, and other responses are related tasks. The input data are the same for every response, and responses may have unlabelled information. The goal is to use related tasks and known parts of the target to predict the unlabelled parts of the target. Modelling on multi-response simultaneously with unlabelled information on the target using KMLA can perform better than modelling each response with unknown information individually. The paired ranking loss is also introduced. Results demonstrate that multi-mode is better than single-mode for regression and ranking.