Boosting as a Product of Experts

In this paper, we derive a novel probabilistic model of boosting as a Product of Experts. We re-derive the boosting algorithm as a greedy incremental model selection procedure which ensures that addition of new experts to the ensemble does not decrease the likelihood of the data. These learning rules lead to a generic boosting algorithm - POE- Boost which turns out to be similar to the AdaBoost algorithm under certain assumptions on the expert probabilities. The paper then extends the POEBoost algorithm to POEBoost.CS which handles hypothesis that produce probabilistic predictions. This new algorithm is shown to have better generalization performance compared to other state of the art algorithms

Bayesian locally weighted online learning

Locally weighted regression is a non-parametric technique of regression that is capable of coping with non-stationarity of the input distribution. Online algorithms like Receptive FieldWeighted Regression and Locally Weighted Projection Regression use a sparse representation of the locally weighted model to approximate a target function, resulting in an efficient learning algorithm. However, these algorithms are fairly sensitive to parameter initializations and have multiple open learning parameters that are usually set using some insights of the problem and local heuristics. In this thesis, we attempt to alleviate these problems by using a probabilistic formulation of locally weighted regression followed by a principled Bayesian inference of the parameters. In the Randomly Varying Coefficient (RVC) model developed in this thesis, locally weighted regression is set up as an ensemble of regression experts that provide a local linear approximation to the target function. We train the individual experts independently and then combine their predictions using a Product of Experts formalism. Independent training of experts allows us to adapt the complexity of the regression model dynamically while learning in an online fashion. The local experts themselves are modeled using a hierarchical Bayesian probability distribution with Variational Bayesian Expectation Maximization steps to learn the posterior distributions over the parameters. The Bayesian modeling of the local experts leads to an inference procedure that is fairly insensitive to parameter initializations and avoids problems like overfitting. We further exploit the Bayesian inference procedure to derive efficient online update rules for the parameters. Learning in the regression setting is also extended to handle a classification task by making use of a logistic regression to model discrete class labels. The main contribution of the thesis is a spatially localised online learning algorithm set up in a probabilistic framework with principled Bayesian inference rule for the parameters of the model that learns local models completely independent of each other, uses only local information and adapts the local model complexity in a data driven fashion. This thesis, for the first time, brings together the computational efficiency and the adaptability of ‘non-competitive’ locally weighted learning schemes and the modelling guarantees of the Bayesian formulation

Kernel Carpentry for Online Regression using Randomly Varying Coefficient Model

We present a Bayesian formulation of locally weighted learning (LWL) using the novel concept of a randomly varying coefficient model. Based on thi

Bayesian locally weighted online learning

Locally weighted regression is a non-parametric technique of regression that is capable of coping with non-stationarity of the input distribution. Online algorithms like Receptive FieldWeighted Regression and Locally Weighted Projection Regression use a sparse representation of the locally weighted model to approximate a target function, resulting in an efficient learning algorithm. However, these algorithms are fairly sensitive to parameter initializations and have multiple open learning parameters that are usually set using some insights of the problem and local heuristics. In this thesis, we attempt to alleviate these problems by using a probabilistic formulation of locally weighted regression followed by a principled Bayesian inference of the parameters. In the Randomly Varying Coefficient (RVC) model developed in this thesis, locally weighted regression is set up as an ensemble of regression experts that provide a local linear approximation to the target function. We train the individual experts independently and then combine their predictions using a Product of Experts formalism. Independent training of experts allows us to adapt the complexity of the regression model dynamically while learning in an online fashion. The local experts themselves are modeled using a hierarchical Bayesian probability distribution with Variational Bayesian Expectation Maximization steps to learn the posterior distributions over the parameters. The Bayesian modeling of the local experts leads to an inference procedure that is fairly insensitive to parameter initializations and avoids problems like overfitting. We further exploit the Bayesian inference procedure to derive efficient online update rules for the parameters. Learning in the regression setting is also extended to handle a classification task by making use of a logistic regression to model discrete class labels. The main contribution of the thesis is a spatially localised online learning algorithm set up in a probabilistic framework with principled Bayesian inference rule for the parameters of the model that learns local models completely independent of each other, uses only local information and adapts the local model complexity in a data driven fashion. This thesis, for the first time, brings together the computational efficiency and the adaptability of ‘non-competitive’ locally weighted learning schemes and the modelling guarantees of the Bayesian formulation.EThOS - Electronic Theses Online ServiceGBUnited Kingdo