The supervised hierarchical Dirichlet process

We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another leading method for regression on grouped data, the supervised latent Dirichlet allocation (sLDA) model. We evaluate our method on two real-world classification problems and two real-world regression problems. Bayesian nonparametric regression models based on the Dirichlet process, such as the Dirichlet process-generalised linear models (DP-GLM) have previously been explored; these models allow flexibility in modelling nonlinear relationships. However, until now, Hierarchical Dirichlet Process (HDP) mixtures have not seen significant use in supervised problems with grouped data since a straightforward application of the HDP on the grouped data results in learnt clusters that are not predictive of the responses. The sHDP solves this problem by allowing for clusters to be learnt jointly from the group structure and from the label assigned to each group.Comment: 14 page

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

The role of long-term experiments in validating trait-based approaches to achieving multifunctionality in grasslands

Quantifying the relationships between plant functional traits and ecosystem services has been promoted as an approach to achieving multifunctional grassland systems that balance productivity with other regulating, supporting and cultural services. Establishing trade-offs and synergies between traits and services has largely relied on meta-analyses of studies from different systems and environments. This study demonstrated the value of focused studies of long-term experiments in grassland systems that measure traits and services in the same space and time to better understand the ecological constraints underlying these trade-offs and synergies. An analysis is presented that uses data from the Park Grass Experiment at Rothamsted Research on above-ground productivity, species richness and soil organic carbon stocks to quantify the relationships between these three outcomes and the power of variance in plant functional traits in explaining them. There was a trade-off between plots with high productivity, nitrogen inputs and soil organic carbon and plots with high species richness that was explained by a functional gradient of traits that are indicative of contrasting strategies of resource acquisition of resource conservation. Examples were identified of using functional traits to identify opportunities for mitigating these trade-offs and moving toward more multifunctional systems