arXiv subjects

Paul Pao-Yen Wu

Publications and source records attributed to Paul Pao-Yen Wu.

5 recordsLinked to original sources

arXiv2025

Optimal Clustering with Dependent Costs in Bayesian Networks

Background: Clustering of nodes in Bayesian Networks (BNs) and related graphical models such as Dynamic BNs (DBNs) has been demonstrated to enhance computational efficiency and improve model learning. It typically involves partitioning the underlying Directed Acyclic Graph (DAG) into cliques or optimising for some cost or criteria. Objectives: We focus on a critical but understudied aspect of optimal clustering involving cost dependency. This is where inference outcomes and hence clustering costs depend on both nodes within a cluster and the mapping of clusters that are connected by at least one arc. Methods: We propose a novel algorithm called Dependent Cluster MAPping (DCMAP) which can, given an arbitrary, positive cost function, iteratively and rapidly find near-optimal, then optimal cluster mappings. Results: DCMAP is shown analytically to be optimal in terms of finding all of the least cost cluster mapping solutions and with no more iterations than an equally informed algorithm. Demonstrated on a complex systems seagrass DBN with $9.91\times10^9$ and $1.51\times10^{21}$ possible cluster mappings for 25 and 50 node configurations, it took 856 and 1569 iterations on average to find the first optimal solution, respectively. Conclusions: The effectiveness of DCMAP enables future research in BN learning using optimisation, such as through enhancing computational efficiency or minimising entropy for learning. This is critically important as computation of marginal distributions or updating model parameters is NP-hard.

cs.DS↗

arXiv2024

An Analysis of Pacing Profiles in Sprint Kayak Racing Using Functional Principal Components and Hidden Markov Models

This study analysed sprint kayak pacing profiles in order to categorise and compare an athlete's race profile throughout their career. We used functional principal component analysis of normalised velocity data for 500m and 1000m races to quantify pacing. The first four principal components explained 90.77% of the variation over 500m and 78.80% over 1000m. These principal components were then associated with unique pacing characteristics with the first component defined as a dropoff in velocity and the second component defined as a kick. We then applied a Hidden Markov model to categorise each profile over an athlete's career, using the PC scores, into different types of race profiles. This model included age and event type and we identified a trend for a higher dropoff in development pathway athletes. Using the four different race profile types, four athletes had all their race profiles throughout their careers analysed. It was identified that an athlete's pacing profile can and does change throughout their career as an athlete matures. This information provides coaches, practitioners and athletes with expectations as to how pacing profiles can be expected to change across the course of an athlete's career.

stat.AP↗

arXiv2024

Mathematical modelling and uncertainty quantification for analysis of biphasic coral reef recovery patterns

Coral reefs are increasingly subjected to major disturbances threatening the health of marine ecosystems. Substantial research underway to develop intervention strategies that assist reefs in recovery from, and resistance to, inevitable future climate and weather extremes. To assess potential benefits of interventions, mechanistic understanding of coral reef recovery and resistance patterns is essential. Recent evidence suggests that more than half of the reefs surveyed across the Great Barrier Reef (GBR) exhibit deviations from standard recovery modelling assumptions when the initial coral cover is low ($\leq 10$\%). New modelling is necessary to account for these observed patterns to better inform management strategies. We consider a new model for reef recovery at the coral cover scale that accounts for biphasic recovery patterns. The model is based on a multispecies Richards' growth model that includes a change point in the recovery patterns. Bayesian inference is applied for uncertainty quantification of key parameters for assessing reef health and recovery patterns. This analysis is applied to benthic survey data from the Australian Institute of Marine Sciences (AIMS). We demonstrate agreement between model predictions and data across every recorded recovery trajectory with at least two years of observations following disturbance events occurring between 1992--2020. This new approach will enable new insights into the biological, ecological and environmental factors that contribute to the duration and severity of biphasic coral recovery patterns across the GBR. These new insights will help to inform managements and monitoring practice to mitigate the impacts of climate change on coral reefs.

stat.AP↗

arXiv2023

clusterBMA: Bayesian model averaging for clustering

Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one `best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a consensus matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name.

stat.ME↗

arXiv2020

Peer groups for organisational learning: clustering with practical constraints

Peer-grouping is used in many sectors for organisational learning, policy implementation, and benchmarking. Clustering provides a statistical, data-driven method for constructing meaningful peer groups, but peer groups must be compatible with business constraints such as size and stability considerations. Additionally, statistical peer groups are constructed from many different variables, and can be difficult to understand, especially for non-statistical audiences. We developed methodology to apply business constraints to clustering solutions and allow the decision-maker to choose the balance between statistical goodness-of-fit and conformity to business constraints. Several tools were utilised to identify complex distinguishing features in peer groups, and a number of visualisations are developed to explain high-dimensional clusters for non-statistical audiences. In a case study where peer group size was required to be small ($\leq 100$ members), we applied constrained clustering to a noisy high-dimensional data-set over two subsequent years, ensuring that the clusters were sufficiently stable between years. Our approach not only satisfied clustering constraints on the test data, but maintained an almost monotonic negative relationship between goodness-of-fit and stability between subsequent years. We demonstrated in the context of the case study how distinguishing features between clusters can be communicated clearly to different stakeholders with substantial and limited statistical knowledge.

stat.AP↗