Brian C. Franczak

Unsupervised learning via mixtures of skewed distributions with hypercube contours

A multivariate generalization of the shifted asymmetric Laplace distribution is formulated.This distribution has convex upper level sets, making it excellent for cluster analysis.Finite mixtures of this generalization are developed for unsupervised learning.Parameter estimation is carried out via an EM algorithm.These mixtures give excellent results compared to the current state-of-the-art. Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace distributions. The component densities have a unique combination of features: they include a multivariate weight function and the marginal distributions are asymmetric Laplace. We use these mixtures of multiple scaled shifted asymmetric Laplace distributions for clustering applications, but they could be used in the supervised or semi-supervised paradigms. Parameter estimates are obtained via an expectation-maximization algorithm and the Bayesian information criterion is used for model selection. Simulated and real data sets are utilized to illustrate the approach and, in some cases, to visualize the skewed hypercube structure of the components.

Comparative analysis of chemical similarity methods for modular natural products with a hypothetical structure enumeration algorithm

Natural products represent a prominent source of pharmaceutically and industrially important agents. Calculating the chemical similarity of two molecules is a central task in cheminformatics, with applications at multiple stages of the drug discovery pipeline. Quantifying the similarity of natural products is a particularly important problem, as the biological activities of these molecules have been extensively optimized by natural selection. The large and structurally complex scaffolds of natural products distinguish their physical and chemical properties from those of synthetic compounds. However, no analysis of the performance of existing methods for molecular similarity calculation specific to natural products has been reported to date. Here, we present LEMONS, an algorithm for the enumeration of hypothetical modular natural product structures. We leverage this algorithm to conduct a comparative analysis of molecular similarity methods within the unique chemical space occupied by modular natural products using controlled synthetic data, and comprehensively investigate the impact of diverse biosynthetic parameters on similarity search. We additionally investigate a recently described algorithm for natural product retrobiosynthesis and alignment, and find that when rule-based retrobiosynthesis can be applied, this approach outperforms conventional two-dimensional fingerprints, suggesting it may represent a valuable approach for the targeted exploration of natural product chemical space and microbial genome mining. Our open-source algorithm is an extensible method of enumerating hypothetical natural product structures with diverse potential applications in bioinformatics.

Chapter 2 – Statistics for Use in Discrimination Testing

Abstract This chapter considers statistics used in sensory difference testing from the perspective of business objectives and risks. Selection of an appropriate test method and experimental design must be aligned such that data analysis is able to provide meaningful information that relates back to the business objective and, where applicable, provides an actionable result. Various test methods are discussed and classified. Consideration is given to implications of analysis for unreplicated and replicated data, to statistical power, and to statistical tests for difference and equivalence. The link between experimental design and statistical analysis is stressed.