Andrew Cron

We present a case study and methodological developments in large-scale hierarchical dynamic modelling for personalized prediction in commerce. The context is supermarket sales, where improved forecasting of household-specific purchasing behaviour informs decisions about personalized pricing and promotions. This setting involves many thousands of heterogeneous customers and items. Models developed are fully Bayesian, interpretable and multi-scale, with hierarchical forms overlaid on the inherent… Show more

We present a case study and methodological developments in large-scale hierarchical dynamic modelling for personalized prediction in commerce. The context is supermarket sales, where improved forecasting of household-specific purchasing behaviour informs decisions about personalized pricing and promotions. This setting involves many thousands of heterogeneous customers and items. Models developed are fully Bayesian, interpretable and multi-scale, with hierarchical forms overlaid on the inherent structure of the retail setting. Customer behavior is modelled at several levels of aggregation, and information flows from aggregate to individual levels. Methodological innovations include extensions of Bayesian dynamic mixture models, their integration into multi-scale systems, and forecast evaluation with context-specific metrics. The use of simultaneous predictors from multiple hierarchical levels improves forecasts at the customer-item level of main interest. Show less

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the introduction of a novel copula construction in sequential filtering of coupled sets of dynamic generalized linear models. The new copula approach is integrated into recently introduced multiscale models in which univariate time series are coupled via nonlinear forms… Show more

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the introduction of a novel copula construction in sequential filtering of coupled sets of dynamic generalized linear models. The new copula approach is integrated into recently introduced multiscale models in which univariate time series are coupled via nonlinear forms involving dynamic latent factors representing cross-series relationships. The resulting methodology offers dramatic speed-up in online Bayesian computations for sequential filtering and forecasting in this broad, flexible class of multivariate models. Two examples in nonlinear models for very heterogeneous time series of nonnegative counts demonstrate massive computational efficiencies relative to existing, simulation-based methods, while defining similar filtering and forecasting outcomes. Show less

The use of flow cytometry to count antigen-specific T cells is essential for vaccine development, monitoring of immune-based therapies and immune biomarker discovery. Analysis of such data is challenging because antigen-specific cells are often present in frequencies of less than 1 in 1,000 peripheral blood mononuclear cells (PBMC). Standard analysis of flow cytometry data relies on visual identification of cell subsets by experts, a process that is subjective and often difficult to reproduce… Show more

The use of flow cytometry to count antigen-specific T cells is essential for vaccine development, monitoring of immune-based therapies and immune biomarker discovery. Analysis of such data is challenging because antigen-specific cells are often present in frequencies of less than 1 in 1,000 peripheral blood mononuclear cells (PBMC). Standard analysis of flow cytometry data relies on visual identification of cell subsets by experts, a process that is subjective and often difficult to reproduce. Consequently, there is intense interest in automated approaches for cell subset identification. One popular class of such automated approaches is the use of statistical mixture models. We propose a hierarchical extension of statistical mixture models that has two advantages over standard mixture models. First, it increases the ability to detect extremely rare event clusters that are present in multiple samples. Second, it enables direct comparison of cell subsets by aligning clusters across multiple samples in a natural way arising from the hierarchical formulation. We demonstrate the algorithm on clinically relevant reference PBMC samples with known frequencies of CD8 T cells engineered to express T cell receptors specific for the cancer-testis antigen (NY-ESO-1) and compare its performance with other popular automated analysis approaches. Show less

Content recommendation on a webpage involves recommending content links (items) on multiple slots for each user visit to maximize some objective function, typically the click-through rate (CTR) which is the probability of clicking on an item for a given user visit. Most existing approaches to this problem assume user's response (click/no click) on different slots are independent of each other. This is problematic since in many scenarios CTR on a slot may depend on externalities like items… Show more

Content recommendation on a webpage involves recommending content links (items) on multiple slots for each user visit to maximize some objective function, typically the click-through rate (CTR) which is the probability of clicking on an item for a given user visit. Most existing approaches to this problem assume user's response (click/no click) on different slots are independent of each other. This is problematic since in many scenarios CTR on a slot may depend on externalities like items recommended on other slots. Incorporating the effects of such externalities in the modeling process is important to better predictive accuracy. We therefore propose a hierarchical model that assumes a multinomial response for each visit to incorporate competition among slots and models complex interactions among (user, item, slot) combinations through factor models via a tensor approach. In addition, factors in our model are drawn with means that are based on regression functions of user/item covariates, which helps us obtain better estimates for users/items that are relatively new with little past activity. We show marked gains in predictive accuracy by various metrics. Show less

Effective component relabeling in Bayesian analyses of mixture models is critical to the routine use of mixtures in classification with analysis based on Markov chain Monte Carlo methods. The classification-based relabeling approach here is computationally attractive and statistically effective, and scales well with sample size and number of mixture components concordant with enabling routine analyses of increasingly large data sets. Building on the best of existing methods, practical… Show more

Effective component relabeling in Bayesian analyses of mixture models is critical to the routine use of mixtures in classification with analysis based on Markov chain Monte Carlo methods. The classification-based relabeling approach here is computationally attractive and statistically effective, and scales well with sample size and number of mixture components concordant with enabling routine analyses of increasingly large data sets. Building on the best of existing methods, practical relabeling aims to match data:component classification indicators in MCMC iterates with those of a defined reference mixture distribution. The method performs as well as or better than existing methods in small dimensional problems, while being practically superior in problems with larger data sets as the approach is scalable. We describe examples and computational benchmarks, and provide supporting code with efficient computational implementation of the algorithm that will be of use to others in practical applications of mixture models. Show less

We describe advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via GPU (graphics processing unit) programming. The developments are partly motivated by computational challenges arising in increasingly prevalent biological studies using high-throughput flow cytometry methods, generating many, very large data sets and requiring increasingly high-dimensional mixture models with large numbers of mixture components. The paper describes the… Show more

We describe advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via GPU (graphics processing unit) programming. The developments are partly motivated by computational challenges arising in increasingly prevalent biological studies using high-throughput flow cytometry methods, generating many, very large data sets and requiring increasingly high-dimensional mixture models with large numbers of mixture components. The paper describes the strategies and process for GPU computation in Bayesian simulation and optimization approaches, examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large data sets, while providing a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Show less