To Join Via Zoom: To join this seminar, please request Zoom connection details from headsec@stat.ubc.ca.

Abstract: A quantity of interest in clinical studies is the absolute risk of an event given a patient's covariate profile. In order for the Cox proportional hazard method to recover these absolute risk curves, the baseline hazard needs to be estimated separately, resulting in stepwise estimates in absolute risk that make the curves difficult to interpret. Casebase is an approach that transforms the data into a logistic regression, allowing for survival estimates that vary smoothly over time. We simulate data and compare the prediction performance of penalized casebase methods with penalized and unpenalized Cox methods. Casebase methods perform better in measures of concordance and time-dependent brier scores.

To Join Via Zoom: To join this seminar virtually, please request Zoom connection details from headsec@stat.ubc.ca.

Abstract: Sparse and ensemble methods are the two main approaches in the statistical literature for modeling high-dimensional data. On the one hand, sparse methods yield a single predictive model that is generally interpretable and possesses desirable theoretical properties. On the other hand, multi-model ensemble methods can generally achieve superior prediction accuracy, but current ensemble methodology relies on randomization or boosting to generate diverse models which results in uninterpretable ensembles. The diverse models generated by these “black box” algorithms are not insightful on their own and are only useful when they are pooled together.

In this dissertation, we introduce a new data-driven ensemble framework that combines ideas from sparse modeling and ensemble modeling. We search for optimal ways to select and split the candidate predictors into subsets for the different models that will be combined in an ensemble. Each model in the ensemble provides an alternative explanation for the relationship between the predictor variables and the response variable of interest. The degrees of sparsity of the individual models and diversity among the models are both driven by the data. The task of optimally splitting the candidate predictors into subsets results in a computationally intractable combinatorial optimization problem when the number of predictors is large. To demonstrate the potential of an exhaustive search for the optimal split of the predictors into the different models of an ensemble, we test our new approach on specifically designed low-dimensional data which mimic the typical behavior of high-dimensional data such as low signal-to-noise ratio and the presence of spurious correlations.

In this dissertation, we propose different computational approaches to the optimal split selection problem. We first introduce a multiconvex relaxation in the regression case and develop efficient algorithms to compute solutions for any level of sparsity and diversity. We show that the resulting ensembles yield consistent predictions and consistent individual models, and provide empirical evidence that this method outperforms state-of-the-art sparse and ensemble methods for high-dimensional prediction tasks using simulated data and a chemometrics application. We then extend the methodology, theory and algorithms to classification ensembles, and investigate the performance of the method on simulated data and a large collection of gene expression datasets. We finally propose a direct computational approach to calculate approximate solutions to the optimal split selection problem in the regression case and benchmark the performance of the method against the multi-convex relaxation on simulated and gene expression data.

Efficient software libraries with the implementations of the new computational methods provide researchers with tools to (1) achieve state-of-the-art accuracy for high-dimensional prediction tasks, and (2) aid in the scientific discovery of different mechanisms underlying the relationship between a large number of candidate predictors and the response variable of interest.

To Join Via Zoom: To join this seminar virtually, please request Zoom connection details from headsec@stat.ubc.ca.

Abstract: Boosting is a highly flexible and powerful approach when it comes to making predictions in non-parametric settings. In spite of the popularity and practical success of boosting algorithms, there is a lack of focus on its generalizations to “complex data”, such as data with outliers or functional variables. For data contaminated with outliers, we propose a two-stage boosting algorithm similar to what is done for robust linear MM-regression: it first minimizes a robust residual scale estimator, and then improves it by optimizing a bounded loss function. For data containing functional predictors, we propose a tree-based boosting algorithm that uses “base-learners” constructed with multiple projections. Our proposal incorporates possible interactions between indices, making it capable of approximating complex regression functions. Finally, we extend our proposals to contaminated functional data and explore two variations that can be used to perform robust functional regression. 

To Join Via Zoom: Please register here.

Abstract: The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these dependencies, a novel vine copula mixture model for continuous data is proposed. The model selection and parameter estimation problems are discussed, and further, a new model-based clustering algorithm is formulated. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. The simulation experiments illustrate a significant gain in clustering accuracy when notably asymmetric tail dependencies or/and non-Gaussian margins within the components exist. The analysis of real data sets accompanies the proposed method. The model-based clustering algorithm with vine copula mixture models outperforms others, especially for the non-Gaussian multivariate data.

To join via Zoom: To join this seminar, please register here.

Title: Forming realistic population distributions for flood frequency assessments

Abstract: Forming a population distribution in the frequentist setting typically amounts to choosing a pre-defined family like Gaussian or Exponential, but this may not always be realistic. One such situation is the formation of distributions for the annual maximum river flow in a changing climate when the river is driven by more than one process (eg., snowmelt and rainfall). I will demonstrate this analysis for the Coldwater River in British Columbia, an analysis that has recently been submitted to the Fraser Basin Council following the devastating floods in British Columbia in November 2021. I will also demonstrate how the distplyr R package makes this type of analysis (forming realistic probability distributions) simpler by providing a grammar for manipulating probability distributions.

To Join Via Zoom: To join this seminar, please request Zoom connection details from headsec@stat.ubc.ca.

Abstract: Computer models are used as replacements for physical experiments in a wide variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the model. Historically, Gaussian process (GP) regression has proven to be the almost ubiquitous choice for a fast statistical emulator for such a computer model, due to its flexible form and analytical expressions for predictive uncertainty.

In the first part of this dissertation, we consider complications that arise when the design is moderate to large. Fitting a GP regression can be computationally intractable for even moderate designs, due to computing time increasing with the cube of the design size. We propose a new solution to this problem: adaptive design and analysis via partitioning trees (ADAPT). By taking a data-adaptive approach to the development of a design, and choosing to partition the space in the regions of highest variability, we obtain a higher density of points in these regions and hence accurate prediction for complex computer models.

Next, we consider the scenario where multiple computer models are available for predicting the same physical process—known as multi-model ensembles (MMEs). Such ensembles are common in many applications, such as climate modelling and weather prediction. We present a new statistical methodology for combining output from such models to best describe the underlying physical process, using field data to estimate the weights as- signed to each model. The methodology allows us to make predictions with appropriate measures of uncertainty. Additionally, the weights are allowed to vary with the inputs and thus represent the changing relative importance between the computer models throughout the input space. The methodology is applied to ice sheet models for the deglaciation of North America. Finally, we address several considerations that arise when the MME field data are binary. A new MME model formulation is presented, and applied to ice absence/presence data in the deglaciation application.

In summary, this dissertation presents new methods for two scenarios prevalent in the design and analysis of computer experiments: large designs, and the presence of multiple computer models.

To join via Zoom: Please register here.

Presentation 1

Time: 11:00am – 11:30am

Speaker: Johnny Xi, UBC Statistics MSc student

Title: Indeterminacy in Latent Variable Models: Characterization and Strong Identifiability

Abstract: The history of latent variable models spans nearly 100 years, from factor analysis to modern unsupervised machine learning. An enduring goal is to interpret the latent variables as "true" factors of variation, unique to a sample. Unfortunately, modern non-linear methods are wildly underdetermined, leading to many possible, equally valid solutions, even in the limit of infinite data. I will describe a theoretical framework that rigourously formulates the uniqueness problem as statistical identifiability, unifying existing progress towards this goal. The framework explicitly characterizes the sources of non-identifiability, making it possible to design strongly identifiable latent variable models in a transparent way. Using insights derived from the framework, our work proposes two flexible non-linear models with unique latent variables.

Presentation 2

Time: 11:30am – 12:00pm

Speaker: Naitong Chen, UBC Statistics MSc student

Title: Bayesian Inference via Sparse Hamiltonian Flows

Abstract: A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during Bayesian inference, with the goal of reducing computational cost. Although past work has shown empirically that there often exists a coreset with low inferential error, efficiently constructing such a coreset remains a challenge. Current methods tend to be slow, require a secondary inference step after coreset construction, and do not provide bounds on the data marginal evidence. In this work, we introduce a new method—sparse Hamiltonian flows—that addresses all three of these challenges. The method involves first subsampling the data uniformly, and then optimizing a Hamiltonian flow parametrized by coreset weights and including periodic momentum quasi-refreshment steps. Theoretical results show that the method enables an exponential compression of the dataset in a representative model, and that the quasi-refreshment steps reduce the KL divergence to the target. Real and synthetic experiments demonstrate that sparse Hamiltonian flows provide accurate posterior approximations with significantly reduced runtime compared with competing dynamical-system-based inference methods

To Join via Zoom: To join this seminar, please register here.

Title: Non-Crossing Dual Neural Network: Joint Value at Risk and Conditional Tail Expectation estimations with non-crossing conditions

Abstract: When datasets present long conditional tails on their response variables, algorithms based on Quantile Regression have been widely used to assess extreme quantile behaviors. Value at Risk (VaR) and Conditional Tail Expectation (CTE) allow the evaluation of extreme events to be easily interpretable. The state-of-the-art methodologies to estimate VaR and CTE controlled by covariates are mainly based on linear quantile regression, and usually do not have in consideration non-crossing conditions across VaRs and their associated CTEs. We implement a non-crossing neural network that estimates both statistics simultaneously, for several quantile levels and ensuring a list of non-crossing conditions. We illustrate our method with a household energy consumption dataset from 2015 for quantile levels 0.9, 0.925, 0.95, 0.975 and 0.99, and show its improvements against a Monotone Composite Quantile Regression Neural Network approximation.

To join via Zoom: Please request Zoom connection details from headsec@stat.ubc.ca

Title: Improving multiple-try Metropolis with local balancing

Abstract: Multiple-try Metropolis (MTM) is a popular Markov chain Monte Carlo algorithm which is amenable to parallel computing and thus has great potential. At each iteration, it samples several candidates for the next state of the Markov chain and randomly selects one of them based on a weight function. By leveraging a connection with the work of Zanella (2020), we show that the preferred choice of weight function in the literature, which is proportional to the target density, induces pathological behaviours in high dimensions. Those pathological behaviours are demonstrated through numerical experiments and theoretical results. We propose different weight functions for which those pathological behaviours do not arise. Also, we provide a scaling-limit analysis that allows to characterize the scalability with respect to the dimension of MTM when using the preferred weight function and when using a proposed weight function. In each case, MTM is seen as an approximation to a limiting sampling scheme which is approached under conditions on the rate at which the number of candidates increases with the dimension.

To join via Zoom: To join this seminar, please request Zoom connection details from headsec@stat.ubc.ca.

Abstract: Research on the navigational strategies of marine mammals often uses long-distance migratory data. However, these cost-intensive, long-term monitoring projects are often limited to small sample sizes. One alternative is to use non-migratory trips, where more animals can be tracked. Using shorter trips to investigate navigational hypotheses also allows for a finer-scale investigation of navigational movement, which can aid in exploring pilotage as a potential navigational strategy.

In this project, I explore the potential use of bathymetric landmarks as navigational landmarks by Northern Fur Seals (NFS) during pre-migratory foraging trips. I isolate transiting-type behavior during pre-migratory foraging trips using hidden Markov models, and then use potential functions – a technique traditionally used to model particle or planetary motion – to model the transiting movement of NFS during pre-migratory foraging trips. I then compare these potential functions to the bathymetry of the region.