This thesis proposes a new spatial multivariate count model to jointly analyze the traffic crash-related counts of pedestrians and bicyclists by injury severity. The modeling framework is applied to predict injury counts at a Census tract level, based on crash data from Manhattan, New York. The results highlight the need to use a multivariate modeling system for the analysis of injury counts by road-user type and injury severity level, while also accommodating spatial dependence effects in injury counts. / text

Safety at intersections is of significant interest to transportation professionals due to the large number of possible conflicts that occur at those locations. In particular, rural intersections have been recognized as one of the most hazardous locations on roads. However, most models of crash frequency at rural intersections, and road segments in general, do not differentiate between crash type (such as angle, rear-end or sideswipe) and injury severity (such as fatal injury, non-fatal injury, possible injury or property damage only). Thus, there is a need to be able to identify the differential impacts of intersection-specific and other variables on crash types and severity levels. This thesis builds upon the work of Bhat et al., (2013b) to formulate and apply a novel approach for the joint modeling of crash frequency and combinations of crash type and injury severity. The proposed framework explicitly links a count data model (to model crash frequency) with a discrete choice model (to model combinations of crash type and injury severity), and uses a multinomial probit kernel for the discrete choice model and introduces unobserved heterogeneity in both the crash frequency model and the discrete choice model, while also accommodates excess of zeros. The results show that the type of traffic control and the number of entering roads are the most important determinants of crash counts and crash type/injury severity, and the results from our analysis underscore the value of our proposed model for data fit purposes as well as to accurately estimate variable effects. / text

The focus of this thesis is models for non-parametric clustering of multivariate count data. While there has been significant work in Bayesian non-parametric modelling in the last decade, in the context of mixture models for real-valued data and some forms of discrete data such as multinomial-mixtures, there has been much less work on non-parametric clustering of Multi-variate Count Data. The main challenges in clustering multivariate counts include choosing a suitable multivariate distribution that adequately captures the properties of the data, for instance handling over-dispersed data or sparse multivariate data, at the same time leveraging the inherent dependency structure between dimensions and across instances to get meaningful clusters. As the first contribution, this thesis explores extensions to the Multivariate Poisson distribution, proposing efficient algorithms for non-parametric clustering of multivariate count data. While Poisson is the most popular distribution for count modelling, the Multivariate Poisson often leads to intractable inference and a suboptimal t of the data. To address this, we introduce a family of models based on the Sparse-Multivariate Poisson, that exploit the inherent sparsity in multivariate data, reducing the number of latent variables in the formulation of Multivariate Poisson leading to a better t and more efficient inference. We explore Dirichlet process mixture model extensions and temporal non-parametric extensions to models based on the Sparse Multivariate Poisson for practical use of Poisson based models for non-parametric clustering of multivariate counts in real-world applications. As a second contribution, this thesis addresses moving beyond the limitations of Poisson based models for non-parametric clustering, for instance in handling over dispersed data or data with negative correlations. We explore, for the first time, marginal independent inference techniques based on the Gaussian Copula for multivariate count data in the Dirichlet Process mixture model setting. This enables non-parametric clustering of multivariate counts without limiting assumptions that usually restrict the marginal to belong to a particular family, such as the Poisson or the negative-binomial. This inference technique can also work for mixed data (combination of counts, binary and continuous data) enabling Bayesian non-parametric modelling to be used for a wide variety of data types. As the third contribution, this thesis addresses modelling a wide range of more complex dependencies such as asymmetric and tail dependencies during non-parametric clustering of multivariate count data with Vine Copula based Dirichlet process mixtures. While vine copula inference has been well explored for continuous data, it is still a topic of active research for multivariate counts and mixed multivariate data. Inference for multivariate counts and mixed data is a hard problem owing to ties that arise with discrete marginal. An efficient marginal independent inference approach based on extended rank likelihood, based on recent work in the statistics literature, is proposed in this thesis, extending the use vines for multivariate counts and mixed data in practical clustering scenarios. This thesis also explores the novel systems application of Bulk Cache Preloading by analysing I/O traces though predictive models for temporal non-parametric clustering of multivariate count data. State of the art techniques in the caching domain are limited to exploiting short-range correlations in memory accesses at the milli-second granularity or smaller and cannot leverage long range correlations in traces. We explore for the first time, Bulk Cache Preloading, the process of pro-actively predicting data to load into cache, minutes or hours before the actual request from the application, by leveraging longer range correlation at the granularity of minutes or hours. This enables the development of machine learning techniques tailored for caching due to relaxed timing constraints. Our approach involves a data aggregation process, converting I/O traces into a temporal sequence of multivariate counts, that we analyse with the temporal non-parametric clustering models proposed in this thesis. While the focus of our thesis is models for non-parametric clustering for discrete data, particularly multivariate counts, we also hope our work on bulk cache preloading paves the way to more inter-disciplinary research for using data mining techniques in the systems domain. As an additional contribution, this thesis addresses multi-level non-parametric admixture modelling for discrete data in the form of grouped categorical data, such as document collections. Non-parametric clustering for topic modelling in document collections, where a document is as-associated with an unknown number of semantic themes or topics, is well explored with admixture models such as the Hierarchical Dirichlet Process. However, there exist scenarios, where a doc-ument requires being associated with themes at multiple levels, where each theme is itself an admixture over themes at the previous level, motivating the need for multilevel admixtures. Consider the example of non-parametric entity-topic modelling of simultaneously learning entities and topics from document collections. This can be realized by modelling a document as an admixture over entities while entities could themselves be modeled as admixtures over topics. We propose the nested Hierarchical Dirichlet Process to address this gap and apply a two level version of our model to automatically learn author entities and topics from research corpora.