Dissertations / Theses on the topic 'Statistics and Computer Science'

The visualization of recent episodes regarding apparently unjustifiable deaths of minorities, caused by police and federal law enforcement agencies, has been amplified through today’s social media and television networks. Such events may seem to imply that issues concerning racial inequalities in America are getting worse. However, we do not know whether such indications are factual; whether this is a recent phenomenon, whether racial inequality is escalating relative to earlier decades, or whether it is better in certain regions of the nation compared to others.

We have built a semantic engine for the purpose of querying statistics on various metropolitan areas, based on a database of individual deaths. Separately, we have built a database of demographic data on poverty, income, education attainment, and crime statistics for the top 25 most populous metropolitan areas. These data will ultimately be combined with government data to evaluate this hypothesis, and provide a tool for predictive analytics. In this thesis, we will provide preliminary results in that direction.

The methodology in our research consisted of multiple steps. We initially described our requirements and drew data from numerous datasets, which contained information on the 23 highest populated Metropolitan Statistical Areas in the United States. After all of the required data was obtained we decomposed the Metropolitan Statistical Area records into domain components and created an Ontology/Taxonomy via Protégé to determine an hierarchy level of nouns towards identifying significant keywords throughout the datasets to use as search queries. Next, we used a Semantic Web implementation accompanied with Python programming language, and FuXi to build and instantiate a vocabulary. The Ontology was then parsed for the entered search query and returned corresponding results providing a semantically organized and relevant output in RDF/XML format.

The task of explaining differences across groups is a task that people encounter often, not only in the research environment, but also in less formal settings. Existing statistical tools designed specifically for discovering and understanding differences are limited. The methods developed in this dissertation provide such tools and help understand what properties such tools should have to be successful and to motivate further development of new approaches to discovering and understanding differences.

This dissertation presents a novel approach to comparing groups of data points. The process of comparing groups of data is divided into multiple stages: The learning of maximum a posteriori models for the data in each group, the identification of statistical differences between model parameters, the construction of a single model that captures those differences, and finally, the explanation of inferences of differences in marginal distributions in the form of an account of clinically significant contributions of elemental model differences to the marginal difference. A general framework for the process, applicable to a broad range of model types, is presented. This dissertation focuses on applying this framework to Bayesian networks over multinomial variables.

To evaluate model learning and the detection of parameter differences an empirical evaluation of methods for identifying statistically significant differences and clinically significant differences is performed. To evaluate the generated explanations of how differences in the models account for the differences in probabilities computed from those models, case studies with real clinical data are presented, and the findings generated by explanations are discussed. An interactive prototype that allows a user to navigate through such an explanation is presented, and ideas are discussed for further development of data analysis tools for comparing groups of data.

Generating random samples from a prescribed distribution is one of the most important and challenging problems in machine learning, Bayesian statistics, and the simulation of materials. Markov Chain Monte Carlo (MCMC) methods are usually the required tool for this task, if the desired distribution is known only up to a multiplicative constant. Samples produced by an MCMC method are real values in N-dimensional space, called the configuration space. The distribution of such samples converges to the target distribution in the limit. However, existing MCMC methods still face many challenges that are not well resolved. Difficulties for sampling by using MCMC methods include, but not exclusively, dealing with high dimensional and multimodal problems, high computation cost due to extremely large datasets in Bayesian machine learning models, and lack of reliable indicators for detecting convergence and measuring the accuracy of sampling. This dissertation focuses on new theory and methodology for efficient MCMC methods that aim to overcome the aforementioned difficulties.

One contribution of this dissertation is generalizations of hybrid Monte Carlo (HMC). An HMC method combines a discretized dynamical system in an extended space, called the state space, and an acceptance test based on the Metropolis criterion. The discretized dynamical system used in HMC is volume preserving—meaning that in the state space, the absolute Jacobian of a map from one point on the trajectory to another is 1. Volume preservation is, however, not necessary for the general purpose of sampling. A general theory allowing the use of non-volume preserving dynamics for proposing MCMC moves is proposed. Examples including isokinetic dynamics and variable mass Hamiltonian dynamics with an explicit integrator, are all designed with fewer restrictions based on the general theory. Experiments show improvement in efficiency for sampling high dimensional multimodal problems. A second contribution is stochastic gradient samplers with reduced bias. An in-depth analysis of the noise introduced by the stochastic gradient is provided. Two methods to reduce the bias in the distribution of samples are proposed. One is to correct the dynamics by using an estimated noise based on subsampled data, and the other is to introduce additional variables and corresponding dynamics to adaptively reduce the bias. Extensive experiments show that both methods outperform existing methods. A third contribution is quasi-reliable estimates of effective sample size. Proposed is a more reliable indicator—the longest integrated autocorrelation time over all functions in the state space—for detecting the convergence and measuring the accuracy of MCMC methods. The superiority of the new indicator is supported by experiments on both synthetic and real problems.

Minor contributions include a general framework of changing variables, and a numerical integrator for the Hamiltonian dynamics with fourth order accuracy. The idea of changing variables is to transform the potential energy function as a function of the original variable to a function of the new variable, such that undesired properties can be removed. Two examples are provided and preliminary experimental results are obtained for supporting this idea. The fourth order integrator is constructed by combining the idea of the simplified Takahashi-Imada method and a two-stage Hessian-based integrator. The proposed method, called two-stage simplified Takahashi-Imada method, shows outstanding performance over existing methods in high-dimensional sampling problems.

In machine learning predictive area, unsupervised learning will be applied when the labels of the data are unavailable, laborious to obtain or with limited proportion. Based on the special properties of data, we can build models by understanding the properties and making some reasonable assumptions. In this thesis, we will introduce three practical problems and discuss them in detail. This thesis produces 3 papers as follow: Wei, Wutao, et al. "A Non-parametric Hidden Markov Clustering Model with Applications to Time Varying User Activity Analysis." ICMLA2015 Wei, Wutao, et al. "Dynamic Bayesian predictive model for box office forecasting." IEEE Big Data 2017. Wei, Wutao, Bowei Xi, and Murat Kantarcioglu. "Adversarial Clustering: A Grid Based Clustering Algorithm Against Active Adversaries." Submitted

User Profiling Clustering: Activity data of individual users on social media are easily accessible in this big data era. However, proper modeling strategies for user profiles have not been well developed in the literature. Existing methods or models usually have two limitations. The first limitation is that most methods target the population rather than individual users, and the second is that they cannot model non-stationary time-varying patterns. Different users in general demonstrate different activity modes on social media. Therefore, one population model may fail to characterize activities of individual users. Furthermore, online social media are dynamic and ever evolving, so are users’ activities. Dynamic models are needed to properly model users’ activities. In this paper, we introduce a non-parametric hidden Markov model to characterize the time-varying activities of social media users. In addition, based on the proposed model, we develop a clustering method to group users with similar activity patterns.

Adversarial Clustering: Nowadays more and more data are gathered for detecting and preventing cyber-attacks. Unique to the cyber security applications, data analytics techniques have to deal with active adversaries that try to deceive the data analytics models and avoid being detected. The existence of such adversarial behavior motivates the development of robust and resilient adversarial learning techniques for various tasks. In the past most of the work focused on adversarial classification techniques, which assumed the existence of a reasonably large amount of carefully labeled data instances. However, in real practice, labeling the data instances often requires costly and time-consuming human expertise and becomes a significant bottleneck. Meanwhile, a large number of unlabeled instances can also be used to understand the adversaries' behavior. To address the above mentioned challenges, we develop a novel grid based adversarial clustering algorithm. Our adversarial clustering algorithm is able to identify the core normal regions, and to draw defensive walls around the core positions of the normal objects utilizing game theoretic ideas. Our algorithm also identifies sub-clusters of attack objects, the overlapping areas within clusters, and outliers which may be potential anomalies.

Dynamic Bayesian Update for Profiling Clustering: Movie industry becomes one of the most important consumer business. The business is also more and more competitive. As a movie producer, there is a big cost in movie production and marketing; as an owner of a movie theater, it is also a problem that how to arrange the limited screens to the current movies in theater. However, all the current models in movie industry can only give an estimate of the opening week. We improve the dynamic linear model with a Bayesian framework. By using this updating method, we are also able to update the streaming adversarial data and make defensive recommendation for the defensive systems.

Urn models have a storied part in the history of probability and have been studied extensively over the past century for their wide range of applications. We analyze a generalized class of urn models introduced in the past decade, the so-called "multiset" class, in which more than one ball is sampled at a time. We investigate sufficient conditions for a multiset urn process to be tenable, meaning the process can continue indefinitely without getting stuck. We fully characterize the "strongly tenable" class of Pólya urn schemes, which is tenable under any starting conditions that allow the process to begin. We find several "weakly tenable" classes of Pólya urn schemes that are tenable only under restricted starting conditions. We enumerate the size of some of these tenable classes using combinatorics, probabilistically analyze them, and provide an algorithm to assess the tenability of an arbitrary urn scheme using breadth-first search. We further analyze the computational complexity of the tenability problem itself. By showing how to encode the Boolean satisfiability problem within a Pólya urn scheme, we find that the problem of determining whether a multiset urn scheme is untenable is in the complexity class NP-hard, and this places constraints on the kinds of tenability theorems we can hope to find. Finally, we analyze a generalized “fault tolerant” urn model that can take action to avoid getting stuck, and by showing that this model is Turing-equivalent, we show that the tenability problem for this model is undecidable.

Interactive systems that interact with and learn from user behavior are ubiquitous today. Machine learning algorithms are core components of such systems. In this thesis, we will study how we can re-use logged user behavior data to evaluate interactive systems and train their machine learned components in a principled way. The core message of the thesis is • Using simple techniques from causal inference, we can improve popular machine learning algorithms so that they interact reliably. • These improvements are effective and scalable, and complement current algorithmic and modeling advances in machine learning. • They open further avenues for research in Counterfactual Evaluation and Learning to ensure machine learned components interact reliably with users and with each other. This thesis explores two fundamental tasks—evaluation and training of interactive systems. Solving evaluation and training tasks using logged data is an exercise in counterfactual reasoning. So we will first review concepts from causal inference for counterfactual reasoning, assignment mechanisms, statistical estimation and learning theory. The thesis then contains two parts.

In the first part, we will study scenarios where unknown assignment mechanisms underlie the logged data we collect. These scenarios often arise in learning-to-rank and learning-to-recommend applications. We will view these applications through the lens of causal inference and modularize the problem of building a good ranking engine or recommender system into two components—first, infer a plausible assignment mechanism and second, reliably learn to rank or recommend assuming this mechanism was active when collecting data.

The second part of the thesis focuses on scenarios where we collect logged data from past interventions. We will formalize these scenarios as batch learning from logged contextual bandit feedback. We will first develop better off-policy estimators for evaluating online user-centric metrics in information retrieval applications. In subsequent chapters, we will study the bias-variance trade-off when learning from logged interventions. This study will yield new learning principles, algorithms and insights into the design of statistical estimators for counterfactual learning.

The thesis outlines a few principles, tools, datasets and software that hopefully prove to be useful to you as you build your interactive learning system.

In the era of the internet, we are connected to an overwhelming abundance of information. As more facets of our lives become digitized, there is a growing need for automatic tools to help us find the content we care about. To tackle the problem of information overload, a standard machine learning approach is to perform dimensionality reduction, transforming complicated high-dimensional data into a manageable, low-dimensional form. Probabilistic latent variable models provide a powerful and elegant framework for performing this transformation in a principled way. This thesis makes several advances for modeling two of the most ubiquitous types of online information: networks and text data.

Our first contribution is to develop a model for social networks as they vary over time. The model recovers latent feature representations of each individual, and tracks these representations as they change dynamically. We also show how to use text information to interpret these latent features.

Continuing the theme of modeling networks and text data, we next build a model of citation networks. The model finds influential scientific articles and the influence relationships between the articles, potentially opening the door for automated exploratory tools for scientists. The increasing prevalence of web-scale data sets provides both an opportunity and a challenge. With more data we can fit more accurate models, as long as our learning algorithms are up to the task. To meet this challenge, we present an algorithm for learning latent Dirichlet allocation topic models quickly, accurately and at scale. The algorithm leverages stochastic techniques, as well as the collapsed representation of the model. We use it to build a topic model on 4.6 million articles from the open encyclopedia Wikipedia in a matter of hours, and on a corpus of 1740 machine learning articles from the NIPS conference in seconds.

Finally, evaluating the predictive performance of topic models is an important yet computationally difficult task. We develop one algorithm for comparing topic models, and another for measuring the progress of learning algorithms for these models. The latter method achieves better estimates than previous algorithms, in many cases with an order of magnitude less computational effort.

This work provides a framework for Design Day analysis. First, we estimate the temperature conditions which are expected to be colder than all but one day in N years. This temperature is known as the Design Day condition. Then, we forecast an upper bound on natural gas demand when temperature is at the Design Day condition.

Natural gas distribution companies (LDCs) need to meet demand during extreme cold days. Just as bridge builders design for a nominal load, natural gas distribution companies need to design for a nominal temperature. This nominal temperature is the Design Day condition. The Design Day condition is the temperature that is expected to be colder than every day except one in N years. Once Design Day conditions are estimated, LDCs need to prepare for the Design Day demand. We provide an upper bound on Design Day demand to ensure LDCs will be able to meet demand.

Design Day conditions are determined in a variety of ways. First, we fit a kernel density function to surrogate temperatures - this method is referred to as the Surrogate Kernel Density Fit. Second, we apply Extreme Value Theory - a field dedicated to finding the maxima or minima of a distribution. In particular, we apply Block-Maxima and Peak-Over-Threshold (POT) techniques. The upper bound of Design Day demand is determined using a modified version of quantile regression.

Similar Design Day conditions are estimated by both the Surrogate Kernel Density Fit and Peaks-Over-Threshold methods. Both methods perform well. The theory supporting the POT method and the empirical performance of the SKDF method lends confidence in the Design Day conditions estimates. The upper bound of demand on these conditions is well modeled by the modified quantile regression technique.

With the great progress in information and communications technologies in the past few decades, intelligent transportation systems (ITS) have accumulated vast amounts of data regarding the movement iof people and goods from one location to another. Besides the traditional fixed sensors and GPS devices, new emerging data sources and approaches such as social media and crowdsourcing can be used to extract travel-related data, especially given the wide popularity of mobile devices such as smartphones and tablets, along with their associated apps. To take advantage of all these data and to address the associated challenges, big data techniques, and a new emerging field called data science, are currently receiving more and more attention. Data science employs techniques and theories from many fields such as statistics, machine learning, data mining, analytical models and computer programming to solve the data analysis task. It is therefore timely and important to explore how data science may be best employed for transportation data analysis. In this doctoral study, an integrative approach is proposed for data science applications in ITS. The proposed approach constitutes to an integration of multiple steps in the data analysis process, or integration of different models to build a more powerful one. The integrative approach is applied and tested on two case studies: border crossing delay prediction and traffic accident data analysis.

For the first case study, a two-step border crossing delay prediction model is proposed, consisting of a short-term traffic volume prediction model and a multi-server queueing model. As such, this can be seen as an integration of data-driven models and analytical models. For the first step, the short-term traffic volume prediction model, an integration of data "width" decreasing (i.e., data grouping) step and model development step is applied. For model development, a model combination step of a Seasonal Autoregressive Integrated Moving Average Model (SARIMA) and Support Vector Regression (SVR) is applied to realize better performance than when using each single model. In addition, the spinning network (SPN) forecasting paradigm is enhanced for border crossing traffic prediction through the utilization of a dynamic time warping (DTW) similarity metric. The DTW-SPN is shown to yield several advantages such as computational efficiency and accuracy as demonstrated by a promising Mean Absolute Percent Error (MAPE) compared to SARIMA and SVR.

This dissertation also proposes the introduction of a data diagnosis step before short-term traffic prediction. In order to develop a methodology for model selection guidance, the author calculated the statistical measures of nonlinearity and complexity for multiple datasets and correlated those to the performances of multiple models SARIMA, SVR and k nearest neighbor (k-NN). Based on this, useful insights are revealed pertaining to parameter setting and model selection based on the data diagnosis results.

For the second step, namely the queueing model development, heuristic solutions are presented for two types of queueing models M/E _K/n and BMAP/PH/n. These models take the predicted traffic volume as input, and use it to calculate future waiting time. The analytical results are compared to the results from a VISSIM model simulation results, and shown to be comparable. . Finally, an android smartphone app, which utilizes the two-step border prediction model methodology described above, is developed to collect, share and predict waiting time at the three Niagara Frontier border crossings.

For the second case study involving traffic accident data analysis, first an integration of a data "depth" decreasing step and a model development step is once again applied. To do this, the modularity-optimizing community detection algorithm is used to cluster the dataset, and for each cluster, the association rule algorithm is applied to yield insight into traffic accident hotspots and incident clearance time. The results show that more meaningful association rules can be derived when the data is clustered compared to when using the whole dataset directly. Secondly, an integration of a data "width" decreasing step (variable selection) and model development step is applied for real-time traffic accident risk prediction. For this, a novel variable selection method based on the Frequent Pattern tree (FP tree) algorithm is proposed and tested, before applying Bayesian networks and the k-NN algorithms. The experiment shows the models based on variables selected by FP tree always performed better than those using variables selected by the random forecast method. Lastly, an integration of the data mining model, M5P tree, and the hazard-based duration model (HBDM) statistical method is applied to traffic accident duration prediction. The M5P-HBDM method is shown to be capable of identifying more meaningful factors that impact the traffic accident duration, and to have a better prediction performance, than either M5P or HBDM.

The two case studies considered in this dissertation serve to illustrate the advantages of an integrative data science approach to analyzing transportation data. With this approach, invaluable insight is gained that can help solve transportation problems and guide public policy.

Chronic pain affects more than 100 million Americans and more than 1.5 billion people worldwide. Pain is a multidimensional construct, expressed through a variety of means. Facial expressions are one such type of pain expression. Automatic facial expression recognition, and in particular pain expression recognition, are fields that have been studied extensively. However, nothing has explored the possibility of an automatic pain quantification algorithm, able to output pain levels based upon a facial image.

Developed for a remote monitoring context, a computational pain quantification algorithm has been developed and validated by two distinct sets of data. The second set of data also included associated data for the fields of age, gender, culture and cause of pain. These four fields were investigated for their effect on automatic pain quantification, determining that age and gender have a definite impact and should be involved in the algorithm, while culture and cause require further investigation.

Understanding gene interactions in complex living systems is one of the central tasks in system biology. With the availability of microarray and RNA-Seq technologies, a multitude of gene expression datasets has been generated towards novel biological knowledge discovery through statistical analysis and reconstruction of gene regulatory networks (GRN). Reconstruction of GRNs can reveal the interrelationships among genes and identify the hierarchies of genes and hubs in networks. The new algorithms I developed in this dissertation are specifically focused on the reconstruction of GRNs with increased accuracy from microarray and RNA-Seq high-throughput gene expression data sets.

The first algorithm (Chapter 2) focuses on modeling the transcriptional regulatory relationships between transcription factors (TF) and pathway genes. Multiple linear regression and its regularized version, such as Ridge regression and LASSO, are common tools that are usually used to model the relationship between predictor variables and dependent variable. To deal with the outliers in gene expression data, the group effect of TFs in regulation and to improve the statistical efficiency, it is proposed to use Huber function as loss function and Berhu function as penalty function to model the relationships between a pathway gene and many or all TFs. A proximal gradient descent algorithm was developed to solve the corresponding optimization problem. This algorithm is much faster than the general convex optimization solver CVX. Then this Huber-Berhu regression was embedded into partial least square (PLS) framework to deal with the high dimension and multicollinearity property of gene expression data. The result showed this method can identify the true regulatory TFs for each pathway gene with high efficiency.

The second algorithm (Chapter 3) focuses on building multilayered hierarchical gene regulatory networks (ML-hGRNs). A backward elimination random forest (BWERF) algorithm was developed for constructing an ML-hGRN operating above a biological pathway or a biological process. The algorithm first divided construction of ML-hGRN into multiple regression tasks; each involves a regression between a pathway gene and all TFs. Random forest models with backward elimination were used to determine the importance of each TF to a pathway gene. Then the importance of a TF to the whole pathway was computed by aggregating all the importance values of the TF to the individual pathway gene. Next, an expectation maximization algorithm was used to cut the TFs to form the first layer of direct regulatory relationships. The upper layers of GRN were constructed in the same way only replacing the pathway genes by the newly cut TFs. Both simulated and real gene expression data were used to test the algorithms and demonstrated the accuracy and efficiency of the method.

The third algorithm (Chapter 4) focuses on Joint Reconstruction of Multiple Gene Regulatory Networks (JRmGRN) using gene expression data from multiple tissues or conditions. In the formulation, shared hub genes across different tissues or conditions were assumed. Under the framework of the Gaussian graphical model, JRmGRN method constructs the GRNs through maximizing a penalized log-likelihood function. It was formulated as a convex optimization problem, and then solved it with an alternating direction method of multipliers (ADMM) algorithm. Both simulated and real gene expression data manifested JRmGRN had better performance than existing methods.

The past decade has seen an abundance of applications that utilize sensors to collect data. One such example is a gigapixel image, which combines a multitude of high-quality images into a panorama capable of viewing hundreds of acres. The resulting datasets can be quite large, making analysis time consuming and resource intensive. Moreover, coverage of such broad environments can mean numerous sensor feeds to which one must attend. A suitable approach for analysis and sense-making of such data is to focus on “interesting” samples of data, namely regions of interest, or ROI. ROIs are especially useful in wide-area sensing situations that return datasets that are largely similar from one instance to the next, but also possess small differences. Identifying subtle changes is relevant to certain scenarios in surveillance, such as the evidence of human activity. Several ROI detection techniques exist in the research literature. My work focuses on ROI detection tuned to subtle differences for images at varying zoom levels. My thesis consists of developing a method that identifies regions of interest for subtle changes in images. In this pursuit, my contributions will address key questions including the characterization of image information dynamics through introduction of dynamic zoom, the definition and measurement of subtlety, and an approach for scoring and selecting ROIs. This work will provide an automated attention mechanism for zoomed images, but is also applicable to domains include satellite imagery and cyber security.

Classification is a ubiquitous decision activity. Regardless of whether it is predicting the future, e.g., a weather forecast, determining an existing state, e.g., a medical diagnosis, or some other activity, classifier outputs drive future actions. Because of their importance, classifier research and development is an active field.

Regardless of whether one is a classifier developer or an end user, evaluating and comparing classifier output quality is important. Intuitively, classifier evaluation may seem simple, however, it is not. There is a plethora of classifier summary statistics and new summary statistics seem to surface regularly. Summary statistic users appear not to be satisfied with the existing summary statistics. For end users, many existing summary statistics do not provide actionable information. This dissertation addresses the end user's quandary.

The work consists of four parts: 1. Considering eight summary statistics with regard to their purpose (what questions do they quantitatively answer) and efficacy (as defined by measurement theory). 2. Characterizing the classification problem from the end user's perspective and identifying four axioms for end user efficacious classifier evaluation summary statistics. 3. Applying the axia and measurement theory to evaluate eight summary statistics and create two compliant (end user efficacious) summary statistics. 4. Using the compliant summary statistics to show the actionable information they generate.

By applying the recommendations in this dissertation, both end users and researchers benefit. Researchers have summary statistic selection and classifier evaluation protocols that generate the most usable information. End users can also generate information that facilitates tool selection and optimal deployment, if classifier test reports provide the necessary information.

Binary classification plays an important role in many decision-making processes. Random forests can build a strong ensemble classifier by combining weaker classification trees that are de-correlated. The strength and correlation among individual classification trees are the key factors that contribute to the ensemble performance of random forests. We propose roughened random forests, a new set of tools which show further improvement over random forests in binary classification. Roughened random forests modify the original dataset for each classification tree and further reduce the correlation among individual classification trees. This data modification process is composed of artificially imposing missing data that are missing completely at random and subsequent missing data imputation.

Through this dissertation we aim to answer a few important questions in building roughened random forests: (1) What is the ideal rate of missing data to impose on the original dataset? (2) Should we impose missing data on both the training and testing datasets, or only on the training dataset? (3) What are the best missing data imputation methods to use in roughened random forests? (4) Do roughened random forests share the same ideal number of covariates selected at each tree node as the original random forests? (5) Can roughened random forests be used in medium- to high- dimensional datasets?

Our daily lives increasingly involve interactions with others via different communication channels, such as email, text messaging, and social media. In this context, the ability to analyze and understand our communication patterns is becoming increasingly important. This dissertation focuses on generative probabilistic models for describing different characteristics of communication behavior, focusing primarily on email communication.

First, we present a two-parameter kernel density estimator for estimating the probability density over recipients of an email (or, more generally, items which appear in an itemset). A stochastic gradient method is proposed for efficiently inferring the kernel parameters given a continuous stream of data. Next, we apply the kernel model and the Bernoulli mixture model to two important prediction tasks: given a partially completed email recipient list, 1) predict which others will be included in the email, and 2) rank potential recipients based on their likelihood to be added to the email. Such predictions are useful in suggesting future actions to the user (i.e. which person to add to an email) based on their previous actions. We then investigate a piecewise-constant Poisson process model for describing the time-varying communication rate between an individual and several groups of their contacts, where changes in the Poisson rate are modeled as latent state changes within a hidden Markov model.

We next focus on the time it takes for an individual to respond to an event, such as receiving an email. We show that this response time depends heavily on the individual's typical daily and weekly patterns - patterns not adequately captured in standard models of response time (e.g. the Gamma distribution or Hawkes processes). A time-warping mechanism is introduced where the absolute response time is modeled as a transformation of effective response time, relative to the daily and weekly patterns of the individual. The usefulness of applying the time-warping mechanism to standard models of response time, both in terms of log-likelihood and accuracy in predicting which events will be quickly responded to, is illustrated over several individual email histories.

Metastatic, castrate-resistant prostate cancer (mCRPC) is one of the most prevalent cancers and is the third leading cause of cancer death among men. Several treatment options have been developed to combat mCRPC, however none have produced any tangible benefits to patients' overall survivability. As part of a crowd-sourced algorithm development competition, participants were asked to develop new prognostic models for mCRPC patients treated with docetaxel. Such results could potentially assist in clinical decision making for future mCRPC patients.

In this thesis, we present a new ensemble prognostic model to perform risk prediction for mCRPC patients treated with docetaxel. We rely on traditional survival analysis model like the Cox Proportional Hazard model, as well as more recently developed boosting model that incorporates smooth approximation of the concordance index for direct optimization. Our model performs better than the the current state-of-the-art mCRPC prognostic models for the concordance index performance measure and is competitive with these models on the integrated time-dependent area under the receiver operating characteristic curve.

Markov random walk models are powerful analytical tools for multiple areas in machine learning, numerical optimizations and data mining tasks. The key assumption of a first-order Markov chain is memorylessness, which restricts the dependence of the transition distribution to the current state only. However in many applications, this assumption is not appropriate. We propose a set of higher-order random walk techniques and discuss their applications to tensor co-clustering, user trails modeling, and solving linear systems. First, we develop a new random walk model that we call the super-spacey random surfer, which simultaneously clusters the rows, columns, and slices of a nonnegative three-mode tensor. This algorithm generalizes to tensors with any number of modes. We partition the tensor by minimizing the exit probability between clusters when the super-spacey random walk is at stationary. The second application is user trails modeling, where user trails record sequences of activities when individuals interact with the Internet and the world. We propose the retrospective higher-order Markov process as a two-step process by first choosing a state from the history and then transitioning as a first-order chain conditional on that state. This way the total number of parameters is restricted and thus the model is protected from overfitting. Lastly we propose to use a time-inhomogeneous Markov chain to approximate the solution of a linear system. Multiple simulations of the random walk are conducted to approximate the solution. By allowing the random walk to transition based on multiple matrices, we decrease the variance of the simulations, and thus increase the speed of the solver.