Diffusion processes in networks can be used to model many real-world processes, such as the propagation of a rumor on social networks and cascading failures on power networks. Analysis of diffusion processes in networks can help us answer important questions such as the role and the importance of each node in the network for spreading the diffusion and how to top or contain a cascading failure in the network. This dissertation consists of three parts.

In the first part, we study the problem of locating multiple diffusion sources in networks under the Susceptible-Infected-Recovered (SIR) model. Given a complete snapshot of the network, we developed a sample-path-based algorithm, named clustering and localization, and proved that for regular trees, the estimators produced by the proposed algorithm are within a constant distance from the real sources with a high probability. Then, we considered the case in which only a partial snapshot is observed and proposed a new algorithm, named Optimal-Jordan-Cover (OJC). The algorithm first extracts a subgraph using a candidate selection algorithm that selects source candidates based on the number of observed infected nodes in their neighborhoods. Then, in the extracted subgraph, OJC finds a set of nodes that "cover" all observed infected nodes with the minimum radius. The set of nodes is called the Jordan cover, and is regarded as the set of diffusion sources. We proved that OJC can locate all sources with probability one asymptotically with partial observations in the Erdos-Renyi (ER) random graph. Multiple experiments on different networks were done, which show our algorithms outperform others.

In the second part, we tackle the problem of reconstructing the diffusion history from partial observations. We formulated the diffusion history reconstruction problem as a maximum a posteriori (MAP) problem and proved the problem is NP hard. Then we proposed a step-by- step reconstruction algorithm, which can always produce a diffusion history that is consistent with the partial observations. Our experimental results based on synthetic and real networks show that the algorithm significantly outperforms some existing methods.

In the third part, we consider the problem of improving the robustness of an interdependent network by rewiring a small number of links during a cascading attack. We formulated the problem as a Markov decision process (MDP) problem. While the problem is NP-hard, we developed an effective and efficient algorithm, RealWire, to robustify the network and to mitigate the damage during the attack. Extensive experimental results show that our algorithm outperforms other algorithms on most of the robustness metrics.

The game held by National Basketball Association (NBA) is the most popular basketball event on earth. Each year, tons of statistical data are generated from this industry. Meanwhile, managing teams, sports media, and scientists are digging deep into the data ocean. Recent research literature is reviewed with respect to whether NBA teams could be analyzed as connected networks. However, it becomes very time-consuming, if not impossible, for human labor to capture every detail of game events on court of large amount. In this study, an alternative method is proposed to parse public resources from NBA related websites to build degenerated game-wise flow graphs. Then, three different statistical techniques are tested to observe the network properties of such offensive strategy in terms of Home-Away team manner. In addition, a new algorithm is developed to infer real game ball distribution networks at the player level under low-rank constraints. The ball-passing degree matrix of one game is recovered to the optimal solution of low-rank ball transition network by constructing a convex operator. The experimental results on real NBA data demonstrate the effectiveness of the proposed algorithm.

Major Depression, clinically called Major Depressive Disorder, is a mood disorder that affects about one eighth of population in US and is projected to be the second leading cause of disability in the world by the year 2020. Recent advances in biotechnology have enabled us to collect a great variety of data which could potentially offer us a deeper understanding of the disorder as well as advancing personalized medicine.

This dissertation focuses on developing methods for three different aspects of predictive analytics related to the disorder: automatic diagnosis, prognosis, and prediction of long-term treatment outcome. The data used for each task have their specific characteristics and demonstrate unique problems. Automatic diagnosis of melancholic depression is made on the basis of metabolic profiles and micro-array gene expression profiles where the presence of missing values and strong empirical correlation between the variables is not unusual. To deal with these problems, a method of generating a representative set of features is proposed. Prognosis is made on data collected from rating scales and questionnaires which consist mainly of categorical and ordinal variables and thus favor decision tree based predictive models. Decision tree models are known for the notorious problem of overfitting. A decision tree pruning method that overcomes the shortcomings of a greedy nature and reliance on heuristics inherent in traditional decision tree pruning approaches is proposed. The method is further extended to prune Gradient Boosting Decision Tree and tested on the task of prognosis of treatment outcome. Follow-up studies evaluating the long-term effect of the treatments on patients usually measure patients' depressive symptom severity monthly, resulting in the actual time of relapse upper bounded by the observed time of relapse. To resolve such uncertainty in response, a general loss function where the hypothesis could take different forms is proposed to predict the risk of relapse in situations where only an interval for time of relapse can be derived from the observed data.

Large-scale $\ell_1$-regularized loss minimization problems arise in high-dimensional applications such as compressed sensing and high-dimensional supervised learning, including classification and regression problems. In many applications, it remains challenging to apply the sparse learning model to large-scale problems that have massive data samples with high-dimensional features. One popular and promising strategy is to scaling up the optimization problem in parallel. Parallel solvers run multiple cores on a shared memory system or a distributed environment to speed up the computation, while the practical usage is limited by the huge dimension in the feature space and synchronization problems.

In this dissertation, I carry out the research along the direction with particular focuses on scaling up the optimization of sparse learning for supervised and unsupervised learning problems. For the supervised learning, I firstly propose an asynchronous parallel solver to optimize the large-scale sparse learning model in a multithreading environment. Moreover, I propose a distributed framework to conduct the learning process when the dataset is distributed stored among different machines. Then the proposed model is further extended to the studies of risk genetic factors for Alzheimer's Disease (AD) among different research institutions, integrating a group feature selection framework to rank the top risk SNPs for AD. For the unsupervised learning problem, I propose a highly efficient solver, termed Stochastic Coordinate Coding (SCC), scaling up the optimization of dictionary learning and sparse coding problems. The common issue for the medical imaging research is that the longitudinal features of patients among different time points are beneficial to study together. To further improve the dictionary learning model, I propose a multi-task dictionary learning method, learning the different task simultaneously and utilizing shared and individual dictionary to encode both consistent and changing imaging features.

Predictive analytics embraces an extensive area of techniques from statistical modeling to machine learning to data mining and is applied in business intelligence, public health, disaster management and response, and many other fields. To date, visualization has been broadly used to support tasks in the predictive analytics pipeline under the underlying assumption that a human-in-the-loop can aid the analysis by integrating domain knowledge that might not be broadly captured by the system. Primary uses of visualization in the predictive analytics pipeline have focused on data cleaning, exploratory analysis, and diagnostics. More recently, numerous visual analytics systems for feature selection, incremental learning, and various prediction tasks have been proposed to support the growing use of complex models, agent-specific optimization, and comprehensive model comparison and result exploration. Such work is being driven by advances in interactive machine learning and the desire of end-users to understand and engage with the modeling process. However, despite the numerous and promising applications of visual analytics to predictive analytics tasks, work to assess the effectiveness of predictive visual analytics is lacking.

This thesis studies the current methodologies in predictive visual analytics. It first defines the scope of predictive analytics and presents a predictive visual analytics (PVA) pipeline. Following the proposed pipeline, a predictive visual analytics framework is developed to be used to explore under what circumstances a human-in-the-loop prediction process is most effective. This framework combines sentiment analysis, feature selection mechanisms, similarity comparisons and model cross-validation through a variety of interactive visualizations to support analysts in model building and prediction. To test the proposed framework, an instantiation for movie box-office prediction is developed and evaluated. Results from small-scale user studies are presented and discussed, and a generalized user study is carried out to assess the role of predictive visual analytics under a movie box-office prediction scenario.

The National Basketball Association (NBA) is the most popular basketball league in the world. The world-wide mighty high popularity to the league leads to large amount of interesting and challenging research problems. Among them, predicting the outcome of an upcoming NBA match between two specific teams according to their historical data is especially attractive. With rapid development of machine learning techniques, it opens the door to examine the correlation between statistical data and outcome of matches. However, existing methods typically make predictions before game starts. In-game prediction, or real-time prediction, has not yet been sufficiently studied. During a match, data are cumulatively generated, and with the accumulation, data become more comprehensive and potentially embrace more predictive power, so that prediction accuracy may dynamically increase with a match goes on. In this study, I design game-level and player-level features based on realtime data of NBA matches and apply a machine learning model to investigate the possibility and characteristics of using real-time prediction in NBA matches.

Imaging genetics is an emerging and promising technique that investigates how genetic variations affect brain development, structure, and function. By exploiting disorder-related neuroimaging phenotypes, this class of studies provides a novel direction to reveal and understand the complex genetic mechanisms. Oftentimes, imaging genetics studies are challenging due to the relatively small number of subjects but extremely high-dimensionality of both imaging data and genomic data. In this dissertation, I carry on my research on imaging genetics with particular focuses on two tasks---building predictive models between neuroimaging data and genomic data, and identifying disorder-related genetic risk factors through image-based biomarkers. To this end, I consider a suite of structured sparse methods---that can produce interpretable models and are robust to overfitting---for imaging genetics. With carefully-designed sparse-inducing regularizers, different biological priors are incorporated into learning models. More specifically, in the Allen brain image--gene expression study, I adopt an advanced sparse coding approach for image feature extraction and employ a multi-task learning approach for multi-class annotation. Moreover, I propose a label structured-based two-stage learning framework, which utilizes the hierarchical structure among labels, for multi-label annotation. In the Alzheimer's disease neuroimaging initiative (ADNI) imaging genetics study, I employ Lasso together with EDPP (enhanced dual polytope projections) screening rules to fast identify Alzheimer's disease risk SNPs. I also adopt the tree-structured group Lasso with MLFre (multi-layer feature reduction) screening rules to incorporate linkage disequilibrium information into modeling. Moreover, I propose a novel absolute fused Lasso model for ADNI imaging genetics. This method utilizes SNP spatial structure and is robust to the choice of reference alleles of genotype coding. In addition, I propose a two-level structured sparse model that incorporates gene-level networks through a graph penalty into SNP-level model construction. Lastly, I explore a convolutional neural network approach for accurate predicting Alzheimer's disease related imaging phenotypes. Experimental results on real-world imaging genetics applications demonstrate the efficiency and effectiveness of the proposed structured sparse methods.

Cyberbullying is a phenomenon which negatively affects individuals. Victims of the cyberbullying suffer from a range of mental issues, ranging from depression to low self-esteem. Due to the advent of the social media platforms, cyberbullying is becoming more and more prevalent. Traditional mechanisms to fight against cyberbullying include use of standards and guidelines, human moderators, use of blacklists based on profane words, and regular expressions to manually detect cyberbullying. However, these mechanisms fall short in social media and do not scale well. Users in social media use intentional evasive expressions like, obfuscation of abusive words, which necessitates the development of a sophisticated learning framework to automatically detect new cyberbullying behaviors. Cyberbullying detection in social media is a challenging task due to short, noisy and unstructured content and intentional obfuscation of the abusive words or phrases by social media users. Motivated by sociological and psychological findings on bullying behavior and its correlation with emotions, we propose to leverage the sentiment information to accurately detect cyberbullying behavior in social media by proposing an effective optimization framework. Experimental results on two real-world social media datasets show the superiority of the proposed framework. Further studies validate the effectiveness of leveraging sentiment information for cyberbullying detection.

Identifying chemical compounds that inhibit bacterial infection has recently gained a considerable amount of attention given the increased number of highly resistant bacteria and the serious health threat it poses around the world. With the development of automated microscopy and image analysis systems, the process of identifying novel therapeutic drugs can generate an immense amount of data - easily reaching terabytes worth of information. Despite increasing the vast amount of data that is currently generated, traditional analytical methods have not increased the overall success rate of identifying active chemical compounds that eventually become novel therapeutic drugs. Moreover, multispectral imaging has become ubiquitous in drug discovery due to its ability to provide valuable information on cellular and sub-cellular processes using florescent reagents. These reagents are often costly and toxic to cells over an extended period of time causing limitations in experimental design. Thus, there is a significant need to develop a more efficient process of identifying active chemical compounds.

This dissertation introduces novel machine learning methods based on parallelized cellomics to analyze interactions between cells, bacteria, and chemical compounds while reducing the use of fluorescent reagents. Machine learning analysis using image-based high-content screening (HCS) data is compartmentalized into three primary components: (1) \textit{Image Analytics}, (2) \textit{Phenotypic Analytics}, and (3) \textit{Compound Analytics}. A novel software analytics tool called the Insights project is also introduced. The Insights project fully incorporates distributed processing, high performance computing, and database management that can rapidly and effectively utilize and store massive amounts of data generated using HCS biological assessments (bioassays). It is ideally suited for parallelized cellomics in high dimensional space.

Results demonstrate that a parallelized cellomics approach increases the quality of a bioassay while vastly decreasing the need for control data. The reduction in control data leads to less fluorescent reagent consumption. Furthermore, a novel proposed method that uses single-cell data points is proven to identify known active chemical compounds with a high degree of accuracy, despite traditional quality control measurements indicating the bioassay to be of poor quality. This, ultimately, decreases the time and resources needed in optimizing bioassays while still accurately identifying active compounds.

Measuring node centrality is a critical common denominator behind many important graph mining tasks. While the existing literature offers a wealth of different node centrality measures, it remains a daunting task on how to intervene the node centrality in a desired way. In this thesis, we study the problem of minimizing the centrality of one or more target nodes by edge operation. The heart of the proposed method is an accurate and efficient algorithm to estimate the impact of edge deletion on the spectrum of the underlying network, based on the observation that the edge deletion is essentially a local, sparse perturbation to the original network. Extensive experiments are conducted on a diverse set of real networks to demonstrate the effectiveness, efficiency and scalability of our approach. In particular, it is average of 260.95%, in terms of minimizing eigen-centrality, better than the standard matrix-perturbation based algorithm, with lower time complexity.