The presence of noise and corruption in real-world data can be inevitably caused by accidental outliers, transmission loss, or even adversarial data attacks. Unlike traditional random noise usually assume a specific distribution with low corruption ratio, the data collected from crowdsourcing or labeled by weak annotators can contain adversarial data corruption. More challenge, the adversarial data corruption can be arbitrary, unbounded and do not follow any specific distribution. In addition, in the era of data explosion, the fast-growing amount of data makes the robust models more difficult to handle large-scale data sets.

This thesis focuses on the development of methods for scalable robust models under the adversarial data corruption assumptions. Four methods are proposed, including robust regression via heuristic hard-thresholding, online and distributed robust regression with adversarial noises, self-paced robust learning for leveraging clean labels in noisy data, and robust regression via online feature selection with adversarial noises. Moreover, I extended the self-paced robust learning method to its distributed version for the scalability of the proposed algorithm, named distributed self-paced learning in alternating direction method of multiplier. Last, a robust multi-factor personality prediction model is proposed to hand the correlated data noises.

For the first method, existing solutions for robust regression lack rigorous recovery guarantee of regression coefficients under the adversarial data corruption with no prior knowledge of corruption ratio. The proposed contributions of our work include: (1) Propose efficient algorithms to address the robust least-square regression problem; (2) Design effective approaches to estimate the corruption ratio; (3) Provide a rigorous robustness guarantee for regression coefficient recovery; and (4) Conduct extensive experiments for performance evaluation.

For the second method, existing robust learning methods typically focus on modeling the entire dataset at once; however, they may meet the bottleneck of memory and computation as more and more datasets are becoming too large to be handled integrally. The proposed contributions of our work for this task include: (1) Formulate a framework for the scalable robust least-squares regression problem; (2) Propose online and distributed algorithms to handle the adversarial corruption; (3) Provide a rigorous robustness guarantee for regression coefficient recovery; and (4) Conduct extensive experiments for performance evaluations.

For the third method, leveraging the prior knowledge of clean labels in noisy data is actually a crucial issue in practice, but existing robust learning methods typically focus more on eliminating noisy data. However, the data collected by ``weak annotator" or crowd-sourcing can be too noisy for existing robust methods to train an accurate model. Moreover, existing work that utilize additional clean labels are usually designed for some specific problems such as image classification. These methods typically utilize clean labels in large-scale noisy data based on their additional domain knowledge; however, these approaches are difficult to handle extremely noisy data and relied on their domain knowledge heavily, which makes them difficult be used in more general problems. The proposed contributions of our work for this task include: (1) Formulating a framework to leverage the clean labels in noisy data; (2) Proposing a self-paced robust learning algorithm to train models under the supervision of clean labels; (3) Providing a theoretical analysis for the convergence of the proposed algorithm; and (4) Conducting extensive experiments for performance evaluations.

For the fourth method, the presence of data corruption in user-generated streaming data, such as social media, motivates a new fundamental problem that learns reliable regression coefficient when features are not accessible entirely at one time. Until now, several important challenges still cannot be handled concurrently: 1) corrupted data estimation when only partial features are accessible; 2) online feature selection when data contains adversarial corruption; and 3) scaling to a massive dataset. This paper proposes a novel RObust regression algorithm via Online Feature Selection (textit{RoOFS}) that concurrently addresses all the above challenges. Specifically, the algorithm iteratively updates the regression coefficients and the uncorrupted set via a robust online feature substitution method. We also prove that our algorithm has a restricted error bound compared to the optimal solution. Extensive empirical experiments in both synthetic and real-world data sets demonstrated that the effectiveness of our new method is superior to that of existing methods in the recovery of both feature selection and regression coefficients, with very competitive efficiency.

For the fifth method, existing self-paced learning approaches typically focus on modeling the entire dataset at once; however, this may introduce a bottleneck in terms of memory and computation, as today's fast-growing datasets are becoming too large to be handled integrally. The proposed contributions of our work for this task include: (1) Reformulate the self-paced problem into a distributed setting.; (2) A distributed self-paced learning algorithm based on consensus ADMM is proposed to solve the textit{SPL} problem in a distributed setting; (3) A theoretical analysis is provided for the convergence of our proposed textit{DSPL} algorithm; and (4) Extensive experiments have been conducted utilizing both synthetic and real-world data based on a robust regression task.

For the last method, personality prediction in multiple factors, such as openness and agreeableness, is growing in interest especially in the context of social media, which contains massive online posts or likes that can potentially reveal an individual's personality. However, the data collected from social media inevitably contains massive amounts of noise and corruption. To address it, traditional robust methods still suffer from several important challenges, including 1) existence of correlated corruption among multiple factors, 2) difficulty in estimating the corruption ratio in multi-factor data, and 3) scalability to massive datasets. This paper proposes a novel robust multi-factor personality prediction model that concurrently addresses all the above challenges by developing a distributed robust regression algorithm. Specifically, the algorithm optimizes regression coefficients of each factor in parallel with a heuristically estimated corruption ratio and then consolidates the uncorrupted set from multiple factors in two strategies: global consensus and majority voting. We also prove that our algorithm benefits from strong guarantees in terms of convergence rates and coefficient recovery, which can be utilized as a generic framework for the multi-factor robust regression problem with correlated corruption property. Extensive experiment on synthetic and real dataset demonstrates that our algorithm is superior to those of existing methods in both effectiveness and efficiency.