Doctor of Philosophy in

Assumed knowledge: Prior to undertaking an internship opportunity, students must have successfully completed 24 credit hours. 

Course description: The MBZUAI internship with industry is intended to provide the student with hands-on experience, blending practical experiences with academic learning. 

Course description: This course will prepare students to produce professional-quality academic research and solve practical research challenges based on innovative and ethical research principles. This course will provide exposure to a variety of research topics related to AI, research integrity, AI ethics, and organizational challenges. Students will learn to assess their own research projects and scrutinize the research methods and metrics used in their research and critically examine the ethical implications of their work. They will learn about the peer-reviewing process, participate in reviewing their classmates’ work, and learn best-practice for oral and written presentation of research. After completing the course, students will have the skills to develop a research methodology and conduct research that is rigorous and ethical. 

Assumed knowledge: Course work plus a pass in the qualifying exam. 

Course description: Ph.D. thesis research exposes students to cutting-edge and unsolved research problems, where they are required to propose new solutions and significantly contribute towards the body of knowledge. Students pursue an independent research study, under the guidance of a supervisory panel, for a period of three (3) to four (4) years. Ph.D. thesis research helps train graduates to become leaders in their chosen area of research through partly supervised study, eventually transforming them into researchers who can work independently or interdependently to carry out cutting edge research.

Assumed knowledge: Calculus and linear algebra. A calculus-based introduction to probability theory. 

Course description: This course provides an advanced course on probability theory and stochastic processes essential for modeling a variety of real-world scenarios involving uncertainty and randomness. Students will become experts in the language of probability theory, enabling them to effectively analyze and address complex challenges in both pure and applied sciences. Through practical problem solving, they will harness the power of probabilistic thinking to derive insightful solutions. 

Assumed knowledge: Calculus and linear algebra. Measure-based probability theory. An introductory course in statistics is recommended. 

Course description: This course explores statistics based on the principles of probability theory. It takes an in-depth look at the mathematical foundations of decision theory and provides students with tools and techniques for constructing estimators, hypothesis tests, and confidence regions. The course also focuses on the exploration of empirical process theory, emphasizing key optimality results of likelihood methods. In addition, the course highlights several key areas of statistics, such as resampling techniques and nonparametric statistics. 

Assumed knowledge: The course requires a good level of mathematical maturity. Students are expected to have a working knowledge of core concepts in probability theory (basic properties of probabilities such as union bounds, and of conditional expectations, such as the tower property; basic inequalities, such as Markov’s and Jensen’s), statistics (confidence intervals, hypothesis testing), and linear algebra (matrix-vector operations, eigenvalues and eigenvectors; basic inequalities, such as Cauchy-Schwarz’s and Hölder’s). Previous exposure to machine learning is recommended. 

Prerequisite course/s: SDS8102 Advanced Mathematical Statistics 

Course description: This course delves into the theoretical core of statistical learning through a rigorous exploration of algorithmic paradigms, statistical learning frameworks, and optimization strategies. This course provides a principled foundation, enriched by the study of high-dimensional probability and statistics, preparing students to navigate and innovate within the statistical learning landscape. 

Course description: This course prepares Ph.D. students to tackle scientific questions using data within the modern data science life cycle. It emphasizes critical thinking, computational methodology, and trustworthy, reproducible practices. Through open-ended labs in Python students will explore exploratory data analysis, model formulation and validation, simulation, and interpretation, while critically examining the assumptions underpinning standard statistical models and methods. The class will culminate in a group project. 

Assumed knowledge or preparation: Coursework and a pass in qualifying exam.

Course description: Ph.D. thesis research exposes students to cutting-edge and unsolved research problems, where they are required to propose new solutions and significantly contribute towards the body of knowledge. Students pursue an independent research study, under the guidance of a supervisory panel, for a period of three (3) to four (4) years. Ph.D. thesis research helps train graduates to become leaders in their chosen area of research through partly supervised study, eventually transforming them into researchers who can work independently or interdependently to carry out cutting-edge research.

Course description: This course will prepare students to produce professional-quality academic research and solve practical research challenges based on innovative and ethical research principles. This course will provide exposure to a variety of research topics related to AI, research integrity, AI ethics, and organizational challenges. Students will learn to assess their own research projects and scrutinize the research methods and metrics used in their research and critically examine the ethical implications of their work. They will learn about the peer-reviewing process, participate in reviewing their classmates’ work, and learn best-practice for oral and written presentation of research. After completing the course, students will have the skills to develop a research methodology and conduct research that is rigorous and ethical.

Assumed knowledge: Prior to undertaking an internship opportunity, students must have successfully completed 24 credit hours. 

Course description: The MBZUAI internship with industry is intended to provide the student with hands-on experience, blending practical experiences with academic learning. 

Assumed knowledge: Basic optimization class. Basics of linear algebra, calculus, trigonometry, and probability and statistics. Proficiency in Python and PyTorch.

Course description: The course covers advanced topics in continuous optimization, such as stochastic gradient descent and its variants, methods that use more than first-order information, primal-dual methods, and methods for composite problems. Participants will read the current state-of-the-art relevant literature and prepare presentations to the other students. Participants will explore how the presented methods work for optimization problems that arise in various fields of machine learning and test them in real-world optimization formulations to get a deeper understanding of the challenges being discussed. Participants will explore how the presented methods work for optimization problems that arise in various fields of Machine Learning and test them in real-world optimization formulations to get a deeper understanding of the challenges being discussed.

Assumed knowledge: Good understanding of basic reinforcement learning (RL). Basics of linear algebra, calculus, trigonometry, and probability and statistics. Proficiency in Python and good knowledge of Pytorch library.

Course description: The course covers advanced topics in reinforcement learning (RL). Participants will read the current state-of-the-art relevant literature and prepare presentations to the other students. Participants will explore how the presented methods work in simplified computing environments to get a deeper understanding of the challenges that are being discussed. Topics discussed include exploration, imitation learning, hierarchical RL, multi agent RL in both competitive and collaborative setting. The course will also explore multitask and transfer learning in RL setting.

Assumed knowledge: Basic knowledge of linear algebra, probability, and statistical inference. Basics of machine learning. Basics of Python (or Matlab) or Pytorch.

Course description: In the past decades, interesting advances were made in machine learning, philosophy, and statistics for tackling long-standing causality problems, including how to discover causal knowledge from observational data, known as causal discovery, and how to infer the effect of interventions. Furthermore, it has recently been shown that the causal perspective may facilitate understanding and solving various machine learning/artificial intelligence problems such as transfer learning, semi-supervised learning, out-of-distribution prediction, disentanglement, and adversarial vulnerability. This course is concerned with understanding causality, learning causality from observational data, and using causality to tackle a large class of learning problems. The course will include topics like graphical models, causal inference, causal discovery, and counterfactual reasoning. It will also discuss how we can learn causal representations, perform transfer learning, and understand deep generative models.

Assumed knowledge: Advanced calculus, and probability and statistics. Proficiency in programming. Foundation of machine learning. Good Knowledge of optimization tools.

Course description: The course focuses on building foundations and introducing recent advances in dimensionality reduction and manifold learning, which are key topics in machine learning. This course builds upon fundamental concepts in machine learning and assumes familiarity with concepts in optimization and advanced calculus. The course covers advanced topics in spectral, probabilistic, and neural network-based dimensionality reduction and manifold learning, as well as contrastive learning and disentangled representation learning. Students will be engaged through coursework, assignments, presentations, and projects.

Assumed knowledge: This Ph.D.-level course assumes familiarity with core concepts in probability theory, including random variables and basic stochastic processes. Students should have prior exposure to fundamental machine learning methods and neural networks, as well as comfort with Python programming, ideally using frameworks such as PyTorch. Basic understanding of ordinary differential equations (ODEs) and elementary numerical methods is advantageous but not strictly required. Advanced concepts such as measure theory, stochastic differential equations, and optimal transport will be briefly reviewed during the course, though some prior exposure would be beneficial to fully engage with the material. 

Prerequisite course/s: ML8101 Foundations of Machine Learning  

Course description: This advanced course offers an in-depth exploration of diffusion models, flow matching, and consistency models, essential tools for state-of-the-art generative AI. Beginning with foundational principles, students will gain rigorous understanding of diffusion processes, stochastic differential equations, and discrete Markov chains, ensuring a robust conceptual framework. We will examine classical and modern diffusion-based generative techniques, such as denoising diffusion probabilistic models (DDPM) and score-based generative modeling (SGM), alongside detailed mathematical derivations and convergence analysis. The course progresses to flow matching, elucidating the connections and contrasts with diffusion methods through explicit mathematical formulations, focusing on optimal transport theory, continuous normalizing flows, and numerical solutions of differential equations governing generative processes. We will then dive deeply into consistency models, analyzing their theoretical foundations, fast sampling techniques, and how they bridge diffusion and flow-based approaches. The course incorporates practical implementations and case studies in Python, ensuring students achieve both theoretical depth and applied proficiency. Upon completion, participants will be equipped with comprehensive knowledge of the mathematics, theory, and practical applications behind diffusion and flow-based generative models, preparing them for advanced research or industry innovation.  

Assumed knowledge: Good knowledge of calculus, linear algebra, and probability and statistics. 

Course description: This course is an advanced course on algorithms for big data that involves the use of randomized methods, such as sketching, to provide dimensionality reduction. It also discussed topics such as subspace embeddings and low rank approximation. The course lies at the intersection of machine learning and statistics. 

Assumed knowledge: Understanding of calculus, algebra, and probability and statistics. Proficiency in Python or similar language. Basic knowledge of machine learning and deep learning.

Course description: This comprehensive Ph.D.-level course explores the intricacies of modern machine learning (ML), with a specific focus on TinyML, efficient machine learning and deep learning. Through an integration of lectures, readings, and practical labs, students will be exposed to the evolution of TinyML from its traditional roots to the deep learning era. This course will introduce efficient AI computing strategies that facilitate robust deep learning applications on devices with limited resources. We will explore various techniques including model compression, pruning, quantization, neural architecture search, as well as strategies for distributed training, such as data and model parallelism, gradient compression, and methods for adapting models directly on devices. Additionally, the course will focus on specific acceleration approaches tailored for large language models and diffusion models. Participants will gain practical experience in implementing large language models (LLMs) on standard laptops.

Assumed knowledge: Understanding of machine learning (ML) principles and basic algorithms. Good knowledge of multivariate calculus, linear algebra, optimization, probability, and algorithms. Proficiency in some ML frameworks, e.g., PyTorch and TensorFlow.

Course description: This graduate course explores a modern branch of machine learning: collaborative learning (CL). In CL, models are trained across multiple devices or organizations without requiring centralized data collection, with an emphasis on efficiency, robustness, and privacy preservation. CL encompasses approaches such as federated learning, split learning, and decentralized training. It integrates ideas from supervised and unsupervised learning, distributed and edge computing, optimization, communication compression, privacy preservation, and systems design. The field is rapidly evolving, with early production frameworks (e.g., TensorFlow Federated, Flower) and active research addressing both theoretical foundations and practical challenges. This course familiarizes students with key developments and practices including:
– Optimization methods for collaborative learning
– Techniques to mitigate communication and computation bottlenecks
– Handling data and systems heterogeneity
– Client and participant selection strategies
– Ensuring robustness, fairness, and personalization
– Preserving privacy in collaborative settings

Evaluation is based primarily on students’ paper presentations and a final project chosen by each student, encouraging hands-on engagement with cutting-edge research and applications.

Assumed knowledge: Advanced course on mathematical statistics. Advanced course on optimization. 

Course description: Deep learning (DL) is an extremely important applied science that, at present, is poorly understood theoretically. We know that neural networks work well but cannot fully explain why. Nevertheless, in recent years, there has been a rapid growth of publications that shed light on the new mathematics underlying DL, and we see now many interesting connections between DL and various other fields, e.g., approximation theory, differential equations, information theory, random matrix theory, statistical physics. This course aims to introduce students to these cutting-edge developments. 

Assumed knowledge: Fundamental courses on machine learning and statistics. 

Prerequisite course/s: Fundamental courses on machine learning and statistics.

Course description: This comprehensive course delves into the intricate theoretical and mathematical underpinnings of generative modeling techniques. It offers a meticulous exploration of a wide spectrum of models, ranging from the fundamental normalizing flows to the advanced denoising diffusion models. Participants will gain a profound understanding of the core principles, enabling them to harness the power of generative modeling for diverse applications. Through a blend of theoretical insights and practical applications, this course equips learners with the knowledge and skills necessary to navigate the cutting-edge landscape of generative modeling, paving the way for innovation and creativity in fields like artificial intelligence, computer vision, and data science.

Assumed knowledge: Advanced course on probability theory. Advanced course on classical mathematical statistics. 

Course description: High-dimensional probability investigates the behavior of high dimensional random objects such as random vectors and random matrices with the emphasis upon quantifying the role of the dimension. The course also introduces some contemporary statistical problems including principal component analysis in high-dimension, sparse linear regression, and community detection.