This course builds on Statistical Computing I to cover advanced computational techniques for modern statistical analysis, machine learning, and artificial intelligence. Emphasis is placed on scalability, algorithmic design, and integration of cutting-edge AI tools for statistical applications. Students will see both theoretical foundations and practical implementation using high-performance computing resources.
Athena Title
Statistical Computing II
Prerequisite
STAT 8060
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Student learning Outcomes
By the end of this course, students will be able to develop and optimize machine learning algorithms, including stochastic gradient descent, Adam, and backpropagation, for large-scale statistical learning problems.
By the end of this course, students will be able to apply advanced Monte Carlo techniques, including Hamiltonian Monte Carlo and sequential Monte Carlo, to complex statistical models.
By the end of this course, students will be able to implement kernel-based learning methods for high-dimensional data analysis.
By the end of this course, students will be able to design and analyze large-scale subsampling and sketching algorithms for efficient computation with massive datasets.
By the end of this course, students will be able to develop scalable AI and machine learning pipelines integrating modern deep learning architectures and GPU acceleration.
By the end of this course, students will be able to integrate multiple computational techniques to solve advanced statistical problems.
By the end of this course, students will be able to communicate results effectively through technical reports, visualizations, and reproducible computational workflows.
Topical Outline
Machine Learning Algorithms: Introduction to optimization for machine learning; Stochastic Gradient Descent and its variants; Adam (Adaptive Moment Estimation) and momentum-based optimization; Backpropagation for neural network training; Convergence issues and techniques for large-scale learning problems
Advanced Monte Carlo and Optimization: Hamiltonian Monte Carlo, NUTS, and sequential Monte Carlo; Constrained and global optimization methods (interior-point, simulated annealing)
Kernel Methods: Kernel trick and feature space mappings; Kernel regression, density estimation, and PCA; Support vector machines for classification and regression
Subsampling and Sketching for Large-Scale Data: Randomized algorithms for matrix approximation; Subsampling for regression and generalized linear models; CountSketch, Frequent Directions, and Nyström methods; Trade-offs between computational efficiency and statistical accuracy
Introduction to AI in Statistical Computing: Neural network architectures beyond feed-forward (e.g., CNNs, RNNs, Transformers); Overview of reinforcement learning for decision-making problems; Integrating statistical models with AI systems
High-Performance Computing in Statistics: GPU acceleration for kernel methods, deep learning, and Monte Carlo simulations; Distributed computing frameworks for large-scale models; Case studies of large-scale applications in science, engineering, and business
Institutional Competencies Learning Outcomes
Analytical Thinking
The ability to reason, interpret, analyze, and solve problems from a wide array of authentic contexts.
