USC Probability and Statistics Seminar Courses

Score-based Neural Ordinary Differential Equations and Normalizing Flow for Mean Field Control

Explore a novel approach to Mean Field Control using score-based neural ODEs and normalizing flows, with applications in generative models, probability flow matching, and Wasserstein proximal operators.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Non-convex Matrix Sensing: Breaking the Quadratic Rank Barrier in Sample Complexity

Explore groundbreaking research on non-convex matrix sensing, focusing on improved algorithms for reconstructing low-rank matrices using fewer samples through innovative probabilistic decoupling methods.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Differentially Private M-Estimation via Noisy Optimization

Explore differentially private statistical estimation through noisy gradient descent algorithms, focusing on high-dimensional analysis, robust statistics, and confidence interval construction.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Maximum of Poissonian Log-correlated Fields

Explore extreme values of logarithmically correlated fields with Poissonian tails, revealing sub-leading order behavior distinct from Gaussian fields through branching random walks.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

How to Measure Differences in Rankings

Explore a generalized Mallows model framework that learns distance metrics from data to better understand ranking differences across domains like recommendations and hiring decisions.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

The Dynamics of Iterative Algorithms with Random Data - Beyond First-Order Methods

Explore advanced mathematical techniques for analyzing high-dimensional optimization algorithms, including gradient descent and expectation maximization with rigorous theoretical guarantees.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Jackson's Inequality on the Hypercube - Polynomial Approximation and Applications

Delve into polynomial approximation theory on n-dimensional hypercubes, exploring threshold power, sensitivity theorems, and applications to Markov-Bernstein inequalities.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Are Neural Networks Optimal Approximation Algorithms for Constraint Satisfaction Problems?

Explore neural networks' capability to solve NP-hard optimization problems, focusing on constraint satisfaction and their potential as optimal approximation algorithms.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Foundations for Feature Learning via Gradient Descent

Explore the theoretical foundations of feature learning in modern machine learning models, focusing on gradient descent's role in extracting useful features and representations from data.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Classical and Free Zero Bias for Infinite Divisibility

Explore classical and free zero bias in infinite divisibility with Larry Goldstein, delving into probability theory and statistical concepts.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Continuous-in-time Limit for Bandits

Explore the connection between Hamilton-Jacobi-Bellman equations and multi-armed bandit problems, and discover an efficient algorithm for solving MAB challenges.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

The Atypical Growth in Random Interfaces - KPZ Equation and Unusual Growth Patterns

Explore random interface growth phenomena and the KPZ equation, combining probability, PDEs, and integrable systems to understand unusual growth behaviors.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Sample Amplification: Increasing Dataset Size Even When Learning is Impossible

Explore sample amplification techniques to generate larger datasets from limited samples, even when learning the original distribution is impossible.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Latent Multimodal Functional Graphical Model Estimation

Explore latent graphical model estimation for multimodal functional data, focusing on brain connectivity analysis using simultaneous imaging techniques.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

On the Origin of the Boltzmann Distribution

Explore the unique characterization of the Boltzmann distribution in statistical mechanics, focusing on its independence property for uncoupled systems.

• YouTube
• 56 minutes
• Self-Paced
• Free Video