This is a collection of interactive computational notebooks covering various topics in mathematics of information and machine learning. Some of them have been written entirely by me, some entirely by AI, some are a mix of both. Some of them may be non-interactive because too resource intensive to run in the browser, but they can be downloaded and run interactively.
Mathematics of Information
Discrete Fourier Transform
Interactive visualization of the DFT algorithm with time-domain and frequency analysis, signal decomposition, and frequency bin exploration. Adjust signal components with sliders to see how the time-domain signal changes and visualize frequency bins on the unit circle.
ESPRIT Algorithm
(Work in progress)
Estimation of Signal Parameters via Rotational Invariance Techniques. Explore how the algorithm recovers signal parameters from noisy measurements with adjustable signal parameters and interactive visualization of signal reconstruction.
Finite Rate of Innovation
(Work in progress)
Interactive exploration of signals with finite rate of innovation and their reconstruction frameworks.
Lower Beurling Density
Interactive visualization and analysis of lower Beurling density concepts in signal processing.
Multicoset Sampling
Interactive exploration of multicoset sampling techniques and their applications in efficient signal acquisition.
Intro to Machine Learning
Kernel Methods
Comprehensive exploration of kernels and the kernel trick. Start with explicit feature maps, compare explicit vs kernelized computation, verify the representer theorem, and explore different kernels including polynomial, Gaussian, and Laplacian. Visualize kernel regression and how kernels create non-linear decision boundaries.
Neural Networks
Build and train neural networks from scratch, explore MNIST classification, understand backpropagation, and visualize network behavior with interactive parameters.