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Lecture
Stochastic Simulation: Metropolis-Hastings Algorithm
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Signals, Instruments, and Systems
Explores signals, instruments, and systems, covering ADC, Fourier Transform, sampling, signal reconstruction, aliasing, and anti-alias filters.
Monte Carlo Techniques: Sampling and Simulation
Explores Monte Carlo techniques for sampling and simulation, covering integration, importance sampling, ergodicity, equilibration, and Metropolis acceptance.
Filtering and Sampling of Signals
Explores filtering signals with a moving average filter and the process of sampling, emphasizing the importance of signal reconstruction from samples.
Signal Sampling: Bandwidth and Spectrum
Introduces signals, frequencies, bandwidth, filtering, and sampling in signal processing.
Implementation of Sampling and Quantization
Covers the generation of signals with noise, sampling, and conversion to digital.
Metrics for Classification
Covers sampling, cross-validation, quantifying performance, optimal model determination, overfitting detection, and classification sensitivity.
Graph Coloring: Theory and Applications
Covers the theory and applications of graph coloring, focusing on disassortative stochastic block models and planted coloring.
Generative Models: Boltzmann Machine
Covers generative models, focusing on Boltzmann machines and constrained maximization using Lagrange multipliers.
Sampling Signals: Stroboscopic Effect (Spectrum Folding)
Covers the consequences of undersampling signals and the stroboscopic effect.
Markov Chains and Algorithm Applications
Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.