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Topic outline

  • סילבוס וספרים מומלצים

    Computational Physics (Graduate Level) – Syllabus / Ely D. Kovetz 05.03.2023

    1. Lightning Review (Reminder) of Probability and Statistics: Probability, Bayes' theorem. Random variables. Monte Carlo integration. Descriptive statistics. Common distributions. Central limit theorem. Multivariate pdfs. Correlation coefficients. Sampling from arbitrary pdfs. 
    2. Lightning Review (Reminder) of Frequentist Statistical Inference: Frequentist vs Bayesian inference. Maximum likelihood estimation. Homoscedastic Gaussian data, Heteroscedastic Gaussian data, non Gaussian data. Maximum likelihood fit. Role of outliers. Goodness of fit. Model comparison. Gaussian mixtures. Boostrap and jackknife. Hypotesis testing. Comparing distributions, KS test. Histograms. Kernel density estimators. 
    3. Bayesian Statistical Inference: The Bayesian approach to statistics. Prior distributions. Credible regions. Parameter estimation examples (coin flip). Marginalization. Parameter estimation examples (Gaussian data, background). Model comparison: odds ratio. Approximate model comparison. Monte Carlo methods. Markov chains. Burn-in. Metropolis-Hastings algorithm. MCMC diagnostics. Trace plots. Autocorrelation length. Samplers in practice: emcee and PyMC3. Gibbs sampling. Conjugate priors.  Evidence evaluation. Model selection. Nested sampling. Samplers in practice: dynasty. 
    4. Introduction to Data mining and machine learning: Supervised and unsupervised learning. Examples. 
    5. Clustering: K-fold cross validation. Unsupervised clustering. K-Means Clustering. Mean-shift Clustering. Correlation functions. 
    6. Dimensional Reduction: Curse of dimensionality. Principal component analysis. Missing data. Non-negative matrix factorization. Independent component analysis. 
    7. Density estimation: Non-linear dimensional reduction. Locally linear embedding. Isometric mapping. t-distributed stochastic neighbor embedding. Data visualization. Recap of density estimation. KDE. Nearest-Neighbor. Gaussian Mixtures.
    8. Regression: Linear regression. Polynomial regression. Basis function regression. Kernel regression. Over/under fitting. Cross validation. Learning curves. Regularization. Ridge. LASSO. Non-linear regression. Gaussian process regression. Total least squares. 
    9. Classification: Generative vs discriminative classification. Receiver Operating Characteristic (ROC) curve. Naive Bayes. Gaussian naive Bayes. Linear and quadratic discriminant analysis. GMM Bayes classification. K-nearest neighbor classifier. Logistic regression. Support vector machines. Decision trees. Bagging. Random forests. Boosting.  Chapter may be significantly shortened
    10. Deep learning: Loss functions. Gradient descent, learning rate. Adaptive boosting. Neural networks. Backpropagation. Layers, neurons, activation functions, regularization schemes. TensorFlow, keras, and pytorch. Convolutional neural networks. Autoencoders. Generative adversarial networks.  Chapter may be shortened
    11. Quantum Many-Body Systems: Introduction. Direct Sampling. Phase transition and critical exponents. Quantum MCMC: world-line representation, Stochastic series expansion, Fermion sign problem. Exact Diagonalization. Tensor network approaches: Microscopic and macroscopic entanglement, Matrix product states.  Matrix Solutions of the GP equation. Wigner functions. Density matrix renormalization group.
    12. Discrete Fourier Transform. Sampling. Inverse FT. Aliasing. Leakage. FFTlog.

    Main Course Textbook: 

    "Statistics, Data Mining, and Machine Learning in Astronomy", Željko, Andrew, Jacob, and Gray. Princeton University Press, 2012.

    The code to reproduce the figures in the book can be found here.

    Additional Resources:

    Python Programming:

    • פרוייקטים

      במהלך הקורס, על הסטודנטים לבצע שני פרוייקטים.

      פרוייקט פסח בהיקף של 20 נקודות. יכלול ניתוח נתונים בעזרת MCMC.

      פרוייקט סיום בהיקף של 30 נקודות. יכלול ניתוח נתונים בעזרת שיטות קלסיפיקציה, רגרסיה ולמידת מכונה.