Topic outline

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  • General

  • Website

    All material related to this course is at github.com/dgerosa/astrostatistics_bicocca_2022

  • Important

    Data mining and machine learning are computational subjects. One does not understand how to treat scientific data by reading equations on the blackboard: you will need to get your hands dirty (and this is the fun part!). Students are required to come to classes with a laptop or any device where you can code on (larger than a smartphone I would say...). Each class will pair theoretical explanations to hands-on exercises and demonstrations. These are the key content of the course, so please engage with them as much a possible.

  • Skeleton

    • [01-02] 2-3-22. Introduction to class. IT setup. git version control
    • [03-03] 7-3-22. Introduction to probability. Bayes theorem. Monty hall problem. Transformation of random variables.  [The recording was interrupted at some point because the connection in the building dropped.]
    • [05-06] 8-3-22. Monte Carlo integrations. Descriptive statistics. Mean vs population quantities. Typical distributions.
    • [07-08] 9-3-22. Central limit theorem. Multivariate pdfs. Correlation coefficients. Sampling from arbitrary pdfs.
    • [09-10] 14-3-22. Frequentist vs Bayesian inference. Maximum likelihood estimation. Omoscedastic Gaussian data, Heteroscedastic Gaussian data, non Gaussian data.
    • [11-12] 15-3-22. Maximum likelihood fit. Role of outliers. Goodness of fit. Model comparison. Gaussian mixtures. Boostrap and jackknife.
    • [13-14] 16-3-22. Hypothesis testing. Comparing distributions, KS test. Histograms. Kernel density estimators.
    • [15-16] 21-3-22. The Bayesian approach to statistics. Prior distributions. Credible regions. Parameter estimation examples. Marginalization. Parameter estimation examples. Model comparison: odds ratio. Approximate model comparison.
    • [17-18] 23-3-22. Monte Carlo methods. Markov chains. Burn-in. Metropolis-Hastings algorithm.
    • [19-20] 28-3-22. MCMC diagnostics. Traceplots. Autocorrelation lenght. Samplers in practice: emcee and PyMC3. Gibbs sampling. Conjugate priors.
    • [21-22] 30-3-22. Evidence evaluation. Model selection. Nested sampling. Samplers in practice: dynesty.
    • [23-24] 4-4.22. Data mining and machine learning. Supervised and unsupervised learning. Overview of scikit-learn. Examples.
    • [25-26] 6-4.22 . K-fold cross validation. Unsupervised clustering. K-Means Clustering. Mean-shift Clustering. Correlation functions. 
    • [27-28] 20-4-22.  Curse of dimensionality. Principal component analysis. Missing data. Non-negative matrix factorization. Independent component analysis.
    • [29-30] 27-4-22. Non-linear dimensional reduction. Locally linear embedding. Isometric mapping. Stochastic neighbor embedding. Data visualization. Recap of density estimation. KDE. Nearest-Neighbor. Gaussian Mixtures. Modern astrostats with Matthew Mould (Birmingham UK) and Riccardo Buscicchio (Milano-Bicocca, Italy). [There are two gaps in the recording because the connection in the building dropped.]
    • [31-32] 2-5-22 What is regression? Linear regression. Polynomial regression. Basis function regression. Kernel regression. Over/under fitting. Cross validation. Learning curves. [And the connection dropped again, so this is another half-recorded lecture. I'm really sorry, but this is so unreliable. I'll look for an offline recording software]
    • [33-34] 4-5-22 Regularization. Ridge. LASSO. Non-linear regression. Gaussian process regression. Total least squares.
    • [35-36] 9-5-22. 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.
    • [37-28] 11-5-22. Logistic regression. Support vector machines. Decision trees. Bagging. Random forests. Boosting.
    • [39-40] 16-5-22 Loss functions. Gradient descent, learning rate. Adaptive boosting. Neural networks. Backpropagation. Layers, neurons, activation functions, regularization schemes.
    • [41-42] 18-5-22 TensorFlow, keras, and pytorch. Convolutional neural networks. Autoencoders. Generative adversarial networks.

  • Recordings