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Topics in Modern Statistics

(0365.4044)

Lecturer Prof. Felix Abramovich ( felix@tauex.tau.ac.il)
Lecture Hours Monday 13-16, Schreiber 008

Topics:

  • Nonparametric Regression
    • Univariate Nonparametric Regression
      • kernel estimation
      • local polynomial regression
      • smoothing splines
      • generalized Fourier series
        • polynomial series
        • Fourier series
        • wavelets
    • Multiple Nonparametric Regression
      • extensions of univariate methods, curse of dimensionality
      • structural constraints: additive models, backfitting algorithm, single index models, projection pursuit
      • neural networks, deep neural networks
  • Classification
    • misclassification error, Bayes classifier
    • empirical risk minimization, VC-dimension, fundamental theory of statistical learning
    • plug-in classifiers: discriminant analysis, logistic regression, multinomial logistic regression
    • support vector classifiers, support vector machines (SVM)
    • k-nearest neighbour
    • neural networks, deep neural networks
    • classification trees (CART)
    • ensemble classifiers: bagging, boosting, random forests
  • Clustering (unsupervised learning)
    • combinatorial algorithms, K-means, K-medoids
    • convex clustering
    • hierarchical clustering: agglomerative and divisive methods
    • model-based clustering

Literature

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