Inhalt

•  
   Notation
•  
  Basic concepts
•  
   Regression
•  
  Classification
•  
   The classification problem
•  
   Hypothesis
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   Risk minimization
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   Risk minimization and maximum likelihood
•  
   Bayesian model averaging
•  
   Outlook
•  
   Exercises
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   Bayes classifier
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   The optimum Bayes classifier
•  
   Outlook
•  
   Naive Bayes classifier
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   Gaussian naive Bayes classifier
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   Generative vs. discriminative models
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   Exercises
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  K-nearest neighbors model
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   K-nearest neighbors classifier
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   K-nearest neighbors regression model
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   Parametric vs. non-parametric models
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   Outlook
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   Exercises
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  Linear regression
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   Modeling
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   Hidden bias
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   Cost function
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   Convexity
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   Optimization
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   Closed form solution
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   Iterative solution
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   Feature transformation
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   Regularization
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   Closed form solution
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   Iterative solution
•  
  Probabilistic interpretation
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   Noisy outputs
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   Maximum likelihood
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   Maximum a posteriori
•  
   Robust regression
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   Huber regression
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   Least absolute deviations
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   Sparsity regularization
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   Details on LASSO
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   Elastic net
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   Optimization
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   Bayesian linear regression
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   Conjugate priors
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   Kernel regression
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   Dual form of ridge regression
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   Kernels
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   Outlook
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   Exercises
•  
  Logistic regression
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   Modeling
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   Cross entropy and information theory
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   Convexity
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   Optimization
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   2. Order methods
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   Separating hyperplane
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   Feature transformation, regularization & kernelization
•  
   Outlook
•  
   Exercises
•  
  Tree based models
•  
  Decision trees
•  
   Model
•  
   Fitting
•  
  Regression trees
•  
   Fitting
•  
   Random forest
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   Feature relevance
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   Outlook
•  
   Exercises
•  
  Evaluation
•  
  Metrics
•  
   Regression
•  
   Classification
•  
  How to estimate scores
•  
   Train - Test split
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   Cross validation
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   Overfitting & Underfitting
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   Model selection
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  Feature selection
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   Wrapper methods
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   Filter methods
•  
   Embedded methods
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   Exercises
•  
  Dimensionality reduction
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   PCA
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   Derivation - Reconstruction error
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   Derivation - Diagonal covariance matrix
•  
   Kernelized PCA
•  
   Outlook
•  
   Exercises
•  
  Clustering
•  
   K-means
•  
   K-means++
•  
   Voronoi tessellation
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   Agglomerative Clustering
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   DBSCAN
•  
   Spectral clustering
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   Gaussian mixture model
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   Details on the EM-algorithm
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   Outlook
•  
   Exercises
•  
   Appendices
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  Convex optimization
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   Convex set
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   Convex functions
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   Local vs. global optimum
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   Convexity preserving operations
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   Examples
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   Subdifferential
•  
  Convex optimization
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   Closed form solution
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   Gradient descent
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   Intuition behind gradient descent
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   Newton's method
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   Quasi-Newton methods
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   Choosing the step length
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   Coordinate descent
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  Linear programming
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   Example
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  Quadratic programming
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   Eample
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   Lagrangian duality
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   Optimality conditions
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   Example
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   Outlook
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   Exercises
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  Probability theory & Statistical inference
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   Basic probability
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   Conditional probabilities
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   Independence
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  Random variable
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   Algebraic operations
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   Cumulative distribution function
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  Probability distributions
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   Discrete distributions
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   Continuous distributions
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  Expectation
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   Expected value
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   Variance
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   Covariance
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   Transformation
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   Conditional expectation
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   Independence
•  
   Moments
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   Moment-generating function
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  Upper bounds
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   Jensen's inequality
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   Chebyshev's inequality
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   Markov's inequality
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   Chernoff bound
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   Hoeffding's inequality
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   Cauchy–Schwarz inequality
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   Union bound
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   Law of large numbers
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   Central limit theorem
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  Information theory
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   Entropy
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   Kullback-Leibler divergence
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   Mutual information
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   Cross entropy
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  Inference
•  
   Estimator
•  
   Bootstrapping
•  
  Constructing estimators
•  
   Method of moments
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   Maximum likelihood
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   Bayesian inference - Maximum a posteriori
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   Outlook
•  
   Exercises