Machine Learning Fundamentals

Probability

Correlation Matrices: A plotly vizualization of the space of 3x3 correlation matrices using a nice parametrization

Naive Bayes: Introduction, derivation and reconciliation of Naive Bayes - a baseline model for classification.
Linear / Quadratic Discriminant Analysis: Introduction, derivation, properties and examples of LDA/QDA classification
Logistic Regression: Definitions, Binary and multi-class case, Sigmoid and Softmax functions, Cross-Entropy Loss, Regularization, Examples
Decision Tree Classifiers: Graph theory, binary rooted trees, impurity functions, minimal cost-complexity pruning

Linear Regression: A recap of linear regression - a core fundamental of machine learning.
Local Regression: Local regression is a refinement of linear regression that adapts the model at each point of the prediction.
Gaussian Process Regression (GPR): An advanced regression technique that produces not only predictions, but also confidence bounds around them.
Dynamically Controlled Kernel Estimation (DCKE): A combination of local regression, control variates and Gaussian process regression to estimate conditional expectations. The method is model free, data-driven and particularly suited for financial applications.
Decision Tree Regressors: Decision trees can be used for regression as well

Multilayer Perceptrons (MLP): Introduction to the most common form of artificial neural networks (ANN).
Long-Term-Short-Term-Memory networks (LSTM): Introduction to LSTMs, a popular form of recurrent neural networks (RNNs).
Network Topology Selection: A methodology to choose a topology for a neural network, e.g. the number of hidden layers and units.

Newton's Method: A recap of the Newton's method.
Gradient Descent - Basics: Mathematical foundations and basics of gradient descent.
Gradient Descent - Advanced [@lapislago]: Some illustrations, background and examples of gradient descent.
Backpropagation: Derivation of the backpropagation algorithm.
Adjoint Method: Relationship between backpropagation and the adjoint method.

Learning the Sine [@lapislago]: Simple example of how to use keras and tensorflow to learn a curve.
Learning a 2D function [@lapislago]: A slightly more complex example of how to learn a surface.

How deep are financial models?: Learn the pricing function of Black-Scholes and Heston model. Application of network topology selection.
Neural Network Brain Surgery: Can the difference between the Black-Scholes and the Heston model be visualized as the brains of the networks that learn their pricing function?
Calibrating Heston [@lapislago]: Learn the calibration function of a Heston model using a neural network.
Calibrating Hull-White [@lapislago]: Learn the calibration function of a Hull-White model using a neural network.
Autograd [@lapislago]: A small example on how to automatically differentiate the Black-Scholes pricing formula.