Collection of implementations of various statistical / ML techniques and models

Python modules

A collection of python modules exists here for training machine learning mdoels using Numpy.

• DataGenerator.py - A module (object) for generating matrices of synthetic data with one or more features (X) and a response variable (y) with a specified relationship. Currently, these are the supported data generation methods: \
  • DataGenerator.x - The data to be used. Currently, the X data is generated from the Uniform Distribution, by dcefault the Standard Uniform U[0,1]. This can be changed by setting the domain argument to a tuple like (min,max) when instantiating a DataGenerator object.
  • generate_linear(intercept, weights): $y = β_0 + β_1x_1 + β_2x_2 + ... + β_nx_n$
  • generate_polynomial(degrees, coefficients): with added polynomial transformations of the feature(s), that is $y = β_0 + β_1x_1 + β_1x_1^2 + β_2x_2 + \beta_{2}x_{2}^{2}+...+\beta_{n}x_{n}^{n}$
  • generate_synthetic_logisticregression(degrees, coefficients, threshold=0.5) - Generates polynomial X data, with an added transformation via the sigmoid function $\sigma(x)=\frac{1}{1+e^{-x}}$. These probabilities are then thresholded in a binary manner, the threshold of which can be changed via the threshold arg (default=0.5).

Books referenced:

• Peter Dalgaard - Introductory Statistics with R

TODO:

Right now the polynomial models are essentially cheating, since we give it the exact model complexity it needs to predict f. Fix: add a parameter for modek complexity; it would represent essentially the number of exponents you need to raise the data to (add addtl cols).