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Machine Learning

Distributions and LDA

Study of approximations of continuous probability distributions with discrete ones and evaluation of LDA linear frontiers.

Course: Computational StatisticsCo-authors: Javier Mendoza
Distributions and LDA

Objectives

  • 1Visualize the approximation of a continuous probability distribution with a discrete one.
  • 2Relate the approximation error with the parameter of number of approximation rectangles.
  • 3Study the effect of sample size on the approximation error.
  • 4Evaluate linear frontiers of LDA in non-linear frontiers of bivariate normal distributions.

Conclusions

  • As the sample size increases, the shape of the distribution approaches the theoretical model.
  • The error in the mean tends to be very high for very small sample sizes.
  • The linear borders of LDA can approximate simple nonlinear borders, as long as the data are not superimposed.

Technologies

  • Matplotlib
  • Scipy
  • NumPy
  • Seaborn
  • Pandas
  • FastAPI