Lecture Notes

­čôÜAbout This lecture focuses on the theoretical as well as practical aspects of the Support Vector Machines. It is a supervised learning model associated with learning algorithms that analyze data used for classification and regression analysis. Developed at AT&T Bell Laboratories by Vapnik with colleagues (Boser et al., 1992, Guyon […]

Mathematical optimization is a problem that takes the following form (1)   where is a vector containing all the variables of the problem (2)   The function is referred to as the cost or the objective function. Moreover, the functions are referred to as constraint functions. In most cases, our […]

The above lecture is brought to you by Skillshare. In a previous post of mine, we introduced weak alternatives. As a small reminder, consider the following two sets (1)   and (2)   where (3)   is the dual function and is the domain of the problem. Since we did […]

This tutorial is brought to you by DataCamp. The tutorial does the most in rigorously explaining the little bits and pieces of the wonderful Matplotlib. Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python. Matplotlib makes easy things easy and hard things easier. Contents of […]

Let us say we are interested in checking whether system hereby defined as (1)   is feasible or not. In other words, could we find a vector that satisfies set ? In many cases, it may turn out to be hard to answer the question by exhaustively searching all possible […]

In this lecture, we talk about Perturbation and Sensitivity Analysis. But what does that mean ? Well, consider our good old looking optimization problem that looks like this (1)   One way to tell how the above problem reacts to perturbation is to actually perturb it and check how its […]

In this lecture, we talk about equivalent reformulations, that are reformulations done on the initial problem of the form (1)   A very interesting question is the following. Assume we got two problems and that are equivalent problems. Are their duals, (hereby denoted by and , respectively) the same ? […]

SciPy is a free and open-source Python library used for technical computing and scientific computing. SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering. In this lecture, we introduce all SciPy’s functions one will most probably pass through when Jupyter Notebook on Google Chrome, which is one of […]