Posts

Formula student driverless

What is formula student? Studying at the Mechanical Engineering building at the TU Delft, formula student is a well known term. In Delft, every year a group of highly motivated students put their studies on hold to build a race car completely from scratch! They don’t just build it for the heck of it, but the goal is to make a better car than competing univserities throughout the world and win first place in multiple student engineering competitions.

Generalized Linear Models

In my previous posts I have talked about linear and logistic regression. Today I will talk about the broader family of models to which both methods belong Generalized Linear Models. To work our way up to GLMs, we will begin by defining the exponential family. The exponential family: A class of distributions is in the exponential family if it can be written in the form: $$ p(y;\eta) = b(y) \text{exp}(\eta^T T(y) - \alpha(\eta)) $$ More information can be found here

Logistic Regression

Logistic regression Logistic regression unlike linear regression is well suited for classification type problems. The difference lies in the way data is fitted, instead of a linear (hyper)plane it is fitted using the following exponential function (also known as the sigmoid function): \[\begin{aligned} h_{\theta}(x) = \dfrac{1}{1 + \exp{(-\theta^Tx)}} \end{aligned}\] This function has the nice property that, its output is bound between zero and one. This is a usefull property when trying to model the (posterior) probability of something.