## Gaussian Mixture Models

In this project we explore the Gaussian Mixture models. GMMs are universal approximators. This means that any probability density can be approximated to arbitrary precision using mixture of gaussian densities. We saw a glimpse of it in our Hypothesis Testing II project. GMMs are go-to models for unsupervised learning schemes and one of my favorite ML models. In fact, they utilize (usually) EM algorithm, which is an iterative method of estimating statistical parameters similar to and I belive, on par with, backpropagations in Neural nets. In this...

## Neural Nets I

This project is an exercise in building ANN architectures from scratch and writing Backpropagation in numpy. MNIST: Our numpy ANN with 1 hidden layer with only 30 nodes on 10 classes handwritten digit MNIST dataset achieves test error of 4.4% (accuracy 95.6% !!). ...

## Camera Calibration

In this project, I use simple manual camera calibation method. The setup is as follows: Assuming pin hole camera, we can utilize similar triangle methods(see below), and can come up with focal lengths equation: # fx = (dx/dX) * dZ , fy = (dy/dY) * dZ where dX, dY are the physical length & width of the object in view and dZ is the distance from object to camera. dx and dy are the corresponding pixel width & height of the object...

## Hypothesis Testing III – Bayesian Methods

This project is third in the series of Hypothesis testing project whereby we use Bayesian Methods. Here we reformulate the AB testing problem into MultiArm Bandit and implement 4 widely used algorithms: Epsilon Greedy, Optimistic Initial Conditions, UCB1, and Bayesian (Thompson) Sampling for the AB testing. We then compare and contrast the performance of the algorithms wrt the Bandit problem....

## Hypothesis Testing I

In this project I implement AB test in numpy. I compare the result with scipy's ttest results. This is an exercise in hypothesis testing and we will still be using scipy t & chi squared distribution class to get the t and chi squared cumulative distribution function. The t tests can be one or two sided depending on the parameter input....