## Posts

Showing posts from March, 2014

### Linear Regression, Transforms and Regularization

This write up is about the simple linear regression and ways to make it robust to outliers and non linearity. The linear regression method is a simple and powerful method. It is powerful because it helps compress a lot of information through a simple straight line. The complexity of the problem is vastly simplified. However being so simple comes with its set of limitations. For example, the method assumes that after a fit is made, the differences between the predicted and actual values are normally distributed. In reality, we rarely run into such ideal conditions. Almost always there is non-normality and outliers in the data that makes fitting a straight line insufficient. However there are some tricks you could do to make it better.

Statistics: A good book to learn statistics

As an example data set consider some dummy data shown in the table/chart below. Notice, value 33 is an outlier. When charted. you can see there is some non-linearity in the data too, for hig…

### The Lazy Apprentice

Q: A shopkeeper hires an apprentice for his store which gets one customer per minute on average uniformly randomly. The apprentice is expected to leave the shop open until at least 6 minutes have passed when no customer arrives. The shop keeper suspects that the apprentice is lazy and wants to close the shop at a shorter notice. The apprentice claims (and the shopkeeper verifies), that the shop is open for about 2.5hrs on average. How could the shopkeeper back his claim?

Statistics: A good book to learn statistics

A: Per the contract, at least 6 minutes should pass without a single customer showing up before the apprentice can close the shop. To solve this lets tackle a different problem first. Assume you have a biased coin with a probability $$p$$ of landing heads. What is the expected number of tosses before you get $$n$$ heads in a row. The expected number of tosses to get to the first head is simple enough to calculate, its $$\frac{1}{p}$$. How about two head…