We often come across mathematical expressions represented via matrices and assume that numerical calculations exactly happen the way expressions appear. Let’s take for example These are the well known “normal equations” to compute regression coefficients. One might look at this expression and conclude that the code that computes beta inverts the Gramian matrix XTX and then multiplies the inverse with XTy. Totally false. Why? The condition number of the Gramian matrix XTX equals square of the condition number of X.

I was looking for something in my old stack of books when I stumbled on to Sheldon Axler’s fantastic book, ‘'Linear Algebra Done Right". I have fond memories about the book. I think the last time I referred to this book was more than 3.5 years ago. Took a few hours to go over the book again. Like wine that tastes better when aged, I think some books also give the same kind of effect, at least to me.

Our intuition does not serve well in high dimensional spaces. Hence there are few issues with using nearest neighbor methods on high dimensional data. Firstly, the methods that involve capturing a fixed neighborhood around the points gives a high variance for the fit. Secondly, if you relax the fixed neighborhood criterion and try to capture a specific number of neighbors, the methods are no longer local. Hence it pays to think through these issues on whatever dataset you are working on.

Via Tall Tales : [youtube https://www.youtube.com/watch?v=tWfXP0DMgfE?rel=0]

via humansofmumbai : Studying here in Poddar galli (Abhyaas Gali Path) under a street lamp is my choice and its not only mine but for many students who come here in the night to study, the main reason being the environment and the peace which this lane gives me. This place is silent and one can study whatever one want, one don’t see the time, whenever one wants to come, one comes and there is undisturbed studying here.