## L2 regularization intuition

Posted on Sun 22 January 2023 in Mathematics • Tagged with Mathematics, Machine Learning, Deep Learning

A nice intuition for L2 regularization comes from having a prior on the distribution of parameters: the prior assumes that the parameters are close to zero. Let's assume that the prior is $\mathcal{N}(0, \Sigma)$. The MAP estimate of the parameters would then be

## The JEE never fails to amaze

Posted on Mon 19 September 2022 in Mathematics • Tagged with Mathematics, JEE

I promised I wouldn't look at the JEE 2022 paper, but couldn't help sneaking a peek. As always, the professors currently making life difficult occasionally get a chance to make the life of all of India's students difficult, and they never cease to amaze.

Welp, this will be a short …

## A Note on Conditional Probability

Posted on Sat 25 December 2021 in Mathematics • Tagged with Mathematics


## A Note on Random Variables

Posted on Fri 03 December 2021 in Mathematics • Tagged with Mathematics

## ISC 2020 Analysis: An application of Data Science and Statistics

Posted on Sat 11 July 2020 in Mathematics • Tagged with Mathematics, ISC, Data Science

The ISC Exam results were released on 10th June, 3 PM IST. In this article, I'll be analyzing the results of the 117 students in the science stream of my school and showing how they performed. I'll also weave a story with the data and point out things that could …

## Solving the African Integral (from YG file cover)

Posted on Thu 09 July 2020 in Mathematics • Tagged with Mathematics

A long time ago, I gave my friend (Let's call him C) an integral to solve. He came back to me a few days later and the conversation went something like this:

C: Debu, I couldn't solve that African integral you gave me.
Me: Ok, but why are you calling …

## A Compilation of hard limits

Posted on Fri 05 June 2020 in Mathematics • Tagged with Mathematics

This list consists of the limits that I found most challenging.

1. $$\lim_{n \to \infty} \left( \frac{n!}{n^n} \right) ^\frac 1n$$
2. $$\lim_{x \to 0} \left( \frac{1}{\ln(x + \sqrt{x^2+1})} - \frac 1{\ln(x+1)} \right)$$
3. \lim_{n \to \infty} \frac{n + n^2 …

## Limit involving higher order infinitesimals

Posted on Fri 05 June 2020 in Mathematics • Tagged with Mathematics

Simple limit problems consist of the form $\lim_{x \to 0}\frac{O_1(x)O_2(x)..}{O_a(x)O_b(x)..}$, such as $\lim_{x \to 0} \frac{\sin 3x \tan 2x \tan^{-1} 5x}{x^2 \ln(1+x)}$. Here, the infinitesimals are well defined and cancel out easily. Some …

## COVID-19 USA Analysis: effects of the lack of lockdown

Posted on Fri 29 May 2020 in Mathematics • Tagged with Mathematics, COVID 19

The USA currently stands at 1.76 million COVID-19 cases. That's more than the next 5 nations combined. A large number of these cases are due to government inaction against the virus. The lack of a concerted lockdown across the country is also to blame. Here's a graph showing the …

## COVID 19 Regression analysis Update

Posted on Tue 19 May 2020 in Mathematics • Tagged with Mathematics, COVID 19

The Previous COVID regression analysis was fairly accurate. However, the opening of lockdown offset the statistics a bit and now there are more number of projected cases. Here is a recomputation of the statistics, which projects an average of 172,000 cases by June 1 and 520,000 cases overall …

## No square ends in 3

Posted on Fri 15 May 2020 in Mathematics • Tagged with Mathematics

This is an interesting number theory fact that seems strange when taken at face value. Here's a small proof of it:

## COVID 19 regression analysis

Posted on Wed 06 May 2020 in Mathematics • Tagged with Mathematics, COVID 19

This is a regression analysis attempt for the COVID-19 spread data. The graphs represent total cases per day. The Orange graph is USA, the smaller graph on the left is China and the graph on the right is India. A Standard gaussian curve of the form $Ae^{-b(x-c)^2 … ## Roots of$f(f(..f(x)..))$, where$ f(x) = ax^2 + bx + c $, are symmetric about$ \frac{-b}{2a} $Posted on Thu 30 April 2020 in Mathematics Define$ f(x) = ax^2 + bx + c , a,b,c \in \mathbb{R}$and$ f^n(x) = f(f^{n-1}(x)), n>1 $. Prove that the real roots of$ f^n(x) $are symmetric about the vertical line passing through vertex i.e.$ x = \frac{-b}{2a} \$

This seems like …