# The Maths Behind Logistic Regression

Let’s have a look at this god-tier math puzzle. Only one out of seven gets it right, and the other six don’t. So, what are the odds for solving it correctly? 1 to 6. Generally, if $$p$$ is the probability that someone will get it right, then his/her odds are $$p/(1-p)$$.

However, it isn’t necessarily true that $$p=1/7$$ for every person because some people are smarter, some have better education and so on. Hence, $$p$$ also depends on the person attempting the puzzle. In a Bayesian framework, we capture this dependence with conditional probability.

# Want to Fight Climate Change? Don’t Waste Food

A few days ago, my roommate and I were getting dinner at an Japanese restaurant. While we waited for food, we were having a brief discussion about the recent heat waves in Europe. Both of us felt very sad about these changes. Continue reading Want to Fight Climate Change? Don’t Waste Food

# A Week of Poetry: Day 4

By Shel Silverstein

And so did he.
He kept it hid
And so did she.
They searched for blue
Their whole life through,
Then passed right by-
And never knew.

# A Week of Poetry: Day 3

### Sonnet 130

By William Shakespeare

My mistress’ eyes are nothing like the sun;
Coral is far more red than her lips’ red;
If snow be white, why then her breasts are dun;
If hairs be wires, black wires grow on her head.
I have seen roses damask’d, red and white,
But no such roses see I in her cheeks; Continue reading A Week of Poetry: Day 3

# A Week of Poetry: Day 2

By Robert Frost

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

# A Week of Poetry: Day 1

I love poetry. Did I ever tell you that? Not really.

I also enjoy world-building, philosophy, travelling to new places, but I never write about any of my experiences. I don’t write about myself much.

Twenty years later, Continue reading A Week of Poetry: Day 1

# An Online Algorithm to Check for Bipartite Graphs

### Bipartite Graphs

A graph $$G(V, E)$$ is called bipartite if its vertices can be divided into two groups $$X$$ and $$Y$$ such that every edge connects one vertex from $$X$$ and one vertex from $$Y$$. The graph drawn below is bipartite.

Given a graph, can you determine if it is bipartite? Continue reading An Online Algorithm to Check for Bipartite Graphs

# How Game of Thrones Should Have Ended

This is a very unusual post for this blog. I hope my regular readers will bear with me.

I love Game of Thrones. I have read the books and the companion novels. I have been following the series for years. I am familiar with most of the fan theories too. Tonight the series finale aired. I didn’t like how the show ended. It felt rushed and very baffling. Continue reading How Game of Thrones Should Have Ended

# A Blind Robot Beside an Infinite Wall

Let’s think about the following problem:

Consider a wall that stretches to infinitely in both directions. There is a robot at position $$0$$ and a door at position $$p\in\mathbb Z$$ along the wall $$(p\neq 0)$$. The robot would like to get to the door, but it knows neither $$p$$, nor the direction to the door. Furthermore, the robot cannot sense or see the door unless it stands right next to it. Give a deterministic algorithm that minimizes the number of steps the robot needs to take to get to the door.

This problem quite famous Continue reading A Blind Robot Beside an Infinite Wall

# Prime Counting Function and Chebyshev Bounds

The distribution of primes plays a central role in number theory. The famous mathematician Gauss had conjectured that the number of primes between $$1$$ and $$n$$ is roughly $$n/\log n$$. This estimation gets more and more accurate as $$n\to \infty$$. We use $$\pi(n)$$ to denote the number of primes between $$1$$ and $$n$$. So, mathematically, Gauss’s conjecture is equivalent to the claim

$\lim_{n\to\infty}\frac{\pi(n)}{n/\log n}=1$