Click Activate above to run the code cells in this post. This post is a companion to the Sharpe post and is meant to dig deeper into scenarios where randomness helps vs hurts. Let’s formulate a lot of real-world scenarios as: You get a random variable X, which you might have some control over, say its mean or distribution. Life then passes it through some function f, and the outcome you observe is…
I used to assume that more granularity in a system is usually a good thing. More price points, more time slots, more ways for users to express what they want, all of this sounds like efficiency. But two recent examples, one from financial markets and one from booking a sports court, made me realize that granularity is not free. In strategic systems, finer choices can create new ways to game…
Click Activate above to run the code cells in this post. This post covers the widely used, but often misunderstood Sharpe ratio. You must have heard this term in some finance / quant lingo: “Our strategy has a Sharpe of 2” or something like: “We don’t run anything with Sharpe < 1.5 on our books”. Well, what does this actually mean? The Sharpe ratio measures how much return you earn per unit of…
This post is a reflection (can also be read as rant ) on my master’s experience - internship hunting, securing funding, and the in-betweens. It attempts to acknowledge the noise and randomness in feedback loops I encountered during this experience. Note: This post is a bit long and at places specific to Stanford, so feel free to skip to the sections that interest you. Disclaimer: The opinions…
We all shuffle cards, but when is a deck truly shuffled? Firstly, what does ‘truly shuffled’ mean? Secondly, are some shuffles just better than others? We’ll explore mixing times, coupling (a technique for analysing markov chains), and why some shuffles are superior than others. Disclaimer: The content presented is not original research, but rather an attempt to explain already known concepts in a…
Disclaimer: Still a 26 year old, figuring out life. This is not some life-changing advice, just a thought that’s helped me. A lot of us implicitly (by our upbringing / parents choices) or explicitly (our own thought process) do what I describe below already. Things that are both hard and fun . Hard is often a proxy of what society values and rewards. For example, becoming a doctor, lawyer, or a…
If you think “hashing is just for lookups”, then this post is your red pill . This two-part series explores how hashing is used beyond hashmaps - in settings where randomness and probabilistic reasoning are the real heroes. In this first part, we will see 2 examples where hashing is used to simulate uniformity, even when the input is highly structured or biased and helps in estimating the…
Proving that something exists, but being too lazy to find it. I am currently taking a course on “Discrete Probabilistic Methods” where we deal with problems of the form: Prove some object X exists with Y properties? Proving the existence of an object with certain properties is often much simpler than actually constructing or finding that object. The tools we use to make these concrete,…
Trusting hardness of problems to keep your crpto safe It’s widely known that 1-way hash functions , particularly SHA-256 , are the cornerstone of modern cryptography. What is a 1-way hash function? A 1-way hash function is a function H(x) where given H(x), finding a corresponding x (even if it’s not unique) is computationally infeasible, requiring brute force on the order of ~2^256 for SHA-256…
Herd mentality meets game theory In my class on “Incentives in CS”, one of the most interesting concepts I came across was on information cascading. This post attempts to describe the concept by discussing improving iterations over a toy-example. We encounter many settings where individuals rely not just on their own observations but also on others’ decisions to make assessments. For instance, in…