Differential Privacy (DP) is, by now, the most widely adopted formal model of privacy protection used in industry [L23] and government [ABS22] but my sense is that its “semantics”, especially in the presence of correlated data and in the adversarial interactive setting, is still not broadly understood in the community, especially among practitioners. In the … More What Can Differential Privacy Actually Protect?
The Bretagnolle-Huber Inequality provides a bound on the total variation distance between two probability distributions in terms of their Kullback-Leibler divergence, and it is better than Pinsker’s Inequality when the KL divergence is larger than two, and it is never vacuous, as shown in this figure from [Canonne2023]. The following is an elementary proof, which … More Notes on the Bretagnolle-Huber Inequality
In this post on the last day of the year, I thought I will share a map of mathematical structures that are useful for thinking about knowledge representation and reasoning (KRR) issues in Artificial Intelligence and Machine Learning. It is built on top of the diagram shown in Max Tegmark’s paper Is “the theory of … More A Map of Mathematical Structures for AI
A few of us have been working with homomorphic encryption for a number of years now, but we never found a paper / book that covers all the foundational mathematical material in one place. So we decided to write one — well my postdoc Kelvin Yang Li decided to write one and Mike Purcell and I assisted … More A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption
Cyclotomic polynomials are widely used in the construction of lattice cryptography and homomorphic encryption schemes based on the Ring Learning With Error problem. In this short note, Kelvin Li and I attempt a self-contained introduction to the cyclotomic polynomials and the Galois groups of cyclotomic extensions.
Data Scientists, because of the versatility and range of their skills, can suffer from the paradox of choice when it comes to choosing a career. According to Barry Schwartz, a strategy for good decision-making when there is an abundance of choices will involve these steps, executed in a way that takes careful consideration of all … More What Kind of a Data Scientist Are You?
I have gone through quite a few articles over the last 12 months in my attempt to get a proper understanding of fully homomorphic encryption (FHE) schemes. The process was somewhat frustrating because most of the articles are either too basic, giving just very high-level intuitions, or too deep, assuming too much background on the … More Useful Technical Tutorials on Fully Homomorphic Encryption
Many beginning researchers find it hard to cope with the sheer amount of reading they have to do to come up to speed in a certain technical field, and the issue is often compounded by the “lacking the prerequisites to the read the prerequisites” problem due to inadequate mathematical training at the undergraduate level. Here’s … More A Note on Problem Solving for Young Researchers
Identify a problem that would benefit from using R Read An Introduction to R by Venables, Smith, and the R Core Team Work on solving the identified problem using R Get access to resources with lots of R code templates for solving different problems (e.g. Handbook of Statistical Analysis using R by Everitt and Hothorn and Data … More The Learn-R Algorithm
Mental Models 4 Life 