Ethan Epperly
@ethanepperly.bsky.social
PhD candidate in applied math at Caltech interested in computational linear algebra he/him
New paper out with Chris Camaño, Raphael Meyer, and Joel Tropp re-examining sketching algorithms! Included: subspace injections as an alternative to subspace embeddings, the theory and practice of sparse sketching, tensor sketching, and much more! arxiv.org/abs/2508.21189
Faster Linear Algebra Algorithms with Structured Random Matrices
To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for low-rank approximation and least-squares regression with structured dimension reduction maps. Despit...
arxiv.org
September 3, 2025 at 5:42 PM
New paper out with Chris Camaño, Raphael Meyer, and Joel Tropp re-examining sketching algorithms! Included: subspace injections as an alternative to subspace embeddings, the theory and practice of sparse sketching, tensor sketching, and much more! arxiv.org/abs/2508.21189
New blog post up about the amazingly useful Gaussian integration by parts formula! As an application, we use it to analyze power iteration from a random start www.ethanepperly.com/index.php/20...
![Gaussian integration by parts. Let z be a standard Gaussian random variable. Then E[zf(z)] = E[f'(z)].](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:choq7wzmsf7n3t6drq3ys27h/bafkreies7hqoujoycvwectbrxkkx4hzkpc6use4tngnlrtwxn7duh6k44y@jpeg)
August 5, 2025 at 5:29 PM
New blog post up about the amazingly useful Gaussian integration by parts formula! As an application, we use it to analyze power iteration from a random start www.ethanepperly.com/index.php/20...
Very excited to share that I’ve been awarded a SIAM student paper prize! I look forward to seeing any of you who will be at #SIAMAN25 in Montréal. Thanks to the committee for selecting me for this honor www.siam.org/publications...
2025 July Prize Spotlight | SIAM
Congratulations to the SIAM prize recipients who will be recognized at AN25, ACDA25, CT25, and GD25!
www.siam.org
July 11, 2025 at 6:28 PM
Very excited to share that I’ve been awarded a SIAM student paper prize! I look forward to seeing any of you who will be at #SIAMAN25 in Montréal. Thanks to the committee for selecting me for this honor www.siam.org/publications...
Reflections on five years of blogging www.ethanepperly.com/index.php/20...
Five Years of Blogging – Ethan N. Epperly
www.ethanepperly.com
July 8, 2025 at 9:37 PM
Reflections on five years of blogging www.ethanepperly.com/index.php/20...
New blog post up about the randomized Kaczmarz algorithm. The classic RK algorithms samples rows according to their squared norms, but what happens if you sample them uniformly? The answer surprised me: Uniform sampling is often just as good or even better www.ethanepperly.com/index.php/20...
June 16, 2025 at 5:25 PM
New blog post up about the randomized Kaczmarz algorithm. The classic RK algorithms samples rows according to their squared norms, but what happens if you sample them uniformly? The answer surprised me: Uniform sampling is often just as good or even better www.ethanepperly.com/index.php/20...
New blog post out about the new Polar Express algorithm of Amsel, Persson, Musco, and Gower for computing the matrix sign function with applications to the Muon optimizer www.ethanepperly.com/index.php/20...
A Neat Not-Randomized Algorithm: Polar Express – Ethan N. Epperly
www.ethanepperly.com
June 7, 2025 at 2:03 AM
New blog post out about the new Polar Express algorithm of Amsel, Persson, Musco, and Gower for computing the matrix sign function with applications to the Muon optimizer www.ethanepperly.com/index.php/20...
New blog post out in my series on Markov chains! In this post, I discuss Poincaré inequalities and their connection to mixing of Markov chains www.ethanepperly.com/index.php/20...
Markov Musings 5: Poincaré Inequalities – Ethan N. Epperly
www.ethanepperly.com
May 24, 2025 at 7:17 PM
New blog post out in my series on Markov chains! In this post, I discuss Poincaré inequalities and their connection to mixing of Markov chains www.ethanepperly.com/index.php/20...
Reposted by Ethan Epperly
🧩 New week, time for our weₐᵉkly quiz! Today, another thing a bit random: Pokémon! Ash and Barry want to catch 'em all: all of them. You know, Pikachu, Jigglypuff, err... Charmander? It's been a while.
So, n Pokémon to catch, and no idea how long it'll take. Gotta help them out! #WeaeklyQuiz
1/
So, n Pokémon to catch, and no idea how long it'll take. Gotta help them out! #WeaeklyQuiz
1/
a bunch of red and white balls in the sky
Alt: A lot of red and white Pokeballs falling from the sky
media.tenor.com
March 10, 2025 at 9:28 AM
🧩 New week, time for our weₐᵉkly quiz! Today, another thing a bit random: Pokémon! Ash and Barry want to catch 'em all: all of them. You know, Pikachu, Jigglypuff, err... Charmander? It's been a while.
So, n Pokémon to catch, and no idea how long it'll take. Gotta help them out! #WeaeklyQuiz
1/
So, n Pokémon to catch, and no idea how long it'll take. Gotta help them out! #WeaeklyQuiz
1/
New blog post with four proofs of the Schur product theorem. Do you know a fifth? www.ethanepperly.com/index.php/20...
February 25, 2025 at 3:23 AM
New blog post with four proofs of the Schur product theorem. Do you know a fifth? www.ethanepperly.com/index.php/20...
New blog post up! In it, I look at the question: how accurate is sketch-and-solve method for least squares? A standard bound suggests the residual is within a 1 + O(η) factor of optimal for an embedding of distortion η. But this isn't the correct answer! www.ethanepperly.com/index.php/20...
Note to Self: How Accurate is Sketch and Solve? – Ethan N. Epperly
www.ethanepperly.com
February 14, 2025 at 7:22 PM
New blog post up! In it, I look at the question: how accurate is sketch-and-solve method for least squares? A standard bound suggests the residual is within a 1 + O(η) factor of optimal for an embedding of distortion η. But this isn't the correct answer! www.ethanepperly.com/index.php/20...
Delightful little tale by Nick Trefethen: people.maths.ox.ac.uk/trefethen/ba...
people.maths.ox.ac.uk
December 16, 2024 at 6:25 AM
Delightful little tale by Nick Trefethen: people.maths.ox.ac.uk/trefethen/ba...
What is your favorite proof of the Cauchy–Schwartz inequality? I wrote about my favorite proof, which uses matrix theory, in a new blog post. Check it out! Also included: a matrix theoretic proof of Jensen’s inequality for 1/x www.ethanepperly.com/index.php/20...
My Favorite Proof of the Cauchy–Schwarz Inequality – Ethan N. Epperly
www.ethanepperly.com
December 12, 2024 at 3:40 PM
What is your favorite proof of the Cauchy–Schwartz inequality? I wrote about my favorite proof, which uses matrix theory, in a new blog post. Check it out! Also included: a matrix theoretic proof of Jensen’s inequality for 1/x www.ethanepperly.com/index.php/20...
Did you know that randomized Nyström approximation of A is equivalent to running the randomized SVD on A⁰ᐧ⁵? This and other surprising facts on this week's blog post on the "Gram correspondence" www.ethanepperly.com/index.php/20...
Low-Rank Approximation Toolbox: The Gram Correspondence – Ethan N. Epperly
www.ethanepperly.com
December 9, 2024 at 5:15 PM
Did you know that randomized Nyström approximation of A is equivalent to running the randomized SVD on A⁰ᐧ⁵? This and other surprising facts on this week's blog post on the "Gram correspondence" www.ethanepperly.com/index.php/20...
This whole “advent of research” series of posts by David is really excellent, but I love this one in particular
The kids and I are going to try the "Skeleton Crew" show in... eight minutes. So today let's see how much I can write about our "advent of research" topic du jour in eight minutes.
We're back to networks today. And physics. And math. A little of all of the above.
We're back to networks today. And physics. And math. A little of all of the above.
December 8, 2024 at 1:10 AM
This whole “advent of research” series of posts by David is really excellent, but I love this one in particular
New blog post up! The randomized Kaczmarz algorithm doesn’t converge for inconsistent systems of linear equations, but—as an estimator for the least-squares solution—it does have an exponentially decreasing bias www.ethanepperly.com/index.php/20...
Randomized Kaczmarz is Asympotically Unbiased for Least Squares – Ethan N. Epperly
www.ethanepperly.com
December 5, 2024 at 5:22 PM
New blog post up! The randomized Kaczmarz algorithm doesn’t converge for inconsistent systems of linear equations, but—as an estimator for the least-squares solution—it does have an exponentially decreasing bias www.ethanepperly.com/index.php/20...
New paper out with Gil Goldshlager and Rob Webber! In it, we show that *tail averaging* can be used to improve the accuracy of the randomized Kaczmarz method for solving least-squares problems. The resulting method, TARK, outcompetes other row-access methods for least squares
December 2, 2024 at 5:06 PM
New paper out with Gil Goldshlager and Rob Webber! In it, we show that *tail averaging* can be used to improve the accuracy of the randomized Kaczmarz method for solving least-squares problems. The resulting method, TARK, outcompetes other row-access methods for least squares
Reposted by Ethan Epperly
Cross-posting this - please join us!
Mailing List link: groups.google.com/g/internatio...
YouTube Channel link: www.youtube.com/@MonteCarloS...
Mailing List link: groups.google.com/g/internatio...
YouTube Channel link: www.youtube.com/@MonteCarloS...
November 30, 2024 at 8:51 PM
Cross-posting this - please join us!
Mailing List link: groups.google.com/g/internatio...
YouTube Channel link: www.youtube.com/@MonteCarloS...
Mailing List link: groups.google.com/g/internatio...
YouTube Channel link: www.youtube.com/@MonteCarloS...
Reposted by Ethan Epperly
A reminder about NY Theory Day in a week! Fri Dec 6th! Talks by Amir Abboud, Sanjeev Khanna, Rotem Oshman, and Ron Rothblum! At NYU Tandon!
sites.google.com/view/nyctheo...
Registration is free, but please register for building access.
See you all there!
sites.google.com/view/nyctheo...
Registration is free, but please register for building access.
See you all there!
Home
About
The New York Theory Day is a workshop aimed to bring together the theoretical computer science community in the New York metropolitan area for a day of interaction and discussion. The Theory Da...
sites.google.com
November 30, 2024 at 5:04 PM
A reminder about NY Theory Day in a week! Fri Dec 6th! Talks by Amir Abboud, Sanjeev Khanna, Rotem Oshman, and Ron Rothblum! At NYU Tandon!
sites.google.com/view/nyctheo...
Registration is free, but please register for building access.
See you all there!
sites.google.com/view/nyctheo...
Registration is free, but please register for building access.
See you all there!
Reposted by Ethan Epperly
Just created the Starter Pack for Optimization Researchers to help you on your journey into optimization! 🚀
Did I miss anyone? Tag them or let me know what to add!
go.bsky.app/VjpyyRw
Did I miss anyone? Tag them or let me know what to add!
go.bsky.app/VjpyyRw
November 23, 2024 at 11:59 PM
Just created the Starter Pack for Optimization Researchers to help you on your journey into optimization! 🚀
Did I miss anyone? Tag them or let me know what to add!
go.bsky.app/VjpyyRw
Did I miss anyone? Tag them or let me know what to add!
go.bsky.app/VjpyyRw
New blog post up presenting some beautiful *exact formulas* for sketched least squares with a Gaussian embedding. These beautiful formulas appear to have only been published as recently as 2020; see post for details! www.ethanepperly.com/index.php/20...
November 21, 2024 at 4:59 PM
New blog post up presenting some beautiful *exact formulas* for sketched least squares with a Gaussian embedding. These beautiful formulas appear to have only been published as recently as 2020; see post for details! www.ethanepperly.com/index.php/20...
Very excited to be attending #NeurIPS2023 next week where I’ll be presenting my work “Kernel quadrature with randomly pivoted Cholesky” with Elvira Moreno. I’ve written a little blog post to explain what kernel quadrature is and what our approach is to it!
Five Interpretations of Kernel Quadrature – Ethan N. Epperly
www.ethanepperly.com
December 5, 2023 at 10:19 PM
Very excited to be attending #NeurIPS2023 next week where I’ll be presenting my work “Kernel quadrature with randomly pivoted Cholesky” with Elvira Moreno. I’ve written a little blog post to explain what kernel quadrature is and what our approach is to it!