Ankit Pensia

A new preprint at the intersection of high-dimensional statistics, convex relaxations, polynomials of subgaussians, sum of squares, and empirical processes: arxiv.org/abs/2410.21194 We show that every subgaussian distribution is "certifiably" so!

Excited to share our recent work introducing 𝗡𝗲𝘂𝗿𝗼𝗻 𝗣𝘂𝗿𝘀𝘂𝗶𝘁 (𝗡𝗣) - a greedy algorithm for training neural networks. arxiv.org/abs/2509.12154

Join us at LeT-All's NeurIPS Social on Thursday 7:30pm and chat with awesome mentors like @aminkarbasi , Cristóbal Guzmàn, @gavinrbrown1 , @vkontonis , @subGaussian (Ankit Pensia), @ramyavinayak , @MAliakbarpour , Erin Grant, @firebat03 (Josh Alman), @SurbhiGoel_ , Vatsal Sharan

@ethanepperly E.g., it is possible for the linear forms. Bounds that are both useful and tighter than Hoeffding can be derived using the properties of spherical caps in the extreme regime. I was wondering if something similar was known for the quadratic form. Thanks again!

@ethanepperly Thanks for the reply! Yes, I was interested in the (admittedly extreme) regime that crucially exploits the boundedness property of the uniform random variable (though not as extreme as the trivial regime of d*lambda_max).

New blog post up about concentration inequalities for quadratic forms xᵀAx with random vectors x drawn from the sphere! The conclusion: xᵀAx has much smaller tail probabilities than gᵀAg for a Gaussian vector g ethanepperly.com/index.php/2024…

@kevinjtian @sp_monte_carlo Thank you for your lecture notes! They are really good!

@sp_monte_carlo I gave this a try: kjtian.github.io/cs395t.html. Hope to have a complete set of notes by Spring 2025 (second time is the charm…)

@kevinjtian Haha! Adding "certifiable" would be redundant now😅

@subGaussian Is it time to change your username to @certifiably_subGaussian?

A new preprint at the intersection of high-dimensional statistics, convex relaxations, polynomials of subgaussians, sum of squares, and empirical processes: arxiv.org/abs/2410.21194 We show that every subgaussian distribution is "certifiably" so!

@thegautamkamath @gavinrbrown1 Yes, and yes!🤯 (There is no contradiction though because all moments of subgaussain distributions are bounded). Some extra context: x.com/subGaussian/st…

@gavinrbrown1 @subGaussian The same is not true of distributions with bounded moments, right (assuming popular conjectures)? That's my interpretation of Sam and Jerry's paper. But it is true when we have subgaussianity? That is unusual to me.

@gavinrbrown1 Our work essentially says that you can apply these existing arguments to Gaussians to get SoS-certificates for Gaussians, and then transfer the (existence of) SoS certificates to subGaussians sometimes (even though the Gaussian-specific arguments might break for subGaussians).

@gavinrbrown1 Hence, existing SoS certificates applied to only a small subset of subgaussian distributions (usually for which, generic high-degree polynomials were well-behaved).

@praveshkkothari Thank you Pravesh! Haha! I had joined Twitter around the time I was thinking about a different "subgaussian" phenomenon (arxiv.org/abs/2007.15618).

@subGaussian Very cool result @subGaussian ! Were you always subgaussian or became one while working on this? :)

The paper is available at arxiv.org/abs/2410.21194. This is joint work with Ilias Diakonikolas, Sam Hopkins (@Samuel_BKH ), and Stefan Tiegel.

Our proof (Section 1.3) uses generic chaining on the (linearized) dual problem and is short, simple, and general. There are many open problems in this area, and we hope our work invites further research