<commit_before>---
layout: post
title:  "Compressed Sensing and Subgaussians"
date:   2019-08-18
categories: machine-learning
---

# Compressed Sensing and Subgaussians

Candes and Tao came up with a broad characterization of compressed sensing solutions [a while ago](https://statweb.stanford.edu/~candes/papers/RIP.pdf). Partially inspired by a past homework problem, I'd like to explore an area of this setting.

This post will dive into the compressed sensing context and then focus on a proof that squared subgaussian random variables are subexponential (the relation between the two will be explained).

## Compressed Sensing

For context, we're interested in the setting where we observe an \\(n\\)-dimensional vector \\(\vy\\) that is a random linear transformation \\(X\\) of a hidden \\(p\\)-dimensional vector \\(\vx_*\\):

\\[<commit_msg>change date<commit_after>---
layout: post
title:  "Compressed Sensing and Subgaussians"
date:   2019-09-11
categories: machine-learning
---

# Compressed Sensing and Subgaussians

Candes and Tao came up with a broad characterization of compressed sensing solutions [a while ago](https://statweb.stanford.edu/~candes/papers/RIP.pdf). Partially inspired by a past homework problem, I'd like to explore an area of this setting.

This post will dive into the compressed sensing context and then focus on a proof that squared subgaussian random variables are subexponential (the relation between the two will be explained).

## Compressed Sensing

For context, we're interested in the setting where we observe an \\(n\\)-dimensional vector \\(\vy\\) that is a random linear transformation \\(X\\) of a hidden \\(p\\)-dimensional vector \\(\vx_*\\):

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