Nice to see some love for wavelets. They're great for many more things. Robust volatility measurement, galerkin methods for numerical solutions to differential equations in finance. Just please don't use a Haar wavelet for anything other than teaching.
Can you use wavelets in analyzing behavioral data (clicks, decisions, etc.)?
Intuitively, wavelets, and SP in general, seem like something behavioral folks could benefit from, but I can't come up with any good use cases that would justify going through all the associated math.
Wavelets have also been used in the physical sciences. Here they are used to translate sea surface patterns into water depths: https://www.mdpi.com/2077-1312/8/10/772
Mathematicians are human just the same and are wont to get their hands on shiny toys too from time to time. There's some value in seeking out novelty.
Apropos deep nets, with the explosion in machine learning in the past few years, I've been seeing a lot of research interest statements change to meet that. In particular, there's an awful lot of numerical linear algebra being done now.
I suspect that things will come full-circle soon enough, and those tools developed in numerical linear algebra (via their connections to functional analysis) will make their way to harmonic analysis.
(This is notwithstanding the fact that compressed sensing is picking up a little momentum as a research area in applied mathematics and other disciplines that study signal processing. Wavelets, curvelets, shearlets, chirplets, etc. will likely see some action there too.)
It's rational to seek out novelty. What's more likely: that you'll be the first to discover a momentous consequence of a theorem published last week, or that you'll be the first to discover a momentous consequence of a theorem published by Euler?
Could you provide some examples of recent numerical linear algebra inspired by machine learning? The only numerical linear algebra related to machine learning, in particular deep learning, is matrix multiplication due to convolution. I am curious what else in numerical linear algebra is impacting machine learning.
> The only numerical linear algebra related to machine learning, in particular deep learning, is matrix multiplication
I suspect the OP is not talking about how deep nets are implemented, but rather how people are trying to understand how and why they work so well, or how to reverse-engineer knowledge out of a trained net, or how to train them faster, etc ...
In that space, you need quite a bit more than matrix multiplication.
