[title: line-fit] Three short pieces on dimensionality reduction

Where I come from

https://hdc.cs.arizona.edu

This talk

• https://cscheid.net/talks/2020-10-16 (I’m using Google Chrome)
• Three pieces on dimensionality reduction (DR):
  • DimReader
  • Deep Inverse
  • UMAP Tour

[slide-data: backgroundImage ../tandon-march-2019/images/tsne/cnn_embed_6k.jpg] [title: line-fit bg-black] t-SNE plots are beautiful, but what are they showing us?

[slide-data: backgroundImage ../tandon-march-2019/images/tsne/cnn_embed_6k.jpg]

DimReader

• Rebecca Faust, David Glickenstein, C.S., InfoVis 2018
• We give DR plots a new visual affordance: where will a point go if one of its attributes changes infinitesimally?

A simple scatterplot

t-SNE

How: tangent maps

author: "User from reddit", CC BY 3.0

How: Automatic Differentiation (autodiff)

• For many programs which produce values of functions, you can get derivatives for about the same effort as just computing thefunction value (!)
• The procedure is entirely synctatic, so a compiler can generate code that produces derivatives
• This is how pytorch and tensorflow work, and partly why neural nets are now so popular
• a quick tutorial on autodiff.

Examples, Applications

Examples, Applications

2: Deep Inverse

• (This is unpublished work by my student Mingwei Li - unpublished because it’s too simple!)
• Same general setup: we have the result of a DR method and we want to “explain it”
• Here, we attempt to find a good “inverse”: a mapping from projection back into input
• This allows us to interactively with the projection

Deep Inverse, cont.

• Obviously no exact solution exists, so we minimize an error measure
• The mapping is given by a deep neural network
• The codebase is a ~300-line Python program and a simple Javascript front-end

Demo

• Digits dataset
• Fashion Items dataset

Why is this exciting?

• This technique is broadly applicable
• The space of UI interactions can be low dimensional (eg. a screen is only 2D)
• Low-dimensional domains are “easy” to learn
• Other stupid ML tricks: use this to hide latency from a slow server

3: UMAP Tour

• Finally, I want to demo what’s currently possible with modern browser technology
• We will use DR to understand the behavior of deep neural networks (the opposite of what we just did!)
• Toward Comparing DNNs with UMAP Tour, by Mingwei Li as well. He will be present this work next Monday.

Thank you!

• I’m cscheid@email.arizona.edu
• I’ll be spending the Fall and Spring working in the ANTARES project
• I’m looking forward to meeting all of you, even if COVID-19 won’t let it be in person!
• Questions?