[title: line-fit] Three short pieces on dimensionality reduction
Associate Professor, UA CS, HDC Lab
Where I come from
(I’m using Google Chrome)
Three pieces on dimensionality reduction (DR):
[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]
Shouldn't our tools provide mechanisms for inspecting their own behavior?
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
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
quick tutorial on autodiff
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(This is unpublished work by my student Mingwei Li - unpublished because it’s too simple!)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
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.
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!