A Probabilistic Look at MDS

Headed to NYC in July! Will be presenting my paper on a probabilistic variant of multi-dimensional scaling (MDS) at the 2016 International Joint Conference on Artificial Intelligence (IJCAI)! The acceptance rate was below 25% so, it’s certainly satisfying that the paper was accepted.

You can read the pre-print here and slides here.

About the work: we take a fresh Bayesian view of MDS—an old dimensionality reduction method—and find connections to popular machine learning methods such as probabilistic matrix factorization (used in recommender systems) and word embedding (for natural language processing).

The probabilistic viewpoint allows us to connect distance/similarity matching to non-parametric learning methods such as sparse Gaussian processes (GPs), and we derive a novel method called the Variational Bayesian MDS Gaussian Process (VBMDS-GP) [yes, a mouthful!]. As concrete examples, we apply it to multi-sensor localization and perhaps more interestingly, political unfolding.

VBMDSGP_PoliticalUnfolding.pngIn the unfolding task, we projected political candidates to a 2-d plane using their associated Wikipedia articles and ~15,000 voter preference survey done in 2004 for other candidates. The projection is not perfect since we use very simple Bag-of-Words (BoW) features—I think Sanders is a more liberal than the map implies—but is nevertheless coherent. We see our favorite political candidate, Donald Drumpf, projected to the conservative section and President Obama projected near the Clintons.

The model can be extended in lots of different ways; I’m working on using more recent variational inference techniques, plus maybe some “deep” extensions.

 

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