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SUMMARY:Dimensionality Reduction via Probabilistic Inference - Aditya Ravu
 ri (University of Cambridge)
DTSTART:20230516T120000Z
DTEND:20230516T130000Z
UID:TALK200551@talks.cam.ac.uk
CONTACT:Mateja Jamnik
DESCRIPTION:Dimensionality reduction (DR) algorithms compress high-dimensi
 onal data into a lower dimensional representation while preserving importa
 nt features of the data. DR is a critical step in many analysis pipelines 
 as it enables visualisation\, noise reduction and efficient downstream pro
 cessing of the data. In this work\, we introduce the ProbDR variational fr
 amework\, which interprets a wide range of classical DR algorithms as prob
 abilistic inference algorithms in this framework. ProbDR encompasses PCA\,
  CMDS\, LLE\, LE\, MVU\, diffusion maps\, kPCA\, Isomap\, (t-)SNE\, and UM
 AP. In our framework\, a low-dimensional latent variable is used to constr
 uct a covariance\, precision\, or a graph Laplacian matrix\, which can be 
 used as part of a generative model for the data. Inference is done by opti
 mizing an evidence lower bound. We demonstrate the internal consistency of
  our framework and show that it enables the use of probabilistic programmi
 ng languages (PPLs) for DR. Additionally\, we illustrate that the framewor
 k facilitates reasoning about unseen data and argue that our generative mo
 dels approximate Gaussian processes (GPs) on manifolds. By providing a uni
 fied view of DR\, our framework facilitates communication\, reasoning abou
 t uncertainties\, model composition\, and extensions\, particularly when d
 omain knowledge is present.\n\n"You can also join us on Zoom":https://zoom
 .us/j/99166955895?pwd=SzI0M3pMVEkvNmw3Q0dqNDVRalZvdz09
LOCATION:Lecture Theatre 2
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