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SUMMARY:Dual-to-kernel learning with ideals - Dr. Franz Kiraly\, Universit
 y College London
DTSTART:20140313T140000Z
DTEND:20140313T150000Z
UID:TALK50833@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:We propose a theory unifying kernel learning and symbolic alge
 braic methods. Kernel methods are a very popular class of algorithms emplo
 ying kernel functions which allow to capture properties of the data in a v
 ery efficient way\, representing them implicitly in the so-called feature 
 space\, the most prominent example being the kernel support vector machine
 . The main advantage of kernels is also their main downside: since the rep
 resentation is implicit it has remained an open question what exactly the 
 structures and features are which make the algorithms work.\n\nSymbolic al
 gebraic methods\, on the other hand\, are by construction structural and d
 eal with the manipulation of explicit equations. So far\, their theoretica
 l complexity and intractable computational cost\, such as for Gröbner bas
 is computations\, has prevented broad application to real-world learning a
 nd data analysis. \n\nWe show that kernel learning and symbolic algebra ar
 e inherently dual to each other\, and we use this duality to combine the s
 tructure-awareness of algebraic methods with the efficiency and generality
  of kernels. The main idea lies in relating polynomial rings to feature sp
 ace\, and ideals to manifolds\, then exploiting this generative-discrimina
 tive duality on kernel matrices. We illustrate this by proposing two algor
 ithms\, IPCA and AVICA\, for simultaneous manifold and feature learning.
LOCATION:LR5\, Cambridge University Engineering Department
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