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Partially labeled classification with Markov random walks

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A discussion on. Partially labeled classification with Markov random walks. By M. Szummer and T. Jaakkola. Xuejun Liao 15 June 2006. Neighborhood graph (undirected). W ik gives the (on-step) connection strength datum i and k.

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slide1

A discussion on

Partially labeled classification with Markov random walks

By M. Szummer and T. Jaakkola

Xuejun Liao

15 June 2006

slide2

Neighborhood graph (undirected)

Wik gives the (on-step) connection strength datum i and k

  • The graph induces a Markov random walk with one-step transitions
  • t-step Markov random walk

where A is the one-step transition matrix with [A]ij=p(k|i)

  • Assuming uniform initial distribution p(i)
slide3

Transduction

  • Likelihood for labeled data
  • Maximizing the likelihood gives

E-step:

M-step:

slide4

Estimation based on margin maximization

where Cdenotes the number of classes and NC(k)gives the number of labeled points in the same class as k, and

  • The solution to this linear program can be found in closed form:
  • For each data k, choose tkas the smallest number of transitions needed to reach a labeled datum from datum k.