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Multitask Learning Using Dirichlet Process

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Multitask Learning Using Dirichlet Process. Ya Xue. July 1, 2005. Outline. Task defined: infinite mixture of priors. Multitask learning. Dirichlet process ... – PowerPoint PPT presentation

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Title: Multitask Learning Using Dirichlet Process


1
Multitask Learning Using Dirichlet Process
  • Ya Xue
  • July 1, 2005

2
Outline
  • Task defined infinite mixture of priors
  • Multitask learning
  • Dirichlet process
  • Task undefined expert network
  • Finite expert network
  • Infinite expert network

3
Multitask Learning- Common Prior Model
M classification tasks
Shared prior of w
4
Drawback of This Model
Assume each wm is a two-dimensional vector.
5
Proposed Model
w is drawn from a Gaussian mixture model
6
Two Special Cases
  • Common prior model - single Gaussian
  • Piecewise linear classifier point mass function

similar vs. identical
7
Clustering
Unknown parameters
Another uncertainty K.
Model selection compute evidence/Marginal
8
Clustering with DP No Model Selection
We rewrite the model in another form
We define a Dirichlet process
prior for parameters
9
Stick-Breaking View of DP
0
1
Finally we get
10
Prediction Rule of DP for Posterior Inference
  • is a new data point.
  • Assuming there are K distinct values of among
    ,
  • belongs to an existing cluster k

belongs to new cluster
11
Toy Problem
12
(No Transcript)
13
Task 1
14
Task 2
15
Task 3
16
Task 4
17
Task 5
18
Task 6
19
Task 7
20
Task 8
21
(No Transcript)
22
Expert Network
23
Mathematical Model
  • Gating node j
  • Likelihood

24
Mathematical Model
is the unique path from the root note to expert m.
where
25
Example
26
Infinite Expert Network
Infinite number of gating node.
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