Active Learning with Statistical Models.pdf

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statmodels.dvi
tures, however, provide an estimate of P(y j x) based on
expectation of
An active learning problem is one where the learner has
ping X ! Y based on a set of training examples
f (x
) g
2 X and y
i
2 Y . The learner
(), a training set f (x
i
) g
y(x
i
1
S
distribution P(y j x)by its estimated mean y(x) and vari-
1
(x; x) S
j w jj w j matrix for each new example, and incorporat-
Unless explicitly denoted, y and
2
y
are functions of x .
79814269.025.png 79814269.026.png 79814269.027.png 79814269.028.png
(x
2
y j x;i
(x)
(x
(x)
h
i =
j i)
(x)(x
j k)
= h
2
y j x;i
(x
2
y j x;i
(x
P (x j i)
h
P (x j j)
(x) h(x x
)=exp( k(x x
2
y j x;i
(x
x)
2
x)(y
2
y j x
P(y j x)=
P(y j x;i)=
(x);
2
y j x;i
(x
h
2
y j x
(x
point sampled from P(y j x; i)andweight this change by
2
y j x;i
(x
P(y j x)=N(y(x);
2
y j x
(x))
79814269.001.png 79814269.002.png 79814269.003.png 79814269.004.png 79814269.005.png 79814269.006.png 79814269.007.png 79814269.008.png 79814269.009.png 79814269.010.png 79814269.011.png 79814269.012.png 79814269.013.png 79814269.014.png 79814269.015.png
1
Neural Network
0.5
2
y j x
0
(x
predicted change
actual change
−0.5
0
0.2
0.4
0.6
0.8
1
~
h(x
~
h(y(x)
x 2 [0; 1]. Changes are not plotted to scale with ts.
~
h(x
)(y(x)
1
Mixture of Gaussians
h
i =
(x)(x
= h
0.5
2
y j x
0
predicted change
actual change
−0.5
0
0.2
0.4
0.6
0.8
1
Regression by local tting. Journal of Econometrics
Sampling. In D. Touretzky, ed., Advances in Neural In-
formation Processing Systems 2 , Morgan Kaufmann.
Advances in Neural Information Processing Systems 6 .
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1
Kernel Regression
(x ,x )
1 2
2
0.5
1
0
predicted change
actual change
−0.5
−1
0
0.2
0.4
0.6
0.8
1
0.025
0.02
1
LOESS
0.015
0.8
0.01
0.6
0.005
0.4
0
0.2
−0.005
0
predicted change
actual change
−0.01 −0.005
0
0.005 0.01 0.015 0.02 0.025
−0.2
predicted delta variance
−0.4
−0.6
0
0.2
0.4
0.6
0.8
1
rithm. J. Royal Statistical Society Series B , 39 :1{38.
V. Fedorov . (1972) Theory of Optimal Experiments .
cise training sets from clean data. IEEE Transactions
on Neural Networks , 4, 305{318.
An Implementation of Memory-based Learning. Control
Systems Magazine , 14(1):57{71.
J. Cowan et al., eds., Advances in Neural Information
Processing Systems 6 . Morgan Kaufmann.
J. Schmidhuber and J. Storck . (1993) Reinforce-
al., eds., Proc. 2nd Int. Conf. on Simulation of Adaptive
Behavior , MIT Press, Cambridge.
D. Specht . (1991) A general regression neural network.
IEEE Trans. Neural Networks , 2(6):568{576.
tions for active data selection, Neural Computation 4(4):
Advances in Neural Information Processing Systems 4 .
Query Construction for Neural Network Models. In this
−0.01
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