Learning Dynamic Regulatory Networks: Inferelator 2'0

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Learning Dynamic Regulatory Networks
Inferelator 2.0

• Aviv Madar

Alex Greenfield, Eric Vanden-Eijnden, Richard
Bonneau
Center for Genomics and Systems Biology, New York
University
2
time
2006
2007
2003
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ODEs to Learn Regulatory Networks
General form additive ODE
Rate of change
Weighted sum
Linear form ODE
Linear case
model parameters
sparse
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Inferelator Version 1
Typical input Microarray data --- time-series,
steady state
time
0
15
40
Graph representation
Output dynamical regulatory network
Mathematical representation
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Inferelator 1 in a sketch
tk
tk1
tk2
Learn parameters that minimize error over leave
out set
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Inferelator 1--- Limitations
tk
tk1
tk2
Error propagation
Predict
Error over long time intervals
Finite difference approximation is poor
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Inferelator 2 Concepts
tk
tk1
Inject intermediate time points
Finite difference approximation is improved
How do we estimate parameters?
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Inferelator 2 Mathematical Overview
Minimize Energy (scoring/objective function)
Error over time series data
Error over steady state data
L2 norm constraint/regularizer
Markov Chain Monte Carlo (MCMC) scheme to sample
parameters
Markov chain
Importance sampling
Gaussian Noise term
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Inferelator 2 Performance 1
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Inferelator 2 Performance 2
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Inferelator 2 Performance 3
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Inferelator 2 Performance 4
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Inferelator 2 Performance 5
time interval
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• Thanks

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Inferelator 2 Gradient Approximation