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Recurrent machines for likelihood-free inference
Antoine Wehenkel
ULiège
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Arthur Pesah
KTH
Gilles Louppe
ULiège
Likelihood-free Inference
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Recurrent machines for likelihood-free inference Arthur Pesah - - PowerPoint PPT Presentation
Recurrent machines for likelihood-free inference Arthur Pesah - - PowerPoint PPT Presentation
Recurrent machines for likelihood-free inference Arthur Pesah Antoine Wehenkel Gilles Louppe KTH ULige ULige 1 Likelihood-free Inference 2 Likelihood-free inference: what? Parameters Goal Finding the parameters corresponding to
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Likelihood-free inference: what?
Simulator
Likelihood Parameters Goal Finding the parameters corresponding to real data But... We don’t have the likelihood!
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How? Maximum likelihood Real data
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Likelihood-free inference: when?
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Likelihood-free inference: when?
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Example: Population biology
The evolution of a population can be modelled by a differential equation that can be solved by a simulator (numerical solver). ODE Solver Coefficients of the differential equations.
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Particle Physics
Likelihood-free inference: when?
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Particle accelerators (like the LHC) produce particle collisions and
- bserve the resulting particles with
detectors. Particle collisions simulator (e.g. Geant4) Physical constants (mass of particles, strength of interactions, etc.) Detectors response after a collision
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Likelihood-free inference: how?
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Likelihood-free inference: how?
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What can we do?
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Likelihood-free inference: how?
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Idea 1: choose a random parameter and simulate it Problem: nothing to do next
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Likelihood-free inference: how?
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Proposal distribution: Idea 2: sample several parameters from a distribution and simulate them
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Likelihood-free inference: how?
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Proposal distribution: Then: comparing the different simulated data and choosing an appropriate direction
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Likelihood-free inference: how?
How to choose the best direction in the parameter space?
- Some algorithms rely on a predefined update rule and a handcrafted similarity measure
between the generated and the real samples.
- Why not learning this optimization procedure and the similarity measure?
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Likelihood-free inference with meta-learning
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Likelihood-free inference with meta-learning
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Before meta-training After meta-training
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
RNN
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Simulator
Likelihood-free inference with meta-learning
Simulator Simulator Simulator Simulator Simulator
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Generate a meta-dataset
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Simulator ALFI
Likelihood-free inference with meta-learning
Simulator ALFI Simulator ALFI Simulator ALFI Simulator ALFI Simulator ALFI
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Generate a meta-dataset Automatic Likelihood-Free Inference (the name of our RNN-based machine)
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
Problem: 1 Step: 1/3
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
Problem: 1 Step: 2/3
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
Problem: 1 Step: 3/3
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
Problem: 200 Step: 1/3
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
Problem: 200 Step: 2/3
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ALFI: Automatic Likelihood-free Inference
Principle: learning a descent using an Recurrent Neural Network
Problem: 200 Step: 3/3
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Results
Poisson:
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With a known likelihood function: With an unknown likelihood function:
Weinberg:
- Electron muon collision.
- Parameters are the
beam energy and the fermi constant.
- Observations are the
angle between the two muons.
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Limitations and future work
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Limitations
- Scaling it up on more complex simulators
- Learning intensive in the number of simulator calls
Future work
- Getting a better understanding of the optimization procedure learned by ALFI:
○ Is it comparable to other existing methods? ○ Does it generalize to other simulators?
- Training the model on more complex simulators and compare it to state-of-the-art
likelihood-free inference methods
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Conclusion
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Thanks
ArXiv: 1811.12932 - Recurrent machines for likelihood-free inference GitHub: github.com/artix41/ALFI-pytorch