5. Empirical risk minimization
Train model through standard framework
Trading bias-variance through regularization
Bias Variance Regularized
(Crossvalidated)
Regularized + order
(Crossvalidated)
6. Point estimates
ERM is based on point estimates (one set of weights, for a fixed model)
The bias-variance trade-off pops up because we require a distinct choice.
Idea:
- consider a continuous range of potential models
- Some of them are more likely, others are not
I can live with doubt, and uncertainty. I think it's much more interesting to live not
knowing than to have answers which might be wrong.
- Richard Feynman
8. Bayesian nonparametric model: richer class of approximations
We will use the multivariate Gaussian to put a
prior directly on the function (a Gaussian process)
I can live with doubt, and uncertainty. I think it's
much more interesting to live not knowing than to
have answers which might be wrong.
- Richard Feynman
11. How to optimize?
Solving for gradient = 0?
- Too complex
- Gradient unavailable
Numerical optimization?
- Multi-modality
- Gradient unavailable
Meta-heuristics?
- Too many evaluations
- Nature took a long time to optimize
12. Dynamic programming
Let’s split the task:
- Decide location for next evaluation
- Data structure: probabilistic model
- Optimize acquisition function (sampling policy)
Goal: optimality
24. Stabilizing space telescope
Camera field can not be guaranteed(!)
Small movements cause changes in light distribution
To severe for reliable detection of earth-like plants
28. Results
Schölkopf, Bernhard, et al. "Removing systematic errors for exoplanet search via latent causes."
Proceedings of the 32nd International Conference on Machine Learning (ICML-15). 2015.
SAP represents relative flux measure
30. Take home message
AI is coming!
… enormous business potential
… but it will require more effort (time x money) than you all think
… europe is not at the forefront
(... forget about killer robots)
Theory is not to be avoided!
… without, experiments are shots in the dark
… probabilistic models know what they don’t know
… provide some confidence
Multidisciplinary teams are a must to tackle cases
… and they’ll need time
@javdrher joachim@ml2grow.com www.ml2grow.com