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PPSE

Frame

The objective of this project is to extend the idea proposed by the PSE model exploration method. PPSE objective is to discover all the patterns that a model can produce and to associate a probability to each pattern.

Pattern probability

The probability of a pattern is defined as the probability of reaching this zone of the output space when one sample the input space at random using a uniform distribution.

The marginal likelihood, model evidence or pattern likelihood $$p(\mathbf{X}) = \int p(\mathbf{X}\mid\theta) p(\theta) d\theta$$

Stochastic models

The pattern probability extends trivially to stochastic model. The probability of a given pattern is the sum of probabilities of reaching this pattern among all the output distribution computed using replication while sampling the input space uniformly.

Naive approach

A naive approach is to sample uniformly in the input space and count the reached pattern. This work but is highly inefficient as shown in the previous work achieved by PSE. The intuition, used in PSE, that sampling more intensively near inputs leading to rare patterns is an efficient way of finding other rare patterns should be used as well in PPSE.

Prior work

Importance sampling

The importance sampling can be used to compute statistic estimators of f(x) when x is drawn in a distribution p(x) and sampling directly in p(x) is hard.

It doesn't seem to be a solution to this problem since the distribution that is sampled in this method is a uniform distribution which is simple to sample.

Distribution based evolution strategies

Extend CMAES evolutionnary strategy to sample in gaussian mixutres: https://hal.inria.fr/hal-01420342 GCES is a stochastic method for multimodal optimization of nonlinear nonconvex functions: https://sci-hub.se/https://ieeexplore.ieee.org/document/6729097

TODO

29/08/2023 Utilisation de JSAT gmm sans pondérer les données Resultats encourageants:

  • 60 patterns sur 500 avec une erreur en 10-7 alors qu'il reste 400 pattern et une erreur un 10-6 pour le sampling uniforme

A regarder:

  • Probleme dans emgmm dans JSAT, instabilité => des tps en tps mStep ne fini pas => refaire des teste avec l'implem maison

  • L'algo group 3 ensemble de pattern dans 1 seuls gaussienne, pourquoi ?

  • Passer le résultat du clustering à l'init de emgmm

  • Rendre polymorphe le switch d'implem

  • Consider auto-adjusting explorationProbability depending on how much pattern have been discovered by sampling in the GMM in the previours steps.

  • Consider integrating the cluster with a single point. Randomly use covariance of other clusters.