xtractis® Technologies

Avoid the common pitfalls of empirical modelling.

Empirical modelling refers to methods that allow extracting structured knowledge from a database collected from the process under study, in order to understand it and/or to predict its behaviour in unknown situations. Depending on his former knowledge, one may relate empirical modelling to regression, clustering, Machine Learning, Knowledge Discovery from Data...

xtractis® provides tools and methods to address a wide range of empirical modelling problems without any specific knowledge, and to avoid the common pitfalls appearing in most real life situations.

Interpretability

Empirical modelling consists in identifying a model that represents as best as possible a phenomenon for which a given data sample is available. This task is usually an ill-posed problem, and as such may allow several equally performing solutions. The interpretability of the extracted models is then a must to be able to differentiate between models that actually encompass knowledge about the underlying phenomenon from models that originate from purely incidental numerical artefacts.

The xtractis® technology is based on the fuzzy theory that allows the extracted models to be linguistically interpreted and validated by a field specialist. To learn more about interpretability and fuzzy logic:

• Introduction to fuzzy logic.  
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• Introduction à la logique floue.
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Complexity handling

The complexity of real world processes has 3 main grounds: non linearity, high dimensionality and interactions between variables. Analyses on latent variables (such as Principal Component Analysis, Partial Least Square, etc.) are widely used to a priori reduce the dimensionality of the problem, as well as decoupling variables. However, such analyses are linear and as such usually prevent an efficient modelling of a non linear process. Moreover, the identified latent variables, defined as a linear combination of all original variables, are usually difficult to interpret.

Fuzzy Theory is intrinsically suited for non linear modelling, and xtractis® algorithms allow extracting models on a reduced set of original variables. In this way, xtractis® has no need to perform an a priori transformation of the original variables, thus allowing the resulting models to encompass any possible interactions between explanatory variables to explain and predict the studied variable. Moreover, this also preserves the interpretability of the model, as the original variables do have a meaning for the field specialist who will validate the model.

Robustness

The robustness of an estimator is a measure of its validity on individuals not included in the learning sample, in other words of its generalisation capacity. The machine learning community has long shown that computing the performance of a model on its learning sample was a disastrous way to assess its robustness. Going further, you will also find out in the following paper that the widely accepted Hold Out Set method (2/3 of sample for learning, 1/3 for model validation) is a very poor robustness estimator in most circumstances.

In order to give the most realistic estimations of robustness, xtractis® relies on intensive cross validation techniques that have been widely adopted by the machine learning community.

• Contribution of xtractis® methodology to the automatic extraction of robust fuzzy models
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