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Genetic Programming With Boosting for Ambiguities in Regression ProblemPowerPoint Presentation

Genetic Programming With Boosting for Ambiguities in Regression Problem

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### Genetic Programming With Boosting for Ambiguities in Regression Problem

Grégory Paris

Laboratoire d’informatique du Littoral

Université du Littoral-côte d’Opale

62228 Calais Cedex, France

What Are Ambiguities? Regression Problem

For a given x, several values are possible for f(x).

Contents Regression Problem

- Boosting to get several values
- Boosting in few words
- GPboost: our algorithm for regression problem
- Boosting deals with ambiguities, clusters the data

- Dealing with several values: Dendrograms
- Presentation
- Application

- Results and conclusion

Presentation of Boosting Regression Problem

- Introduced by Freund and Schapire in 90’s
- Improvement of machine learning methods
- For weak learners methods (methods that perform better than a random search)
- Decrease of error on learning set is assured
- Makes several hypothesis on different distributions
- Makes them vote to get a final hypothesis

Boosting and GP Regression Problem

- Iba’s version in 1999
- Distributions are used to build the fitness set
- Our version in 2001
- Distribution is included in the fitness function

Fitness set: Regression Problem

Distribution:

Each example has a weight

Initial weight is for each example

will be run T times (T rounds of boosting) with different distributions

GPboost(notation)« Weak Learner » :

: a GP algorithm including distribution in its fitness

Fitness function:

For do Regression Problem

Run using

The best-of-run is denoted

is the confidence given to function

: error on

: Normalization factor

GPboost (main loop)Update distribution for the next round:

End For

Each function gives a value for x Regression Problem

A median weighted by confidence values is computed

Others medians provide similar results

GPboost(final hypothesis)Using Boosting (1) Regression Problem

- Principle of boosting is to focus on points which have not been matched on previous round
- In ambiguities, all the points can not be matched with one function
- Using weights to alternatively focus on ambiguities.

Target Regression Problem

rms

- e.g.

- We are seeking a fitness function which will focus on extrema rather than average points

Application Regression Problem

- We run GPboost on this ambiguities problem
- We use our fitness function
- We set T=6, the number of rounds

Run of Boosting Regression Problem

Merging the data Regression Problem

- We are given 6 functions
- For a given x, we can provide 6 values
- We have to find a way to pick up 2 values among the 6.
- We propose dendrograms to solve this problem

Dendrogram Regression Problem

- T values
- Cluster the set of values and take the median of each cluster
- To cluster the values, we build dendrogram
- Start with T clusters
- At each step, group the two nearest clusters

Dendrogram (Building) Regression Problem

S={-1.1; -1; 0; 0.15; 1; 1.05}

Cut the dendrogram Regression Problem

- The dendrogram must be cut off at a height corresponding to the number of values we want.

Computing cut-off values Regression Problem

- A fixed cut-off value gives better results but needs a priori knowledge of the problem
- Dynamic cut-off value
- The number of values will be computed in order to reduce the error made on fitness set on each ambiguity

Computing cut-off Value Regression Problem

Other Benchmarks Regression Problem

- Inverting

Other Benchmarks Regression Problem

- Inverting

Conclusion and Future Work Regression Problem

- Good results on classical and simple problems
To do

- Improving cut-off value
- Applying to real problems

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