eql project; rule project draft

Author: nmheim

docs/src/projects.md

@@ -8,10 +8,37 @@ extensive project together.
 For you inspiration of what such a project could look like we have four
 suggestions for you (which you can of course choose to work on as well).
 
-## The *Improved Equation Learner* and its symbolic representation
+## The Equation Learner And Its Symbolic Representation
 
-## An Evolutionary Algorithm applied to Julia's AST
+In many scientific and engineering one searches for interpretable (i.e.
+human-understandable) models instead of the black-box function approximators
+that neural networks provide.
+The [*equation learner*](http://proceedings.mlr.press/v80/sahoo18a.html) (EQL)
+is one approach that can identify concise equations that describe a given
+dataset.
 
-## A Rule Learning Algorithm
+The EQL is essentially a neural network with different unary or binary
+activation functions at each indiviual unit. The network weights are
+regularized during training to obtain a sparse model which hopefully results in
+a model that represents a simple equation.
+
+The goal of this project is to implement the EQL, and if there is enough time
+the [*improved equation learner*](https://arxiv.org/abs/2105.06331) (iEQL).
+The equation learners should be tested on a few toy problems (possibly inspired
+by the tasks in the papers).  Finally, you will implement functionality that
+can transform the learned model into a symbolic, human readable, and exectuable
+Julia expression.
+
+## An Evolutionary Algorithm Applied To Julia's AST
 
 ## Distributed Optimization Package
+
+## A Rule Learning Algorithm
+
+[Rule-based models](https://christophm.github.io/interpretable-ml-book/rules.html)
+are simple and very interpretable models that have been around for a long time
+and are gaining popularity again.
+The goal of this project is to implement a
+[sequential covering](https://christophm.github.io/interpretable-ml-book/rules.html#sequential-covering)
+algorithm called [`RIPPER`](http://www.cs.utsa.edu/~bylander/cs6243/cohen95ripper.pdf)
+and evaluate it on a number of datasets.