srtree: A symbolic regression expression tree structure.

srtree is a Haskell library with a data structure and supporting functions to manipulate expression trees for symbolic regression.

The tree-like structure is defined as a fixed-point of an n-ary tree. The variables and parameters of the regression model are indexed as Inttype and the constant values are Double.

The tree supports leaf nodes containing a variable, a free parameter, or a constant value; internal nodes that represents binary operators such as the four basic math operations, logarithm with custom base, and the power of two expressions; and unary functions specified by Function data type.

The SRTree structure has instances for Num, Fractional, Floating which allows to create an expression as a valid Haskell expression such as:

x = var 0)
y = var 1
expr = x * 2 + sin(y * pi + x) :: Fix SRTree

Other features:

• derivative w.r.t. a variable (deriveByVar) and w.r.t. a parameter (deriveByParam)
• evaluation (evalTree)
• relabel free parameters sequentially (relabelParams)
• gradient calculation with forwardMode, or optimized with gradParams if there is only a single occurrence of each parameter (most of the cases).

TODO:

• support more advanced functions
• support conditional branching (IF-THEN-ELSE)