Bayesian symbolic regression using mcmc sampling.
Paper here: https://arxiv.org/abs/1910.08892
codes/BSR.py: API interface of BSR class
codes/bsr_class.py: definition of BSR class
codes/simulations.py: part of simulation settings in the paper
codes/funcs.py: basic sampling functions
K = 3 # number of trees
MM = 50 # number of iterations
# set hyperparameters alternatively
hyper_params = [{'treeNum': 3, 'itrNum':50, 'alpha1':0.4, 'alpha2':0.4, 'beta':-1}]
# initialize BSR object
my_bsr = BSR(K,MM)
# train (need to fill in parameters)
# train_X is dataframe with each row a datapoint
# train_y is series with default index
my_bsr.fit(train_X,train_y)
# fit new values
# new_X is dataframe of new data
fitted_y = my_bsr.predict(new_X)
# display fitted trees
my_bsr.model()
# complexity, including complexity of each tree & total
complexity = my_bsr.complexity()bsr_paper.pdf: paper for Bayesian Symbolic Regression
Symbolic_Regression_Tree_MCMC.pdf: note for proposed algorithm
The first version, implementing the mcmc method for symbolic regression.
In the ReassignOperator transition, unary and binary operators are able to change to each other.
Let the input operators be stored in a list and can assign weight to the specified operators.
The probability of Grow is
Add new actions, transform and detransform.
Uniformly pick a node and add a unary nonlinear node between it and its parent.
Uniformly pick a unary nonlinear node and substitute it with its child.
P_grow = (1-p_0)/3 * min {1,5/(N_nt+2)}, N_nt is the number of non-terminal nodes
P_prune = (1-p_0)/3 - P_grow
P_detrans = (1-p_0)/3 * (n1 / 2+ n1), n1 is the number of unary nonlinear nodes
P_trans = (1-p_0)/ [3*(N+5)], N is the number of all nodes
P_reop = P_refeat = (1-P_grow-P_prune-P_detrans-P_trans)/2
Modify the definition of transform and detransform.
Uniformly take a candidate node and place some operator as its parent
Uniformly take a candidate node and delete it; the candidate node should be non-terminal, and should not be the root if its child nodes are all terminal.
if it has two child nodes, randomly preserve one child (need to be non-terminal).
P_grow = (1-p_0)/3 * min {1,4/(N_nt+2)}, N_nt is the number of non-terminal nodes
P_prune = (1-p_0)/3 - P_grow
P_delete = (1-p_0)/3 * (Nc / Nc+3), Nc is the number of candidates for deletion.
P_insert = (1-p_0)/ 3 - P_delete; The probs added nodes should be proportional to the preset weights.
P_reop = P_refeat = (1-p_0)/ 6
consider the proportions of (p_grow+p_prune), (p_delete+p_insert), (p_reop+p_refeat)