BCW and K

Experiments with BCW can be run with programs in carts/bcw/ and with K in carts/kyphosis. For the former we used two different priors, the GROWTREE and EDITTREE priors. The GROWTREE prior can be found in carts/bcw/grow/slps/unify.slp while the EDITTREE prior is in carts/bcw/edit/slps/edit.slp. For K, a much smaller data set, only the GROWTREE is present.

The GROWTREE prior, is essentially that used by [Chipman HChipman H1998]. The stochastic process which defines a GROWTREE prior grows a C&RT tree by starting with a single leaf node and then repeatedly splits each leaf node $\eta$ with a probability $\alpha(1+d_{\eta})^{-\beta}$, where $d_\eta$ is the depth of node $\eta$ and $\alpha$ and $\beta$ are prior parameters set by the user to control the size of trees. Unsplit nodes become leaves of the tree. If a node is split, the splitting rule for that split is chosen uniformly. The source is in carts/bcw/grow/slps/unify.slp.

The other type of prior is the EDITTREE prior. Here an `initial' C&RT model is supplied. This can be any tree, for example the tree produced by the standard greedy algorithm or one manually entered by the user. This tree is then probabilistically edited. This approach is closely related to the proposal mechanisms of [Chipman HChipman H1998,Denison H. A.Denison H. A.1998]. The source is in file carts/bcw/edit/slps/edit.slp where, with probability 4/5 the tree is edited. There are three possible editions: growing the tree by splitting a leaf, pruning the tree by merging neighbouring leaves and changing a splitting rule. Our likelihood, file carts/src/cart_llhood, is implementing [Chipman HChipman H1998, Eq.16]. C&RTs, are also displayed using disp_bn/1. Undirected links are drawn in black, with no arrows in either direction.