contrasts

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¶ Learning Contrast Sets tim@menzies.us August'17 This code is a post-processor to the `sdtree` decision-tree learner (and assumes that all attributes are `sym`s or discretized `num`s. It gets called like this: `local CON=require "contrasts" -- this package local TREES=require "trees" -- returns some trees local TREE=require "sdtree" -- the decision tree learner -- lets go local x=TREES.auto() -- a sample tree TREE.show(x) -- show the tree b=CON.branches(x) CON.plans(b) CON.monitors(b)` Contrasts are computed between the branches to all nodes in a tree. (and the contrast is the set delta between the attribute values seen the branches leading to `branch2` from `branch1`. This code ignores dull deltas; i.e. RULE1: the median value of `branch2` is not `better` than `branch1` (where `better` is a customizable predicate, see below). RULE2: The distribution of the target variable is statistically the same in both branches; RULE3: The size of the delta between the branches is larger than zero. These three rules are implemented in the `contrasts` function, show below. Constrast sets can either be plans or monitors. In the former, we seek changes that drive us from a lesser `branch1` to a better `branch2`. In the latter, we seek things to avoid. These are changes which, if they happen, would drive us from a better `branch1` to a worse `branch2`. Hence we can create plans or monitors as follows: `local function more(x,y) return x > y end local function less(x,y) return x < y end -- the above controls what constrast are selected local function plans(branches) return contrasts(branches, more) end local function monitors(branches) return contrasts(branches, less) end`	require "show" local THE=require "config" local TREE=require "sdtree" local TREES=require "trees" local LST=require "lists" local NUM=require "num"
¶ Feature extractor from the brnaches. Collects all the `attr`, `val` pairs.	local function has(branch) local out = {} for i=1,#branch do local step = branch[i] out[#out+1] = {attr=step.attr, val=step.val} end return out end local function have(branches) for _,branch in pairs(branches) do branch.has = has(branch) end return branches end
¶ Generator for the branches. Walk down the tree and, for each node, add the branch `b` to that node to `out`.	local function branches1(tr,out,b) if tr.attr then b[#b+1] = {attr=tr.attr,val=tr.val,_stats=tr.stats} end if #b > 0 then out[#out+1] = b end for _,kid in pairs(tr._kids) do branches1(kid,out,LST.copy(b)) end return out end local function branches(tr) return have(branches1(tr,{},{})) end
¶ Compute the set delta between two branches.	local function member2(twin0,twins) for _,twin1 in pairs(twins) do if twin0.attr == twin1.attr and twin0.val == twin1.val then return true end end return false end local function delta(t1, t2) local out={} for _,twin in pairs(t1) do if not member2(twin,t2) then out[#out+1] = {twin.attr, twin.val} end end return out end
¶ The worker. This code returns at most two branches per node: one showing the branch to maximum improvement; and another showing the branch with mininum delta.	local function contrasts(branches, better) for i,branch1 in pairs(branches) do local out={} for j,branch2 in pairs(branches) do if i ~= j then local num1=LST.last(branch1)._stats local num2=LST.last(branch2)._stats if better(num2.mu, num1.mu) then -- RULE1 if not NUM.same(num1,num2) then -- RULE2 local inc = delta(branch2.has,branch1.has) if #inc > 0 then -- RULE3 out[#out+1] = {i=i,j=j,ninc=#inc,muinc=num2.mu - num1.mu, inc=inc, branch1=branch1.has,mu1=num1.mu, branch2=branch2.has,mu2=num2.mu} end end end end end print("") table.sort(out, function (x,y) return x.muinc > y.muinc end) print(i,"max mu ",out[1]) table.sort(out, function (x,y) return x.ninc < y.ninc end) print(i,"min inc ",out[1]) end end
¶ Plans are things we want to do. Monitors are things we want to avoid.
¶ More specfically, plans are to branches with `more` value.	local function more(x,y) return x > y end
¶ And monitors are to branches with `less` value.	local function less(x,y) return x < y end
¶ Main driver	local function plans(branches) return contrasts(branches, more) end local function monitors(branches) return contrasts(branches, less) end
¶ External interface	return {monitors=monitors, plans=plans,branches=branches}
¶ Legal LURE, Copyright (c) 2017, Tim Menzies All rights reserved, BSD 3-Clause License Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

LURE: contrasts

Learning Contrast Sets

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