[TREE] add interaction constraints (#3466)

* add interaction constraints

* enable both interaction and monotonic constraints at the same time

* fix lint

* add R test, fix lint, update demo

* Use dmlc::JSONReader to express interaction constraints as nested lists; Use sparse arrays for bookkeeping

* Add Python test for interaction constraints

* make R interaction constraints parameter based on feature index instead of column names, fix R coding style

* Fix lint

* Add BlueTea88 to CONTRIBUTORS.md

* Short circuit when no constraint is specified; address review comments

* Add tutorial for feature interaction constraints

* allow interaction constraints to be passed as string, remove redundant column_names argument

* Fix typo

* Address review comments

* Add comments to Python test

R-package/tests/testthat/test_interaction_constraints.R

@@ -0,0 +1,38 @@
+require(xgboost)
+
+context("interaction constraints")
+
+set.seed(1024)
+x1 <- rnorm(1000, 1)
+x2 <- rnorm(1000, 1)
+x3 <- sample(c(1,2,3), size=1000, replace=TRUE)
+y <- x1 + x2 + x3 + x1*x2*x3 + rnorm(1000, 0.001) + 3*sin(x1)
+train <- matrix(c(x1,x2,x3), ncol = 3)
+
+test_that("interaction constraints for regression", {
+  # Fit a model that only allows interaction between x1 and x2
+  bst <- xgboost(data = train, label = y, max_depth = 3,
+                 eta = 0.1, nthread = 2, nrounds = 100, verbose = 0,
+                 interaction_constraints = list(c(0,1)))
+  
+  # Set all observations to have the same x3 values then increment
+  #  by the same amount
+	preds <- lapply(c(1,2,3), function(x){
+		tmat <- matrix(c(x1,x2,rep(x,1000)), ncol=3)
+		return(predict(bst, tmat))
+	})
+
+  # Check incrementing x3 has the same effect on all observations
+  #   since x3 is constrained to be independent of x1 and x2
+  #   and all observations start off from the same x3 value
+	diff1 <- preds[[2]] - preds[[1]]
+	test1 <- all(abs(diff1 - diff1[1]) < 1e-4)
+	
+	diff2 <- preds[[3]] - preds[[2]]
+	test2 <- all(abs(diff2 - diff2[1]) < 1e-4)
+	
+  expect_true({
+    test1 & test2
+  }, "Interaction Contraint Satisfied")
+  
+})