GH-16208: Adding constrained GLM documentation to user guidem [nocheck] [nochecks]

[hannah-tillman]

#16208

[wendycwong]

@hannah-tillman : Can you derive an python example from this:

def test_separate_linear_beta_gaussian():
'''
This test will check that when separate_linear_beta=True, those coefficients should be within the beta constraint
range.
'''
h2o_data = h2o.import_file(
path=pyunit_utils.locate("smalldata/glm_test/gaussian_20cols_10000Rows.csv"))
enum_columns = ["C1", "C2", "C3", "C4", "C5", "C6", "C7", "C8", "C9", "C10"]
for cname in enum_columns:
h2o_data[cname] = h2o_data[cname].asfactor()
myY = "C21"
myX = h2o_data.names.remove(myY)

linear_constraints = [] # this constraint is satisfied by default coefficient initialization
name = "C1.2"
values = 1
types = "Equal"
contraint_numbers = 0
linear_constraints.append([name, values, types, contraint_numbers])

name = "C11"
values = 1
types = "Equal"
contraint_numbers = 0
linear_constraints.append([name, values, types, contraint_numbers])

name = "constant"
values = 13.56 
types = "Equal"
contraint_numbers = 0
linear_constraints.append([name, values, types, contraint_numbers])

name = "C5.2"
values = 1
types = "LessThanEqual"
contraint_numbers = 1
linear_constraints.append([name, values, types, contraint_numbers])

name = "C12"
values = 1
types = "LessThanEqual"
contraint_numbers = 1
linear_constraints.append([name, values, types, contraint_numbers])

name = "C15"
values = 1
types = "LessThanEqual"
contraint_numbers = 1
linear_constraints.append([name, values, types, contraint_numbers])

name = "constant"
values = -5
types = "LessThanEqual"
contraint_numbers = 1
linear_constraints.append([name, values, types, contraint_numbers])

linear_constraints2 = h2o.H2OFrame(linear_constraints)
linear_constraints2.set_names(["names", "values", "types", "constraint_numbers"])

bc = []
name = "C1.1"
c1p1LowerBound = -36
c1p1UpperBound=-35
bc.append([name, c1p1LowerBound, c1p1UpperBound])

name = "C5.2"
c5p2LowerBound=-14
c5p2UpperBound=-13
bc.append([name, c5p2LowerBound, c5p2UpperBound])

name = "C11"
c11LowerBound=25
c11UpperBound=26
bc.append([name, c11LowerBound, c11UpperBound])

name = "C15"
c15LowerBound=14
c15UpperBound=15
bc.append([name, c15LowerBound, c15UpperBound])

beta_constraints = h2o.H2OFrame(bc)
beta_constraints.set_names(["names", "lower_bounds", "upper_bounds"])
      
m_sep = glm(family='gaussian', linear_constraints=linear_constraints2, solver="irlsm", lambda_=0.0,
             beta_constraints=beta_constraints, constraint_eta0=0.1, constraint_tau=10,
             constraint_alpha=0.01, constraint_beta=0.9, constraint_c0=100)
m_sep.train(training_frame=h2o_data,x=myX, y=myY)
coef_sep = m_sep.coef()

[wendycwong]

@hannah-tillman :

The equivalent R example for constrained GLM is:

h2o_data <- h2o.importFile("https://s3.amazonaws.com/h2o-public-test-data/smalldata/glm_test/gaussian_20cols_10000Rows.csv")
enum_columns = c("C1", "C2", "C3", "C4", "C5", "C6", "C7", "C8", "C9", "C10")
for (cname in enum_columns)
h2o.asfactor(h2o_data[cname])
myY = "C21"
col_names <- names(h2o_data)
myX <- col_names[1:20]

constraints <- data.frame(names <- c("C1.2", "C11", "constant", "C5.2", "C12", "C15", "constant"),
values <- c(1, 1, 13.56, 1, 1, 1, -5),
types <- c("Equal", "Equal", "Equal", "LessThanEqual", "LessThanEqual", "LessThanEqual", "LessThanEqual"),
constraint_numbers <- c(0, 0, 0, 1, 1, 1, 1))
constraints_h2o <- as.h2o(constraints)
bc <- data.frame(names <- c("C1.1", "C5.2", "C11", "C15"), lower_bounds <- c(-36, -14, 25, 14), upper_bounds <- c(-35, -13, 26, 15))
bc_h2o <- as.h2o(bc)
m_sep <- h2o.glm(x=myX, y=myY, training_frame=h2o.data, family='gaussian', linear_constraints=linear_constraints2, solver="irlsm", lambda=0.0,
beta_constraints=beta_constraints, constraint_eta0=0.1, constraint_tau=10,
constraint_alpha=0.01, constraint_beta=0.9, constraint_c0=100)
h2o.coef(m_sep)