Function that constructs default or commonly use penalty matrices according
to a (factorial) study design. The constructed penalty matrix can be used
directly in optPenalty.fused.auto or serve as basis for
modification.
default.penalty(
G,
df,
type = c("Complete", "CartesianEqual", "CartesianUnequal", "TensorProd")
)A numeric giving the number of classes. Can also be a
list of length G such as the usual argument Slist from
other rags2ridges functions. Can be omitted if df is given.
A data.frame with G rows and factors in the columns.
Note, the columns has to be of type factor. Can be omitted when
G is given and type == "Complete". The factors can be
ordered.
A character giving the type of fused penalty graph to construct.
Should be 'Complete' (default), 'CartesianEqual', or
'CartesianUnequal' or 'TensorProd' or an unique abbreviation
hereof. See details.
Returns a G by G character matrix which specify the
class of penalty graphs to be used. The output is suitable as input for
the penalty matrix used in optPenalty.fused.auto.
The type gives a number of common choices for the penalty matrix:
'Complete' is the complete penalty graph with equal
penalties.
'CartesianEqual' corresponds to a penalizing along
each "direction" of factors with a common penalty. The choice is named
Cartesian as it is the Cartesian graph product of the complete penalty
graphs for the individual factors.
'CartesianUnequal'
corresponds to a penalizing each direction of factors with individual
penalties.
'TensorProd' correspond to penalizing the
"diagonals" only. It is equivalent to the graph tensor products of the
complete graphs for each individual factor.
Bilgrau, A.E., Peeters, C.F.W., Eriksen, P.S., Boegsted, M., and van Wieringen, W.N. (2020). Targeted Fused Ridge Estimation of Inverse Covariance Matrices from Multiple High-Dimensional Data Classes. Journal of Machine Learning Research, 21(26): 1-52.
# Handling one-way designs
default.penalty(2)
#> 1 2
#> 1 "ridge" "fusion"
#> 2 "fusion" "ridge"
default.penalty(4)
#> 1 2 3 4
#> 1 "ridge" "fusion" "fusion" "fusion"
#> 2 "fusion" "ridge" "fusion" "fusion"
#> 3 "fusion" "fusion" "ridge" "fusion"
#> 4 "fusion" "fusion" "fusion" "ridge"
Slist <- vector("list", 6)
default.penalty(Slist) # The function uses only the length of the list
#> 1 2 3 4 5 6
#> 1 "ridge" "fusion" "fusion" "fusion" "fusion" "fusion"
#> 2 "fusion" "ridge" "fusion" "fusion" "fusion" "fusion"
#> 3 "fusion" "fusion" "ridge" "fusion" "fusion" "fusion"
#> 4 "fusion" "fusion" "fusion" "ridge" "fusion" "fusion"
#> 5 "fusion" "fusion" "fusion" "fusion" "ridge" "fusion"
#> 6 "fusion" "fusion" "fusion" "fusion" "fusion" "ridge"
df0 <- expand.grid(Factor = c("lvl1", "lvl2"))
default.penalty(df0)
#> lvl1 lvl2
#> lvl1 "ridge" "fusion"
#> lvl2 "fusion" "ridge"
# A more elaborate example
df1 <- expand.grid(DS = c("DS1", "DS2", "DS3"), ER = c("ER+", "ER-"))
# Usage (various interface demonstrations)
default.penalty(6, df1, type = "Complete")
#> DS1:ER+ DS2:ER+ DS3:ER+ DS1:ER- DS2:ER- DS3:ER-
#> DS1:ER+ "ridge" "fusion" "fusion" "fusion" "fusion" "fusion"
#> DS2:ER+ "fusion" "ridge" "fusion" "fusion" "fusion" "fusion"
#> DS3:ER+ "fusion" "fusion" "ridge" "fusion" "fusion" "fusion"
#> DS1:ER- "fusion" "fusion" "fusion" "ridge" "fusion" "fusion"
#> DS2:ER- "fusion" "fusion" "fusion" "fusion" "ridge" "fusion"
#> DS3:ER- "fusion" "fusion" "fusion" "fusion" "fusion" "ridge"
default.penalty(6, type = "CartesianEqual") # GIVES WARNING
#> Warning: No data.frame 'df' given and 'type' does not equal 'Complete'. Setting 'type' to 'Complete'
#> 1 2 3 4 5 6
#> 1 "ridge" "fusion" "fusion" "fusion" "fusion" "fusion"
#> 2 "fusion" "ridge" "fusion" "fusion" "fusion" "fusion"
#> 3 "fusion" "fusion" "ridge" "fusion" "fusion" "fusion"
#> 4 "fusion" "fusion" "fusion" "ridge" "fusion" "fusion"
#> 5 "fusion" "fusion" "fusion" "fusion" "ridge" "fusion"
#> 6 "fusion" "fusion" "fusion" "fusion" "fusion" "ridge"
default.penalty(6, df1, type = "CartesianEqual")
#> DS1:ER+ DS1:ER- DS2:ER+ DS2:ER- DS3:ER+ DS3:ER-
#> DS1:ER+ "ridge" "fusion" "fusion" "" "fusion" ""
#> DS1:ER- "fusion" "ridge" "" "fusion" "" "fusion"
#> DS2:ER+ "fusion" "" "ridge" "fusion" "fusion" ""
#> DS2:ER- "" "fusion" "fusion" "ridge" "" "fusion"
#> DS3:ER+ "fusion" "" "fusion" "" "ridge" "fusion"
#> DS3:ER- "" "fusion" "" "fusion" "fusion" "ridge"
default.penalty(Slist, df1, type = "CartesianEqual")
#> DS1:ER+ DS1:ER- DS2:ER+ DS2:ER- DS3:ER+ DS3:ER-
#> DS1:ER+ "ridge" "fusion" "fusion" "" "fusion" ""
#> DS1:ER- "fusion" "ridge" "" "fusion" "" "fusion"
#> DS2:ER+ "fusion" "" "ridge" "fusion" "fusion" ""
#> DS2:ER- "" "fusion" "fusion" "ridge" "" "fusion"
#> DS3:ER+ "fusion" "" "fusion" "" "ridge" "fusion"
#> DS3:ER- "" "fusion" "" "fusion" "fusion" "ridge"
default.penalty(6, df1, type = "CartesianUnequal")
#> DS1:ER+ DS1:ER- DS2:ER+ DS2:ER- DS3:ER+ DS3:ER-
#> DS1:ER+ "ridge" "ER" "DS" "" "DS" ""
#> DS1:ER- "ER" "ridge" "" "DS" "" "DS"
#> DS2:ER+ "DS" "" "ridge" "ER" "DS" ""
#> DS2:ER- "" "DS" "ER" "ridge" "" "DS"
#> DS3:ER+ "DS" "" "DS" "" "ridge" "ER"
#> DS3:ER- "" "DS" "" "DS" "ER" "ridge"
default.penalty(df1)
#> DS1:ER+ DS2:ER+ DS3:ER+ DS1:ER- DS2:ER- DS3:ER-
#> DS1:ER+ "ridge" "fusion" "fusion" "fusion" "fusion" "fusion"
#> DS2:ER+ "fusion" "ridge" "fusion" "fusion" "fusion" "fusion"
#> DS3:ER+ "fusion" "fusion" "ridge" "fusion" "fusion" "fusion"
#> DS1:ER- "fusion" "fusion" "fusion" "ridge" "fusion" "fusion"
#> DS2:ER- "fusion" "fusion" "fusion" "fusion" "ridge" "fusion"
#> DS3:ER- "fusion" "fusion" "fusion" "fusion" "fusion" "ridge"
# A 2 by 2 by 2 design
df2 <- expand.grid(A = c("A1", "A2"), B = c("B1", "B2"), C = c("C1", "C3"))
default.penalty(df2)
#> A1:B1:C1 A2:B1:C1 A1:B2:C1 A2:B2:C1 A1:B1:C3 A2:B1:C3 A1:B2:C3
#> A1:B1:C1 "ridge" "fusion" "fusion" "fusion" "fusion" "fusion" "fusion"
#> A2:B1:C1 "fusion" "ridge" "fusion" "fusion" "fusion" "fusion" "fusion"
#> A1:B2:C1 "fusion" "fusion" "ridge" "fusion" "fusion" "fusion" "fusion"
#> A2:B2:C1 "fusion" "fusion" "fusion" "ridge" "fusion" "fusion" "fusion"
#> A1:B1:C3 "fusion" "fusion" "fusion" "fusion" "ridge" "fusion" "fusion"
#> A2:B1:C3 "fusion" "fusion" "fusion" "fusion" "fusion" "ridge" "fusion"
#> A1:B2:C3 "fusion" "fusion" "fusion" "fusion" "fusion" "fusion" "ridge"
#> A2:B2:C3 "fusion" "fusion" "fusion" "fusion" "fusion" "fusion" "fusion"
#> A2:B2:C3
#> A1:B1:C1 "fusion"
#> A2:B1:C1 "fusion"
#> A1:B2:C1 "fusion"
#> A2:B2:C1 "fusion"
#> A1:B1:C3 "fusion"
#> A2:B1:C3 "fusion"
#> A1:B2:C3 "fusion"
#> A2:B2:C3 "ridge"
default.penalty(df2, type = "CartesianEqual")
#> A1:B1:C1 A1:B1:C3 A1:B2:C1 A1:B2:C3 A2:B1:C1 A2:B1:C3 A2:B2:C1
#> A1:B1:C1 "ridge" "fusion" "fusion" "" "fusion" "" ""
#> A1:B1:C3 "fusion" "ridge" "" "fusion" "" "fusion" ""
#> A1:B2:C1 "fusion" "" "ridge" "fusion" "" "" "fusion"
#> A1:B2:C3 "" "fusion" "fusion" "ridge" "" "" ""
#> A2:B1:C1 "fusion" "" "" "" "ridge" "fusion" "fusion"
#> A2:B1:C3 "" "fusion" "" "" "fusion" "ridge" ""
#> A2:B2:C1 "" "" "fusion" "" "fusion" "" "ridge"
#> A2:B2:C3 "" "" "" "fusion" "" "fusion" "fusion"
#> A2:B2:C3
#> A1:B1:C1 ""
#> A1:B1:C3 ""
#> A1:B2:C1 ""
#> A1:B2:C3 "fusion"
#> A2:B1:C1 ""
#> A2:B1:C3 "fusion"
#> A2:B2:C1 "fusion"
#> A2:B2:C3 "ridge"
default.penalty(df2, type = "CartesianUnequal")
#> A1:B1:C1 A1:B1:C3 A1:B2:C1 A1:B2:C3 A2:B1:C1 A2:B1:C3 A2:B2:C1
#> A1:B1:C1 "ridge" "C" "B" "" "A" "" ""
#> A1:B1:C3 "C" "ridge" "" "B" "" "A" ""
#> A1:B2:C1 "B" "" "ridge" "C" "" "" "A"
#> A1:B2:C3 "" "B" "C" "ridge" "" "" ""
#> A2:B1:C1 "A" "" "" "" "ridge" "C" "B"
#> A2:B1:C3 "" "A" "" "" "C" "ridge" ""
#> A2:B2:C1 "" "" "A" "" "B" "" "ridge"
#> A2:B2:C3 "" "" "" "A" "" "B" "C"
#> A2:B2:C3
#> A1:B1:C1 ""
#> A1:B1:C3 ""
#> A1:B2:C1 ""
#> A1:B2:C3 "A"
#> A2:B1:C1 ""
#> A2:B1:C3 "B"
#> A2:B2:C1 "C"
#> A2:B2:C3 "ridge"