# Copyright 2014 Google Inc. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
library(limSolve)
library(Matrix)
# The next two functions create a matrix (G) and a vector (H) encoding
# linear inequality constraints that a solution vector (x) must satisfy:
# G * x >= H
# Currently represent three sets of constraints on the solution vector:
# - all solution coefficients are nonnegative
# - the sum total of all solution coefficients is no more than 1
# - in each of the coordinates of the target vector (estimated Bloom filter)
# we don't overshoot by more than three standard deviations.
MakeG <- function(n, X) {
d <- Diagonal(n)
last <- rep(-1, n)
rbind2(rbind2(d, last), -X)
}
MakeH <- function(n, Y, stds) {
# set the floor at 0.01 to avoid degenerate cases
YY <- apply(Y + 3 * stds, # in each bin don't overshoot by more than 3 stds
1:2,
function(x) min(1, max(0.01, x))) # clamp the bound to [0.01,1]
c(rep(0, n), # non-negativity condition
-1, # coefficients sum up to no more than 1
-as.vector(t(YY)) # t is important!
)
}
MakeLseiModel <- function(X, Y, stds) {
m <- dim(X)[1]
n <- dim(X)[2]
# no slack variables for now
# slack <- Matrix(FALSE, nrow = m, ncol = m, sparse = TRUE)
# colnames(slack) <- 1:m
# diag(slack) <- TRUE
#
# G <- MakeG(n + m)
# H <- MakeH(n + m)
#
# G[n+m+1,n:(n+m)] <- -0.1
# A = cbind2(X, slack)
w <- as.vector(t(1 / stds))
w_median <- median(w[!is.infinite(w)])
if(is.na(w_median)) # all w are infinite
w_median <- 1
w[w > w_median * 2] <- w_median * 2
w <- w / mean(w)
list(# coerce sparse Boolean matrix X to sparse numeric matrix
A = Diagonal(x = w) %*% (X + 0),
B = as.vector(t(Y)) * w, # transform to vector in the row-first order
G = MakeG(n, X),
H = MakeH(n, Y, stds),
type = 2) # Since there are no equality constraints, lsei defaults to
# solve.QP anyway, but outputs a warning unless type == 2.
}
# CustomLM(X, Y)
ConstrainedLinModel <- function(X,Y) {
model <- MakeLseiModel(X, Y$estimates, Y$stds)
coefs <- do.call(lsei, model)$X
names(coefs) <- colnames(X)
coefs
}
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