1# Copyright 2014 Google Inc. All rights reserved. 2# 3# Licensed under the Apache License, Version 2.0 (the "License"); 4# you may not use this file except in compliance with the License. 5# You may obtain a copy of the License at 6# 7# http://www.apache.org/licenses/LICENSE-2.0 8# 9# Unless required by applicable law or agreed to in writing, software 10# distributed under the License is distributed on an "AS IS" BASIS, 11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12# See the License for the specific language governing permissions and 13# limitations under the License. 14 15library(limSolve) 16library(Matrix) 17 18# The next two functions create a matrix (G) and a vector (H) encoding 19# linear inequality constraints that a solution vector (x) must satisfy: 20# G * x >= H 21 22# Currently represent three sets of constraints on the solution vector: 23# - all solution coefficients are nonnegative 24# - the sum total of all solution coefficients is no more than 1 25# - in each of the coordinates of the target vector (estimated Bloom filter) 26# we don't overshoot by more than three standard deviations. 27MakeG <- function(n, X) { 28 d <- Diagonal(n) 29 last <- rep(-1, n) 30 rbind2(rbind2(d, last), -X) 31} 32 33MakeH <- function(n, Y, stds) { 34 # set the floor at 0.01 to avoid degenerate cases 35 YY <- apply(Y + 3 * stds, # in each bin don't overshoot by more than 3 stds 36 1:2, 37 function(x) min(1, max(0.01, x))) # clamp the bound to [0.01,1] 38 39 c(rep(0, n), # non-negativity condition 40 -1, # coefficients sum up to no more than 1 41 -as.vector(t(YY)) # t is important! 42 ) 43} 44 45MakeLseiModel <- function(X, Y, stds) { 46 m <- dim(X)[1] 47 n <- dim(X)[2] 48 49# no slack variables for now 50# slack <- Matrix(FALSE, nrow = m, ncol = m, sparse = TRUE) 51# colnames(slack) <- 1:m 52# diag(slack) <- TRUE 53# 54# G <- MakeG(n + m) 55# H <- MakeH(n + m) 56# 57# G[n+m+1,n:(n+m)] <- -0.1 58# A = cbind2(X, slack) 59 60 w <- as.vector(t(1 / stds)) 61 w_median <- median(w[!is.infinite(w)]) 62 if(is.na(w_median)) # all w are infinite 63 w_median <- 1 64 w[w > w_median * 2] <- w_median * 2 65 w <- w / mean(w) 66 67 list(# coerce sparse Boolean matrix X to sparse numeric matrix 68 A = Diagonal(x = w) %*% (X + 0), 69 B = as.vector(t(Y)) * w, # transform to vector in the row-first order 70 G = MakeG(n, X), 71 H = MakeH(n, Y, stds), 72 type = 2) # Since there are no equality constraints, lsei defaults to 73 # solve.QP anyway, but outputs a warning unless type == 2. 74} 75 76# CustomLM(X, Y) 77ConstrainedLinModel <- function(X,Y) { 78 model <- MakeLseiModel(X, Y$estimates, Y$stds) 79 coefs <- do.call(lsei, model)$X 80 names(coefs) <- colnames(X) 81 82 coefs 83}