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