# Bivariate ReLU Distribution

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## Bivariate ReLU Distribution

 Hi, I would rather have a Statistics related question hope experts here can provide some suggestions. I have posted this request in some other forum but failed to generate meaningful response I am looking for some technical document on deriving the Distribution function for sum of 2ย ReLU(๐)=max{0,๐} distributions i.eย max{0,๐1} +ย max{0,๐2} where X1 and X2 jointly follow some bivariate Nomal distribution. There are few technical notes available for univariateย ReLU distribution, however I failed to find any spec for bivariate/multivariate setup. Any pointer on above subject will be highly helpful.         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Bivariate ReLU Distribution

 NOTE: LIMITED TESTING (You may want to check this carefully, if you're interested in using it). library (kubik) library (mvtnorm) sim.cdf <- function (mx, my, sdx, sdy, cor, ..., n=2e5)     sim.cdf.2 (mx, my, sdx^2, sdy^2, sdx * sdy * cor, n=n) sim.cdf.2 <- function (mx, my, vx, vy, cov, ..., n=2e5) {   m <- c (mx, my)     v <- matrix (c (vx, cov, cov, vy), 2, 2)     u <- rmvnorm (2 * n, m, v)     for (i in 1:(2 * n) )         u [i] <- max (0, u [i])     z <- u [1:n] + u [(n + 1):(2 * n)]     P0 <- sum (z == 0) / n     z2 <- z [z != 0]     z2 <- c (-z2, z2)     de <- density (z2)     xFh <- chs.integral (de\$x, de\$y)     cx <- seq (0, max (de\$x), length.out=60)     cy <- xFh (cx)     cy <- cy - cy [1]     cy <- P0 + cy * (1 - P0) / cy [60]     cs = chs.constraints (increasing=TRUE)     chs (cx, cy, constraints=cs, outside = c (0, cy [60]) ) } #X1, X2 means: 0 and 2 #X1, Y2 sds: 1.5 and 3.5 #cor (X1, X2): 0.75 Fh <- sim.cdf (0, 2, 1.5, 3.5, 0.75) plot (Fh, ylim = c (0, 1.05), yaxs="i") #prob 1 < U < 2 Fh (2) - Fh (1) On Sat, Jul 11, 2020 at 1:49 AM Arun Kumar Saha via R-help <[hidden email]> wrote: > > Hi, > I would rather have a Statistics related question hope experts here can provide some suggestions. I have posted this request in some other forum but failed to generate meaningful response > I am looking for some technical document on deriving the Distribution function for sum of 2 ReLU(๐)=max{0,๐} distributions i.e max{0,๐1} + max{0,๐2} where X1 and X2 jointly follow some bivariate Nomal distribution. > There are few technical notes available for univariate ReLU distribution, however I failed to find any spec for bivariate/multivariate setup. > Any pointer on above subject will be highly helpful. >         [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Bivariate ReLU Distribution

 Last line should use outside = c (0, 1). But not that important. On Sat, Jul 11, 2020 at 1:31 PM Abby Spurdle <[hidden email]> wrote: > > NOTE: LIMITED TESTING > (You may want to check this carefully, if you're interested in using it). > > library (kubik) > library (mvtnorm) > > sim.cdf <- function (mx, my, sdx, sdy, cor, ..., n=2e5) >     sim.cdf.2 (mx, my, sdx^2, sdy^2, sdx * sdy * cor, n=n) > > sim.cdf.2 <- function (mx, my, vx, vy, cov, ..., n=2e5) > {   m <- c (mx, my) >     v <- matrix (c (vx, cov, cov, vy), 2, 2) >     u <- rmvnorm (2 * n, m, v) >     for (i in 1:(2 * n) ) >         u [i] <- max (0, u [i]) >     z <- u [1:n] + u [(n + 1):(2 * n)] > >     P0 <- sum (z == 0) / n > >     z2 <- z [z != 0] >     z2 <- c (-z2, z2) >     de <- density (z2) >     xFh <- chs.integral (de\$x, de\$y) > >     cx <- seq (0, max (de\$x), length.out=60) >     cy <- xFh (cx) >     cy <- cy - cy [1] >     cy <- P0 + cy * (1 - P0) / cy [60] > >     cs = chs.constraints (increasing=TRUE) >     chs (cx, cy, constraints=cs, outside = c (0, cy [60]) ) > } > > #X1, X2 means: 0 and 2 > #X1, Y2 sds: 1.5 and 3.5 > #cor (X1, X2): 0.75 > Fh <- sim.cdf (0, 2, 1.5, 3.5, 0.75) > > plot (Fh, ylim = c (0, 1.05), yaxs="i") > > #prob 1 < U < 2 > Fh (2) - Fh (1) > > > On Sat, Jul 11, 2020 at 1:49 AM Arun Kumar Saha via R-help > <[hidden email]> wrote: > > > > Hi, > > I would rather have a Statistics related question hope experts here can provide some suggestions. I have posted this request in some other forum but failed to generate meaningful response > > I am looking for some technical document on deriving the Distribution function for sum of 2 ReLU(๐)=max{0,๐} distributions i.e max{0,๐1} + max{0,๐2} where X1 and X2 jointly follow some bivariate Nomal distribution. > > There are few technical notes available for univariate ReLU distribution, however I failed to find any spec for bivariate/multivariate setup. > > Any pointer on above subject will be highly helpful. > >         [[alternative HTML version deleted]] > > > > ______________________________________________ > > [hidden email] mailing list -- To UNSUBSCRIBE and more, see > > https://stat.ethz.ch/mailman/listinfo/r-help> > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.