performance - R: Speed up multiple lm() -
i want estimate parameters of non linear model.
the model equation z = * exp(- * x) + b * exp(- b * y) + c
- x , y predictors
- a, b, a, b parameters estimate
what did transform model linear problem doing exponential transformation before doing linear regression:
- for
a,bbetween 0 , 1, computeexp_x = exp(- * x),exp_y = exp(- b * y) - i linear regression
z ~ exp_x + exp_y
it works can see in simulation
x = 1:10 y = 1:10 combination = expand.grid(x = x, y = y) df = data.frame( x = combination$x, y = combination$y, z = 2 * exp(-0.3 * combination$x) + 5 * exp(-0.6 * combination$y) + rnorm(n = 100, mean = 0, sd = 0.1 ) ) a_hat = 0 b_hat = 0 best_ols = null best_rsquared = 0 (a in seq(0.01, 1, 0.01)){ (b in seq(0.01, 1, 0.01)){ df$exp_x = exp(- * df$x) df$exp_y = exp(- b *df$y) ols = lm(data = df, formula = z ~ exp_x + exp_y) r_squared = summary(ols)$r.squared if (r_squared > best_rsquared){ best_rsquared = r_squared a_hat = b_hat = b best_ols = ols } } } a_hat b_hat best_ols best_rsquared > a_hat [1] 0.34 > b_hat [1] 0.63 > best_ols call: lm(formula = z ~ exp_x + exp_y, data = df) coefficients: (intercept) exp_x exp_y 0.0686 2.0550 5.1189 > best_rsquared [1] 0.9898669 problem: slow
it takes around 10 secs , need thousands times on others data frame.
how drastically speed up?
perhaps use nls instead. since did not set.seed(), cannot see whether our predictions similar, @ least got a , b estimates "right" after edit:
nmod <- nls( z ~ a*exp(-a*x)+b*exp(-b*y), data=df, start=list(a=0.5, b=0.5, a=.1,b=.1)) > coef(nmod) b b 2.0005670 4.9541553 0.2951589 0.5937909 #-------- > nmod nonlinear regression model model: z ~ * exp(-a * x) + b * exp(-b * y) data: df b b 2.0006 4.9542 0.2952 0.5938 residual sum-of-squares: 0.9114 number of iterations convergence: 9 achieved convergence tolerance: 5.394e-06 much faster 10 second experience. , on 8 year-old machine.
> system.time( nmod <- nls( z ~ a*exp(-a*x)+b*exp(-b*y), data=df, start=list(a=0.5, b=0.5, a=.1,b=.1)) ) user system elapsed 0.036 0.002 0.033
Comments
Post a Comment