Recently, I run into performance issue when fitting a linear model together with a resampling scheme and a tuning grid (via caret). The dataset was recently large - some 200k rows and approx. 20 columns (`nycflights13`

train). Still, I was suprised that my machine got stuck during the computation. Now I wonder whether I ran into memory constraints (16BG on my machine), or whether some other stuff went wrong.

# Load packages

```
library(tidyverse)
library(caret)
library(stringr)
```

# Load data

```
data("flights", package = "nycflights13")
glimpse(flights)
#> Observations: 336,776
#> Variables: 19
#> $ year <int> 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 2…
#> $ month <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
#> $ day <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
#> $ dep_time <int> 517, 533, 542, 544, 554, 554, 555, 557, 557, 558,…
#> $ sched_dep_time <int> 515, 529, 540, 545, 600, 558, 600, 600, 600, 600,…
#> $ dep_delay <dbl> 2, 4, 2, -1, -6, -4, -5, -3, -3, -2, -2, -2, -2, …
#> $ arr_time <int> 830, 850, 923, 1004, 812, 740, 913, 709, 838, 753…
#> $ sched_arr_time <int> 819, 830, 850, 1022, 837, 728, 854, 723, 846, 745…
#> $ arr_delay <dbl> 11, 20, 33, -18, -25, 12, 19, -14, -8, 8, -2, -3,…
#> $ carrier <chr> "UA", "UA", "AA", "B6", "DL", "UA", "B6", "EV", "…
#> $ flight <int> 1545, 1714, 1141, 725, 461, 1696, 507, 5708, 79, …
#> $ tailnum <chr> "N14228", "N24211", "N619AA", "N804JB", "N668DN",…
#> $ origin <chr> "EWR", "LGA", "JFK", "JFK", "LGA", "EWR", "EWR", …
#> $ dest <chr> "IAH", "IAH", "MIA", "BQN", "ATL", "ORD", "FLL", …
#> $ air_time <dbl> 227, 227, 160, 183, 116, 150, 158, 53, 140, 138, …
#> $ distance <dbl> 1400, 1416, 1089, 1576, 762, 719, 1065, 229, 944,…
#> $ hour <dbl> 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6…
#> $ minute <dbl> 15, 29, 40, 45, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
#> $ time_hour <dttm> 2013-01-01 05:00:00, 2013-01-01 05:00:00, 2013-0…
flights2 <- flights %>%
select(-year) %>%
drop_na()
```

Any NAs?

```
anyNA(flights2)
#> [1] FALSE
```

# Define computation load

Let’s run with some different sample size to gauge the performance.

Define the grid for the computation load, ie., sample size and number of predictors:

```
sample_size <- c(100, 500, 1000, 5000, 1e04, 2*1e04, 1e05)
k <- c(1, 2, 5, 10)
```

# Discard outcome vars

We do not want to draw the outcome variabls as predictors, hence we exclude them:

```
outcome_vars <- c("dep_delay", "arr_delay")
pred_names <- names(flights2)[!(names(flights2) %in% outcome_vars)]
pred_names
#> [1] "month" "day" "dep_time" "sched_dep_time"
#> [5] "arr_time" "sched_arr_time" "carrier" "flight"
#> [9] "tailnum" "origin" "dest" "air_time"
#> [13] "distance" "hour" "minute" "time_hour"
str(pred_names)
#> chr [1:16] "month" "day" "dep_time" "sched_dep_time" "arr_time" ...
pred_names[outcome_vars]
#> [1] NA NA
names(flights2)[outcome_vars]
#> [1] NA NA
```

Discarding using `purrr`

:

```
dummy <- str_detect(names(flights2), "_delay") %>% discard(.x = names(flights2), .p = .)
dummy
#> [1] "month" "day" "dep_time" "sched_dep_time"
#> [5] "arr_time" "sched_arr_time" "carrier" "flight"
#> [9] "tailnum" "origin" "dest" "air_time"
#> [13] "distance" "hour" "minute" "time_hour"
str(dummy)
#> chr [1:16] "month" "day" "dep_time" "sched_dep_time" "arr_time" ...
names(flights2)[outcome_vars]
#> [1] NA NA
```

Define index numbers of predictors:

```
set.seed(42)
pred_positions <- sample(x = 1:length(pred_names), size = 3)
pred_positions
#> [1] 1 5 16
pred_names <- pred_names[pred_positions]
pred_names
#> [1] "month" "arr_time" "time_hour"
```

And now we draw the desired number of preditors:

`flights_k <- select(flights, one_of(pred_names))`

Put that into a function, and wait: some categorical columns are a pain. Consider `dest`

with many levels. Let’s put in a lever to include ony numerical columns.

```
draw_preds_flights <- function(df = flights2, k, numeric_only = TRUE) {
if (numeric_only == TRUE) {
df <- df %>% select_if(is.numeric)
}
pred_names <- str_detect(names(df), "_delay") %>% discard(.x = names(df), .p = .)
pred_positions <- sample(x = 1:length(pred_names), size = k)
pred_names_selected <- pred_names[pred_positions]
flights_k <- select(df, one_of(pred_names_selected))
return(flights_k)
}
```

Test the function:

```
draw_preds_flights(k = 7) %>% str()
#> Classes 'tbl_df', 'tbl' and 'data.frame': 327346 obs. of 7 variables:
#> $ distance : num 1400 1416 1089 1576 762 ...
#> $ hour : num 5 5 5 5 6 5 6 6 6 6 ...
#> $ sched_dep_time: int 515 529 540 545 600 558 600 600 600 600 ...
#> $ day : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ air_time : num 227 227 160 183 116 150 158 53 140 138 ...
#> $ month : int 1 1 1 1 1 1 1 1 1 1 ...
#> $ minute : num 15 29 40 45 0 58 0 0 0 0 ...
```

Appears to work.

Here’s a cross val scheme:

```
my_crossval <- trainControl(method = "cv",
number = 5,
allowParallel = TRUE)
```

Here’s a scheme to turn it off:

`no_crossval <- trainControl(method = "none")`

Now craft a function that performs a lm fit using caret given the compution load.

```
lm_flights <- function(df = flights2, n, n_preds, crossval = my_crossval) {
df <- draw_preds_flights(df = df, k = n_preds)
# add outcome var:
df <- df %>%
bind_cols(flights2 %>% select(arr_delay))
df <- sample_n(df, size = n)
lm_fit1 <- train(arr_delay ~ .,
data = df,
method = "lm",
trControl = my_crossval)
return(lm_fit1)
}
```

Test the function.

```
start <- Sys.time()
dummy <- lm_flights(n = 200, n_preds = 3)
end <- Sys.time()
time_taken <- end - start
cat("Time taken: ", time_taken)
#> Time taken: 0.5061591
```

```
start <- Sys.time()
dummy <- lm_flights(n = 1000, n_preds = 3)
end <- Sys.time()
time_taken <- end - start
cat("Time taken: ", time_taken)
#> Time taken: 0.8717802
```

```
start <- Sys.time()
dummy <- lm_flights(n = 1e5, n_preds = 3)
end <- Sys.time()
time_taken <- end - start
cat("Time taken: ", time_taken)
#> Time taken: 2.815394
```

Register cores:

`doMC::registerDoMC(cores = 2)`

Now with more cores:

```
start <- Sys.time()
dummy <- lm_flights(n = 200, n_preds = 3)
end <- Sys.time()
time_taken <- end - start
cat("Time taken: ", time_taken)
#> Time taken: 0.565805
```

Half the time!

```
start <- Sys.time()
dummy <- lm_flights(n = 200, n_preds = 3, crossval = no_crossval)
end <- Sys.time()
time_taken <- end - start
cat("Time taken: ", time_taken)
#> Time taken: 0.5536761
summary(dummy)
#>
#> Call:
#> lm(formula = .outcome ~ ., data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -61.39 -22.68 -10.33 11.97 233.35
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -11.98724 10.39743 -1.153 0.25035
#> minute -0.03708 0.16008 -0.232 0.81706
#> air_time -0.02181 0.03611 -0.604 0.54662
#> hour 1.79362 0.64672 2.773 0.00608 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 42.72 on 196 degrees of freedom
#> Multiple R-squared: 0.0383, Adjusted R-squared: 0.02358
#> F-statistic: 2.602 on 3 and 196 DF, p-value: 0.05326
```

Define function that just gives back the time taken:

```
lm_flights_duration <- function(df = flights2, n, k, crossval = my_crossval) {
start <- Sys.time()
dummy <- lm_flights(df = df, n = n, n_preds = k, crossval = crossval)
end <- Sys.time()
rm(dummy)
time_taken <- end - start
return(time_taken)
}
```

Test it:

```
lm_flights_duration(n = 200, k = 3)
#> Time difference of 0.537606 secs
lm_flights_duration(n = 1000, k = 3)
#> Time difference of 0.5362749 secs
lm_flights_duration(n = 1e5, k = 3)
#> Time difference of 2.059408 secs
```

Low put that into a loop:

```
time_df <- tibble(n = NA,
k = NA,
time_taken = NA,
trial = NA,
run = NA)
i <- 1
j <- 1
trial <- 1
max_trial <- 10
run <- 1
for (i in seq_along(sample_size)) { # loop for sample size
cat("n = ", sample_size[i], "\n")
for (j in seq_along(k)) { # loop for number of predictors (k)
cat(" k = ", k[j], "\n")
for (trial in 1:max_trial) {
cat(" trial = ", trial, "\n")
cat(" run = ", run, "\n")
lm_duration <- lm_flights_duration(n = sample_size[i], k = k[j])
cat("Time taken for present model computation: ", lm_duration, " s \n")
time_df <- time_df %>%
add_row(n = sample_size[i],
k = k[j],
trial = trial,
time_taken = lm_duration,
run = run)
run <- run + 1
}
}
}
#> n = 100
#> k = 1
#> trial = 1
#> run = 1
#> Time taken for present model computation: 1.081863 s
#> trial = 2
#> run = 2
#> Time taken for present model computation: 0.4767709 s
#> trial = 3
#> run = 3
#> Time taken for present model computation: 0.4721088 s
#> trial = 4
#> run = 4
#> Time taken for present model computation: 0.438689 s
#> trial = 5
#> run = 5
#> Time taken for present model computation: 0.4379151 s
#> trial = 6
#> run = 6
#> Time taken for present model computation: 0.4470088 s
#> trial = 7
#> run = 7
#> Time taken for present model computation: 0.437305 s
#> trial = 8
#> run = 8
#> Time taken for present model computation: 0.437597 s
#> trial = 9
#> run = 9
#> Time taken for present model computation: 0.437248 s
#> trial = 10
#> run = 10
#> Time taken for present model computation: 0.435257 s
#> k = 2
#> trial = 1
#> run = 11
#> Time taken for present model computation: 0.4330289 s
#> trial = 2
#> run = 12
#> Time taken for present model computation: 0.443146 s
#> trial = 3
#> run = 13
#> Time taken for present model computation: 0.4344649 s
#> trial = 4
#> run = 14
#> Time taken for present model computation: 0.437479 s
#> trial = 5
#> run = 15
#> Time taken for present model computation: 0.440253 s
#> trial = 6
#> run = 16
#> Time taken for present model computation: 0.4336469 s
#> trial = 7
#> run = 17
#> Time taken for present model computation: 0.444977 s
#> trial = 8
#> run = 18
#> Time taken for present model computation: 0.4379861 s
#> trial = 9
#> run = 19
#> Time taken for present model computation: 0.4363792 s
#> trial = 10
#> run = 20
#> Time taken for present model computation: 0.5396779 s
#> k = 5
#> trial = 1
#> run = 21
#> Time taken for present model computation: 0.4446821 s
#> trial = 2
#> run = 22
#> Time taken for present model computation: 0.441684 s
#> trial = 3
#> run = 23
#> Time taken for present model computation: 0.4409502 s
#> trial = 4
#> run = 24
#> Time taken for present model computation: 0.5154259 s
#> trial = 5
#> run = 25
#> Time taken for present model computation: 0.439065 s
#> trial = 6
#> run = 26
#> Time taken for present model computation: 0.4437191 s
#> trial = 7
#> run = 27
#> Time taken for present model computation: 0.4360859 s
#> trial = 8
#> run = 28
#> Time taken for present model computation: 0.445807 s
#> trial = 9
#> run = 29
#> Time taken for present model computation: 0.4463658 s
#> trial = 10
#> run = 30
#> Time taken for present model computation: 0.4561081 s
#> k = 10
#> trial = 1
#> run = 31
#> Time taken for present model computation: 0.4590909 s
#> trial = 2
#> run = 32
#> Time taken for present model computation: 0.445292 s
#> trial = 3
#> run = 33
#> Time taken for present model computation: 0.439853 s
#> trial = 4
#> run = 34
#> Time taken for present model computation: 0.4462152 s
#> trial = 5
#> run = 35
#> Time taken for present model computation: 0.444721 s
#> trial = 6
#> run = 36
#> Time taken for present model computation: 0.4642301 s
#> trial = 7
#> run = 37
#> Time taken for present model computation: 0.44784 s
#> trial = 8
#> run = 38
#> Time taken for present model computation: 0.443491 s
#> trial = 9
#> run = 39
#> Time taken for present model computation: 0.448123 s
#> trial = 10
#> run = 40
#> Time taken for present model computation: 0.4442511 s
#> n = 500
#> k = 1
#> trial = 1
#> run = 41
#> Time taken for present model computation: 0.4442301 s
#> trial = 2
#> run = 42
#> Time taken for present model computation: 0.5318801 s
#> trial = 3
#> run = 43
#> Time taken for present model computation: 0.5844562 s
#> trial = 4
#> run = 44
#> Time taken for present model computation: 0.4407461 s
#> trial = 5
#> run = 45
#> Time taken for present model computation: 0.4416189 s
#> trial = 6
#> run = 46
#> Time taken for present model computation: 0.4451249 s
#> trial = 7
#> run = 47
#> Time taken for present model computation: 0.4442358 s
#> trial = 8
#> run = 48
#> Time taken for present model computation: 0.4367981 s
#> trial = 9
#> run = 49
#> Time taken for present model computation: 0.4361279 s
#> trial = 10
#> run = 50
#> Time taken for present model computation: 0.4720929 s
#> k = 2
#> trial = 1
#> run = 51
#> Time taken for present model computation: 0.5250502 s
#> trial = 2
#> run = 52
#> Time taken for present model computation: 0.441947 s
#> trial = 3
#> run = 53
#> Time taken for present model computation: 0.4436438 s
#> trial = 4
#> run = 54
#> Time taken for present model computation: 0.4400389 s
#> trial = 5
#> run = 55
#> Time taken for present model computation: 0.6254661 s
#> trial = 6
#> run = 56
#> Time taken for present model computation: 0.4434049 s
#> trial = 7
#> run = 57
#> Time taken for present model computation: 0.442023 s
#> trial = 8
#> run = 58
#> Time taken for present model computation: 0.444391 s
#> trial = 9
#> run = 59
#> Time taken for present model computation: 0.447026 s
#> trial = 10
#> run = 60
#> Time taken for present model computation: 0.446955 s
#> k = 5
#> trial = 1
#> run = 61
#> Time taken for present model computation: 0.4426479 s
#> trial = 2
#> run = 62
#> Time taken for present model computation: 0.6556299 s
#> trial = 3
#> run = 63
#> Time taken for present model computation: 0.631006 s
#> trial = 4
#> run = 64
#> Time taken for present model computation: 0.6135962 s
#> trial = 5
#> run = 65
#> Time taken for present model computation: 0.6482961 s
#> trial = 6
#> run = 66
#> Time taken for present model computation: 0.443377 s
#> trial = 7
#> run = 67
#> Time taken for present model computation: 0.4554012 s
#> trial = 8
#> run = 68
#> Time taken for present model computation: 0.4599311 s
#> trial = 9
#> run = 69
#> Time taken for present model computation: 0.455996 s
#> trial = 10
#> run = 70
#> Time taken for present model computation: 0.4931841 s
#> k = 10
#> trial = 1
#> run = 71
#> Time taken for present model computation: 0.4936209 s
#> trial = 2
#> run = 72
#> Time taken for present model computation: 0.497539 s
#> trial = 3
#> run = 73
#> Time taken for present model computation: 0.8787749 s
#> trial = 4
#> run = 74
#> Time taken for present model computation: 0.809119 s
#> trial = 5
#> run = 75
#> Time taken for present model computation: 0.5426331 s
#> trial = 6
#> run = 76
#> Time taken for present model computation: 0.464215 s
#> trial = 7
#> run = 77
#> Time taken for present model computation: 0.5386751 s
#> trial = 8
#> run = 78
#> Time taken for present model computation: 0.453577 s
#> trial = 9
#> run = 79
#> Time taken for present model computation: 0.4623952 s
#> trial = 10
#> run = 80
#> Time taken for present model computation: 0.4489491 s
#> n = 1000
#> k = 1
#> trial = 1
#> run = 81
#> Time taken for present model computation: 0.4592569 s
#> trial = 2
#> run = 82
#> Time taken for present model computation: 0.4496381 s
#> trial = 3
#> run = 83
#> Time taken for present model computation: 0.451736 s
#> trial = 4
#> run = 84
#> Time taken for present model computation: 0.4546001 s
#> trial = 5
#> run = 85
#> Time taken for present model computation: 0.4720671 s
#> trial = 6
#> run = 86
#> Time taken for present model computation: 0.446197 s
#> trial = 7
#> run = 87
#> Time taken for present model computation: 0.463027 s
#> trial = 8
#> run = 88
#> Time taken for present model computation: 0.4518969 s
#> trial = 9
#> run = 89
#> Time taken for present model computation: 0.449012 s
#> trial = 10
#> run = 90
#> Time taken for present model computation: 0.4623961 s
#> k = 2
#> trial = 1
#> run = 91
#> Time taken for present model computation: 0.4603031 s
#> trial = 2
#> run = 92
#> Time taken for present model computation: 0.457056 s
#> trial = 3
#> run = 93
#> Time taken for present model computation: 0.4493222 s
#> trial = 4
#> run = 94
#> Time taken for present model computation: 0.4531391 s
#> trial = 5
#> run = 95
#> Time taken for present model computation: 0.450547 s
#> trial = 6
#> run = 96
#> Time taken for present model computation: 0.472997 s
#> trial = 7
#> run = 97
#> Time taken for present model computation: 0.5127561 s
#> trial = 8
#> run = 98
#> Time taken for present model computation: 0.4521949 s
#> trial = 9
#> run = 99
#> Time taken for present model computation: 0.593178 s
#> trial = 10
#> run = 100
#> Time taken for present model computation: 0.5076699 s
#> k = 5
#> trial = 1
#> run = 101
#> Time taken for present model computation: 0.4637768 s
#> trial = 2
#> run = 102
#> Time taken for present model computation: 0.471168 s
#> trial = 3
#> run = 103
#> Time taken for present model computation: 0.487745 s
#> trial = 4
#> run = 104
#> Time taken for present model computation: 0.592675 s
#> trial = 5
#> run = 105
#> Time taken for present model computation: 0.5066102 s
#> trial = 6
#> run = 106
#> Time taken for present model computation: 0.585495 s
#> trial = 7
#> run = 107
#> Time taken for present model computation: 0.4994502 s
#> trial = 8
#> run = 108
#> Time taken for present model computation: 0.539782 s
#> trial = 9
#> run = 109
#> Time taken for present model computation: 0.49896 s
#> trial = 10
#> run = 110
#> Time taken for present model computation: 0.4953618 s
#> k = 10
#> trial = 1
#> run = 111
#> Time taken for present model computation: 0.5023279 s
#> trial = 2
#> run = 112
#> Time taken for present model computation: 0.5025802 s
#> trial = 3
#> run = 113
#> Time taken for present model computation: 0.509032 s
#> trial = 4
#> run = 114
#> Time taken for present model computation: 0.4841821 s
#> trial = 5
#> run = 115
#> Time taken for present model computation: 0.498765 s
#> trial = 6
#> run = 116
#> Time taken for present model computation: 0.4866431 s
#> trial = 7
#> run = 117
#> Time taken for present model computation: 0.499033 s
#> trial = 8
#> run = 118
#> Time taken for present model computation: 0.5038011 s
#> trial = 9
#> run = 119
#> Time taken for present model computation: 0.5065711 s
#> trial = 10
#> run = 120
#> Time taken for present model computation: 0.4977269 s
#> n = 5000
#> k = 1
#> trial = 1
#> run = 121
#> Time taken for present model computation: 0.5383601 s
#> trial = 2
#> run = 122
#> Time taken for present model computation: 0.5369561 s
#> trial = 3
#> run = 123
#> Time taken for present model computation: 0.5346379 s
#> trial = 4
#> run = 124
#> Time taken for present model computation: 0.5241148 s
#> trial = 5
#> run = 125
#> Time taken for present model computation: 0.5374188 s
#> trial = 6
#> run = 126
#> Time taken for present model computation: 0.5398779 s
#> trial = 7
#> run = 127
#> Time taken for present model computation: 0.573046 s
#> trial = 8
#> run = 128
#> Time taken for present model computation: 0.5561271 s
#> trial = 9
#> run = 129
#> Time taken for present model computation: 0.7098169 s
#> trial = 10
#> run = 130
#> Time taken for present model computation: 0.6438732 s
#> k = 2
#> trial = 1
#> run = 131
#> Time taken for present model computation: 0.5494349 s
#> trial = 2
#> run = 132
#> Time taken for present model computation: 0.5612428 s
#> trial = 3
#> run = 133
#> Time taken for present model computation: 0.536979 s
#> trial = 4
#> run = 134
#> Time taken for present model computation: 0.5327849 s
#> trial = 5
#> run = 135
#> Time taken for present model computation: 0.5426998 s
#> trial = 6
#> run = 136
#> Time taken for present model computation: 0.5875919 s
#> trial = 7
#> run = 137
#> Time taken for present model computation: 0.5822392 s
#> trial = 8
#> run = 138
#> Time taken for present model computation: 0.7569931 s
#> trial = 9
#> run = 139
#> Time taken for present model computation: 0.5909822 s
#> trial = 10
#> run = 140
#> Time taken for present model computation: 0.6130528 s
#> k = 5
#> trial = 1
#> run = 141
#> Time taken for present model computation: 0.5605171 s
#> trial = 2
#> run = 142
#> Time taken for present model computation: 0.66048 s
#> trial = 3
#> run = 143
#> Time taken for present model computation: 0.8047049 s
#> trial = 4
#> run = 144
#> Time taken for present model computation: 0.6085701 s
#> trial = 5
#> run = 145
#> Time taken for present model computation: 0.7481561 s
#> trial = 6
#> run = 146
#> Time taken for present model computation: 0.8513651 s
#> trial = 7
#> run = 147
#> Time taken for present model computation: 1.098596 s
#> trial = 8
#> run = 148
#> Time taken for present model computation: 0.7258921 s
#> trial = 9
#> run = 149
#> Time taken for present model computation: 0.823082 s
#> trial = 10
#> run = 150
#> Time taken for present model computation: 0.5915329 s
#> k = 10
#> trial = 1
#> run = 151
#> Time taken for present model computation: 0.6477251 s
#> trial = 2
#> run = 152
#> Time taken for present model computation: 0.628072 s
#> trial = 3
#> run = 153
#> Time taken for present model computation: 0.6369081 s
#> trial = 4
#> run = 154
#> Time taken for present model computation: 0.5999858 s
#> trial = 5
#> run = 155
#> Time taken for present model computation: 0.6012709 s
#> trial = 6
#> run = 156
#> Time taken for present model computation: 0.579746 s
#> trial = 7
#> run = 157
#> Time taken for present model computation: 0.610817 s
#> trial = 8
#> run = 158
#> Time taken for present model computation: 0.9687049 s
#> trial = 9
#> run = 159
#> Time taken for present model computation: 1.114943 s
#> trial = 10
#> run = 160
#> Time taken for present model computation: 0.820246 s
#> n = 10000
#> k = 1
#> trial = 1
#> run = 161
#> Time taken for present model computation: 0.9626641 s
#> trial = 2
#> run = 162
#> Time taken for present model computation: 0.9527571 s
#> trial = 3
#> run = 163
#> Time taken for present model computation: 0.8696439 s
#> trial = 4
#> run = 164
#> Time taken for present model computation: 0.7900901 s
#> trial = 5
#> run = 165
#> Time taken for present model computation: 0.6508131 s
#> trial = 6
#> run = 166
#> Time taken for present model computation: 0.9293659 s
#> trial = 7
#> run = 167
#> Time taken for present model computation: 0.8383338 s
#> trial = 8
#> run = 168
#> Time taken for present model computation: 0.6500361 s
#> trial = 9
#> run = 169
#> Time taken for present model computation: 0.7106299 s
#> trial = 10
#> run = 170
#> Time taken for present model computation: 1.070245 s
#> k = 2
#> trial = 1
#> run = 171
#> Time taken for present model computation: 0.7441781 s
#> trial = 2
#> run = 172
#> Time taken for present model computation: 0.6520219 s
#> trial = 3
#> run = 173
#> Time taken for present model computation: 0.664592 s
#> trial = 4
#> run = 174
#> Time taken for present model computation: 0.7777629 s
#> trial = 5
#> run = 175
#> Time taken for present model computation: 0.6470389 s
#> trial = 6
#> run = 176
#> Time taken for present model computation: 0.6708791 s
#> trial = 7
#> run = 177
#> Time taken for present model computation: 0.774122 s
#> trial = 8
#> run = 178
#> Time taken for present model computation: 1.122771 s
#> trial = 9
#> run = 179
#> Time taken for present model computation: 0.8425469 s
#> trial = 10
#> run = 180
#> Time taken for present model computation: 0.723881 s
#> k = 5
#> trial = 1
#> run = 181
#> Time taken for present model computation: 0.8225582 s
#> trial = 2
#> run = 182
#> Time taken for present model computation: 1.084098 s
#> trial = 3
#> run = 183
#> Time taken for present model computation: 0.7142301 s
#> trial = 4
#> run = 184
#> Time taken for present model computation: 0.987601 s
#> trial = 5
#> run = 185
#> Time taken for present model computation: 1.043293 s
#> trial = 6
#> run = 186
#> Time taken for present model computation: 1.091965 s
#> trial = 7
#> run = 187
#> Time taken for present model computation: 0.963506 s
#> trial = 8
#> run = 188
#> Time taken for present model computation: 1.372548 s
#> trial = 9
#> run = 189
#> Time taken for present model computation: 1.107177 s
#> trial = 10
#> run = 190
#> Time taken for present model computation: 0.9992149 s
#> k = 10
#> trial = 1
#> run = 191
#> Time taken for present model computation: 1.086515 s
#> trial = 2
#> run = 192
#> Time taken for present model computation: 0.8890159 s
#> trial = 3
#> run = 193
#> Time taken for present model computation: 1.135766 s
#> trial = 4
#> run = 194
#> Time taken for present model computation: 0.770365 s
#> trial = 5
#> run = 195
#> Time taken for present model computation: 1.076935 s
#> trial = 6
#> run = 196
#> Time taken for present model computation: 0.784188 s
#> trial = 7
#> run = 197
#> Time taken for present model computation: 1.018505 s
#> trial = 8
#> run = 198
#> Time taken for present model computation: 1.161256 s
#> trial = 9
#> run = 199
#> Time taken for present model computation: 1.088395 s
#> trial = 10
#> run = 200
#> Time taken for present model computation: 1.568357 s
#> n = 20000
#> k = 1
#> trial = 1
#> run = 201
#> Time taken for present model computation: 1.249474 s
#> trial = 2
#> run = 202
#> Time taken for present model computation: 1.129212 s
#> trial = 3
#> run = 203
#> Time taken for present model computation: 1.116724 s
#> trial = 4
#> run = 204
#> Time taken for present model computation: 1.263537 s
#> trial = 5
#> run = 205
#> Time taken for present model computation: 1.090505 s
#> trial = 6
#> run = 206
#> Time taken for present model computation: 1.047199 s
#> trial = 7
#> run = 207
#> Time taken for present model computation: 1.096708 s
#> trial = 8
#> run = 208
#> Time taken for present model computation: 1.192962 s
#> trial = 9
#> run = 209
#> Time taken for present model computation: 1.170878 s
#> trial = 10
#> run = 210
#> Time taken for present model computation: 1.300999 s
#> k = 2
#> trial = 1
#> run = 211
#> Time taken for present model computation: 1.056511 s
#> trial = 2
#> run = 212
#> Time taken for present model computation: 1.19051 s
#> trial = 3
#> run = 213
#> Time taken for present model computation: 1.245578 s
#> trial = 4
#> run = 214
#> Time taken for present model computation: 1.007171 s
#> trial = 5
#> run = 215
#> Time taken for present model computation: 0.9098899 s
#> trial = 6
#> run = 216
#> Time taken for present model computation: 1.03809 s
#> trial = 7
#> run = 217
#> Time taken for present model computation: 1.060952 s
#> trial = 8
#> run = 218
#> Time taken for present model computation: 1.403779 s
#> trial = 9
#> run = 219
#> Time taken for present model computation: 1.09942 s
#> trial = 10
#> run = 220
#> Time taken for present model computation: 1.27247 s
#> k = 5
#> trial = 1
#> run = 221
#> Time taken for present model computation: 1.019589 s
#> trial = 2
#> run = 222
#> Time taken for present model computation: 1.178619 s
#> trial = 3
#> run = 223
#> Time taken for present model computation: 1.08717 s
#> trial = 4
#> run = 224
#> Time taken for present model computation: 0.9382942 s
#> trial = 5
#> run = 225
#> Time taken for present model computation: 0.8877261 s
#> trial = 6
#> run = 226
#> Time taken for present model computation: 0.8789959 s
#> trial = 7
#> run = 227
#> Time taken for present model computation: 0.881546 s
#> trial = 8
#> run = 228
#> Time taken for present model computation: 0.916564 s
#> trial = 9
#> run = 229
#> Time taken for present model computation: 0.8839359 s
#> trial = 10
#> run = 230
#> Time taken for present model computation: 0.9359338 s
#> k = 10
#> trial = 1
#> run = 231
#> Time taken for present model computation: 1.303608 s
#> trial = 2
#> run = 232
#> Time taken for present model computation: 1.121285 s
#> trial = 3
#> run = 233
#> Time taken for present model computation: 1.179266 s
#> trial = 4
#> run = 234
#> Time taken for present model computation: 1.120013 s
#> trial = 5
#> run = 235
#> Time taken for present model computation: 1.624908 s
#> trial = 6
#> run = 236
#> Time taken for present model computation: 1.045926 s
#> trial = 7
#> run = 237
#> Time taken for present model computation: 1.011557 s
#> trial = 8
#> run = 238
#> Time taken for present model computation: 0.988035 s
#> trial = 9
#> run = 239
#> Time taken for present model computation: 1.648639 s
#> trial = 10
#> run = 240
#> Time taken for present model computation: 1.673923 s
#> n = 1e+05
#> k = 1
#> trial = 1
#> run = 241
#> Time taken for present model computation: 4.281005 s
#> trial = 2
#> run = 242
#> Time taken for present model computation: 4.204582 s
#> trial = 3
#> run = 243
#> Time taken for present model computation: 3.944786 s
#> trial = 4
#> run = 244
#> Time taken for present model computation: 2.798044 s
#> trial = 5
#> run = 245
#> Time taken for present model computation: 2.558156 s
#> trial = 6
#> run = 246
#> Time taken for present model computation: 2.953777 s
#> trial = 7
#> run = 247
#> Time taken for present model computation: 3.665101 s
#> trial = 8
#> run = 248
#> Time taken for present model computation: 3.418542 s
#> trial = 9
#> run = 249
#> Time taken for present model computation: 3.354636 s
#> trial = 10
#> run = 250
#> Time taken for present model computation: 2.95774 s
#> k = 2
#> trial = 1
#> run = 251
#> Time taken for present model computation: 3.145113 s
#> trial = 2
#> run = 252
#> Time taken for present model computation: 2.544685 s
#> trial = 3
#> run = 253
#> Time taken for present model computation: 2.571834 s
#> trial = 4
#> run = 254
#> Time taken for present model computation: 2.700399 s
#> trial = 5
#> run = 255
#> Time taken for present model computation: 2.548327 s
#> trial = 6
#> run = 256
#> Time taken for present model computation: 2.915473 s
#> trial = 7
#> run = 257
#> Time taken for present model computation: 2.859279 s
#> trial = 8
#> run = 258
#> Time taken for present model computation: 2.73993 s
#> trial = 9
#> run = 259
#> Time taken for present model computation: 2.883709 s
#> trial = 10
#> run = 260
#> Time taken for present model computation: 2.709883 s
#> k = 5
#> trial = 1
#> run = 261
#> Time taken for present model computation: 3.273748 s
#> trial = 2
#> run = 262
#> Time taken for present model computation: 2.935905 s
#> trial = 3
#> run = 263
#> Time taken for present model computation: 2.833582 s
#> trial = 4
#> run = 264
#> Time taken for present model computation: 3.734762 s
#> trial = 5
#> run = 265
#> Time taken for present model computation: 3.014805 s
#> trial = 6
#> run = 266
#> Time taken for present model computation: 3.585858 s
#> trial = 7
#> run = 267
#> Time taken for present model computation: 3.106992 s
#> trial = 8
#> run = 268
#> Time taken for present model computation: 2.803939 s
#> trial = 9
#> run = 269
#> Time taken for present model computation: 2.900499 s
#> trial = 10
#> run = 270
#> Time taken for present model computation: 3.422959 s
#> k = 10
#> trial = 1
#> run = 271
#> Time taken for present model computation: 3.97062 s
#> trial = 2
#> run = 272
#> Time taken for present model computation: 4.130229 s
#> trial = 3
#> run = 273
#> Time taken for present model computation: 3.900531 s
#> trial = 4
#> run = 274
#> Time taken for present model computation: 5.105087 s
#> trial = 5
#> run = 275
#> Time taken for present model computation: 5.50513 s
#> trial = 6
#> run = 276
#> Time taken for present model computation: 4.338999 s
#> trial = 7
#> run = 277
#> Time taken for present model computation: 4.343665 s
#> trial = 8
#> run = 278
#> Time taken for present model computation: 4.533405 s
#> trial = 9
#> run = 279
#> Time taken for present model computation: 5.312447 s
#> trial = 10
#> run = 280
#> Time taken for present model computation: 4.613441 s
```

# Show the results

Now let’s put that together.

```
time_df <- time_df %>%
mutate(id = 1:nrow(time_df)) %>%
group_by(k, n) %>%
mutate(time_taken_avg = mean(time_taken, na.rm = TRUE)) %>%
ungroup()
time_df <- time_df %>%
drop_na()
```

```
time_df %>%
ggplot(aes(x = n, y = time_taken, color = factor(k))) +
geom_point() +
scale_x_log10(breaks = sample_size) +
geom_line(aes(y = time_taken_avg, group = k)) +
labs(color = "k",
y = "computation time [sec]") +
scale_color_viridis_d() +
theme_light()
```

For small samples, there’s a large variance in computation time, with sample sizes augmenting, the computation time differences become more stable.

```
time_df %>%
drop_na() %>%
ggplot(aes(x = n, y = time_taken, color = factor(k))) +
geom_point() +
scale_x_log10(breaks = c(1e1, 1e03, 1e04, 1e05)) +
geom_line(aes(y = time_taken_avg, group = k)) +
facet_wrap(~ k, labeller = label_context) +
labs(color = "k") +
scale_color_viridis_d() +
theme_light()
```

# Debrief

On average, the time for each model was acceptable. However, two things should be noted: First, non-numeric variables can consume much more time (if many levels are present). Second, parameter tuning and cross validation will soak up a lot of time. Assume there are 3 tuning parameters, and we test 5 values each (thus yielding 15 models). Assume further we will use a 10 times cross validation with 10 folds each, giving 100 repetitions. In sum, 15k repetitions will be needed. That will take ages, and possible a lot of memory can be exhausted.