Just to close this off I did some more experiments and it is clear that
using the "\"-based solving is the main performance enhancement (2-25 times
faster for N & M in the 10:5000 range I've tested with!) while
UniformScaling gives a rather small improvement (few percent) on top of
that (expected since the latter scales only with N and not with M) and not
always.
Even for N > M the "\"-based solving is faster, actually relatively more so
than when N << M.
As usual, Julia's performance is overall impressive with the optimized L0
EM algorithm being practical (run time less than 20 secs) even for M being
500,000 (if N is < 200 and k < 8).
p-values below are from Wilcoxon test which is used to run as few repeated
executions as possible in determining a speed difference.
Cheers,
Robert
N = 500, M = 5000, k = 2
| Row # | Function | Avg | Reps | Relative | p | Signif
slower? |
| 1 | "solve " | "0.34sec" | 6 | 1.0 | 1.0 | ""
|
| 2 | "unisc & solve" | "0.36sec" | 6 | 1.07 | 0.026 | "*"
|
| 3 | "unisc " | "0.69sec" | 4 | 2.04 | 0.0095 | "**"
|
| 4 | "original " | "0.75sec" | 4 | 2.25 | 0.0095 | "**"
|
N = 5000, M = 500, k = 2
| Row # | Function | Avg | Reps | Relative | p | Signif
slower? |
| 1 | "unisc & solve" | "8.93sec" | 4 | 1.0 | 1.0 | ""
|
| 2 | "solve " | "9.11sec" | 4 | 1.02 | 0.029 | "*"
|
| 3 | "unisc " | "3.71mins" | 4 | 25.0 | 0.029 | "*"
|
| 4 | "original " | "3.71mins" | 4 | 25.0 | 0.029 | "*"
|
N = 5000, M = 5000, k = 2
| Row # | Function | Avg | Reps | Relative | p |
Signif slower? |
| 1 | "solve " | "38.13sec" | 15 | 1.0 | 1.0 | ""
|
| 2 | "unisc & solve" | "38.75sec" | 15 | 1.02 | 0.77 | ""
|
| 3 | "unisc " | "5.40mins" | 4 | 8.5 | 0.00052 | "***"
|
| 4 | "original " | "5.42mins" | 4 | 8.53 | 0.00052 | "***"
|
N = 200, M = 500000, k = 2
| Row # | Function | Avg | Reps | Relative | p |
Signif slower? |
| 1 | "unisc & solve " | "5.28 sec" | 5 | 1.0 | 1.0 | ""
|
| 2 | "solve " | "5.45 sec" | 5 | 1.03 | 0.016 |
"*" |
| 3 | "original " | "9.65 sec" | 4 | 1.83 | 0.016 |
"*" |
N = 200, M = 500000, k = 8
| Row # | Function | Avg | Reps | Relative | p |
Signif slower? |
| 1 | "unisc & solve " | "20.04 sec" | 15 | 1.0 | 1.0 |
"" |
| 2 | "solve " | "20.28 sec" | 15 | 1.01 | 0.93 |
"" |
| 3 | "original " | "47.91 sec" | 4 | 2.39 | 0.00052 |
"***" |
>
