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# Introduction

Statistical analysis often involves calculating various measures on large datasets. Speed and efficiency are crucial, especially when dealing with real-time analytics or massive data volumes. The TidyDensity package in R provides a set of fast cumulative functions for common statistical measures like mean, standard deviation, skewness, and kurtosis. But just how fast are these cumulative functions compared to doing the computations directly? In this post, I benchmark the cumulative functions against the base R implementations using the rbenchmark package.

# Setting the bench

To assess the performance of TidyDensity’s cumulative functions, we’ll employ the rbenchmark package for benchmarking and the ggplot2 package for visualization. I’ll benchmark the following cumulative functions on random samples of increasing size:

• `cgmean()` – Cumulative geometric mean
• `chmean()` – Cumulative harmonic mean
• `ckurtosis()` – Cumulative kurtosis
• `cskewness()` – Cumulative skewness
• `cmean()` – Cumulative mean
• `csd()` – Cumulative standard deviation
• `cvar()` – Cumulative variance
```library(TidyDensity)
library(rbenchmark)
library(dplyr)
library(ggplot2)

set.seed(123)

x1 <- sample(1e2) + 1e2
x2 <- sample(1e3) + 1e3
x3 <- sample(1e4) + 1e4
x4 <- sample(1e5) + 1e5
x5 <- sample(1e6) + 1e6

cg_bench <- benchmark(
"100" = cgmean(x1),
"1000" = cgmean(x2),
"10000" = cgmean(x3),
"100000" = cgmean(x4),
"1000000" = cgmean(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

# Run benchmarks for other functions
ch_bench <- benchmark(
"100" = chmean(x1),
"1000" = chmean(x2),
"10000" = chmean(x3),
"100000" = chmean(x4),
"1000000" = chmean(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

ck_bench <- benchmark(
"100" = ckurtosis(x1),
"1000" = ckurtosis(x2),
"10000" = ckurtosis(x3),
"100000" = ckurtosis(x4),
"1000000" = ckurtosis(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

cs_bench <- benchmark(
"100" = cskewness(x1),
"1000" = cskewness(x2),
"10000" = cskewness(x3),
"100000" = cskewness(x4),
"1000000" = cskewness(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

cm_bench <- benchmark(
"100" = cmean(x1),
"1000" = cmean(x2),
"10000" = cmean(x3),
"100000" = cmean(x4),
"1000000" = cmean(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

csd_bench <- benchmark(
"100" = csd(x1),
"1000" = csd(x2),
"10000" = csd(x3),
"100000" = csd(x4),
"1000000" = csd(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

cv_bench <- benchmark(
"100" = cvar(x1),
"1000" = cvar(x2),
"10000" = cvar(x3),
"100000" = cvar(x4),
"1000000" = cvar(x5),
replications = 100L,
columns = c("test","replications","elapsed", "relative","user.self","sys.self")
)

benchmarks <- rbind(cg_bench, ch_bench, ck_bench, cs_bench, cm_bench, csd_bench, cv_bench)

# Arrange benchmarks and plot
bench_tbl <- benchmarks |>
mutate(func = c(
rep("cgmean", 5),
rep("chmean", 5),
rep("ckurtosis", 5),
rep("cskewness", 5),
rep("cmean", 5),
rep("csd", 5),
rep("cvar", 5)
)
) |>
arrange(func, test) |>
select(func, test, everything())

bench_tbl |>
ggplot(aes(x=test, y=elapsed, group = func, color = func)) +
geom_line() +
facet_wrap(~func, scales="free_y") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
labs(title="Cumulative Function Speed Comparison",
x="Sample Size",
y="Elapsed Time (sec)",
color = "Function")```

The results show that the TidyDensity cumulative functions scale extremely well as the sample size increases. The elapsed time remains very low even at 1 million observations. The base R implementations like `var()` and `sd()` perform significantly worse when used inside of an `sapply` at large sample sizes. What was not tested however is `cmedian()` and this is because the performance is very slow once we reach 1e4 compared to the other functions as such that it would take too long to run the benchmark if it ran at all.

So if you need fast statistical functions that can scale to big datasets, the TidyDensity cumulative functions are a great option! They provide massive speedups over base R while returning the same final result.

Let me know in the comments if you have any other benchmark ideas for comparing R packages! I’m always looking for interesting performance comparisons to test out.

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Continue reading: Benchmarking the Speed of Cumulative Functions in TidyDensity

## Analysis of Cumulative Functions in TidyDensity: Implications and Future Developments

Cumulative functions in R’s TidyDensity package provide quicker computations for large datasets, according to the benchmarking results reported by the original blog post on Steve’s Data Tips and Tricks. The functions were tested on increasingly large sample sizes, demonstrating speed and efficiency even when processing a massive 1 million observations. These conclusions could have profound long-term implications for future development in statistical analysis and big data processing.

### Long-Term Implications

With the rise of big data, the need for speedy and efficient statistical computation grows ever more critical. If organizations and researchers can confidently turn to TidyDensity’s fast cumulative functions to handle large datasets, this could potentially open up new possibilities for real-time analytics. Current systems hampered by slow processing times may become obsolete, replaced by more capable and efficient tools powered by solutions like TidyDensity. Moreover, as these cumulative functions continue to prove their value, they are likely to become a standard feature in future data processing and analytical pursuits.

### Future Developments

Based on the current results, the potential for future improvements and developments within TidyDensity’s fast cumulative functions is apparent. For example, the median function, cmedian(), was not tested due to slower performance at larger sets such as 1e4. This could be an area for improvement in future updates of TidyDensity. As technology advances, the potential to fine-tune these functions may unlock even higher levels of performance.

For those dealing with large data volumes or requiring real-time analytics, it may be worth considering switching to TidyDensity’s fast cumulative functions from base R implementations. It’s imperative to run benchmarks to verify their performance based on the specific needs and resources available.

As ever, staying informed about ongoing benchmarking initiatives and the latest developments in R packages like TidyDensity will ensure one’s capacity to handle large datasets remains optimized. Furthermore, sharing your results when benchmarking different R packages can contribute to a broader knowledge base and assist others in their choice of statistical tools.