tdigest

Wicked Fast, Accurate Quantiles Using ‘t-Digests’

Description

The t-Digest construction algorithm uses a variant of 1-dimensional k-means clustering to produce a very compact data structure that allows accurate estimation of quantiles. This t-Digest data structure can be used to estimate quantiles, compute other rank statistics or even to estimate related measures like trimmed means. The advantage of the t-Digest over previous digests for this purpose is that the t-Digest handles data with full floating point resolution. The accuracy of quantile estimates produced by t-Digests can be orders of magnitude more accurate than those produced by previous digest algorithms. Methods are provided to create and update t-Digests and retrieve quantiles from the accumulated distributions.

See the original paper by Ted Dunning & Otmar Ertl for more details on t-Digests.

What’s Inside The Tin

The following functions are implemented:

• as.list.tdigest: Serialize a tdigest object to an R list or unserialize a serialized tdigest list back into a tdigest object
• td_add: Add a value to the t-Digest with the specified count
• td_create: Allocate a new histogram
• td_merge: Merge one t-Digest into another
• td_quantile_of: Return the quantile of the value
• td_total_count: Total items contained in the t-Digest
• td_value_at: Return the value at the specified quantile
• tquantile: Calculate sample quantiles from a t-Digest

Installation

install.packages("tdigest") # NOTE: CRAN version is 0.4.1
# or
remotes::install_gitlab("hrbrmstr/tdigest")

NOTE: To use the ‘remotes’ install options you will need to have the {remotes} package installed.

Usage

library(tdigest)

# current version
packageVersion("tdigest")
## [1] '0.4.2'

Basic (Low-level interface)

td <- td_create(10)

td
## <tdigest; size=0; compression=10; cap=70>

td_total_count(td)
## [1] 0

td_add(td, 0, 1) %>% 
  td_add(10, 1)
## <tdigest; size=2; compression=10; cap=70>

td_total_count(td)
## [1] 2

td_value_at(td, 0.1) == 0
## [1] TRUE
td_value_at(td, 0.5) == 5
## [1] TRUE

quantile(td)
## [1]  0  0  5 10 10

Bigger (and Vectorised)

td <- tdigest(c(0, 10), 10)

is_tdigest(td)
## [1] TRUE

td_value_at(td, 0.1) == 0
## [1] TRUE
td_value_at(td, 0.5) == 5
## [1] TRUE

set.seed(1492)
x <- sample(0:100, 1000000, replace = TRUE)
td <- tdigest(x, 1000)

td_total_count(td)
## [1] 1e+06

tquantile(td, c(0, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99, 1))
##  [1]   0.0000000   0.8099857   9.6725790  19.7533723  29.7448283  39.7544675  49.9966628  60.0235148  70.2067574
## [10]  80.3090454  90.2594642  99.4269454 100.0000000

quantile(td)
## [1]   0.00000  24.74751  49.99666  75.24783 100.00000

Serialization

These [de]serialization functions make it possible to create & populate a tdigest, serialize it out, read it in at a later time and continue populating it enabling compact distribution accumulation & storage for large, “continuous” datasets.

set.seed(1492)
x <- sample(0:100, 1000000, replace = TRUE)
td <- tdigest(x, 1000)

tquantile(td, c(0, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99, 1))
##  [1]   0.0000000   0.8099857   9.6725790  19.7533723  29.7448283  39.7544675  49.9966628  60.0235148  70.2067574
## [10]  80.3090454  90.2594642  99.4269454 100.0000000

str(in_r <- as.list(td), 1)
## List of 7
##  $ compression   : num 1000
##  $ cap           : int 6010
##  $ merged_nodes  : int 226
##  $ unmerged_nodes: int 0
##  $ merged_count  : num 1e+06
##  $ unmerged_count: num 0
##  $ nodes         :List of 2
##  - attr(*, "class")= chr [1:2] "tdigest_list" "list"

td2 <- as_tdigest(in_r)
tquantile(td2, c(0, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99, 1))
##  [1]   0.0000000   0.8099857   9.6725790  19.7533723  29.7448283  39.7544675  49.9966628  60.0235148  70.2067574
## [10]  80.3090454  90.2594642  99.4269454 100.0000000

identical(in_r, as.list(td2))
## [1] TRUE

ALTREP-aware

N <- 1000000
x.altrep <- seq_len(N) # this is an ALTREP in R version >= 3.5.0

td <- tdigest(x.altrep)
td[0.1]
## [1] 93051
td[0.5]
## [1] 491472.5
length(td)
## [1] 1000000

Proof it’s faster

microbenchmark::microbenchmark(
  tdigest = tquantile(td, c(0, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99, 1)),
  r_quantile = quantile(x, c(0, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99, 1))
)
## Unit: microseconds
##        expr       min        lq        mean     median        uq     max neval
##     tdigest     3.198     3.731     7.79369     4.4895    12.792    16.4   100
##  r_quantile 39197.353 39445.444 40069.38938 39584.8030 40062.945 43613.3   100

tdigest Metrics

Lang	# Files	(%)	LoC	(%)	Blank lines	(%)	# Lines	(%)
C	3	0.15	499	0.36	71	0.29	45	0.10
R	6	0.30	161	0.12	35	0.14	156	0.34
C/C++ Header	1	0.05	24	0.02	16	0.07	30	0.06
SUM	10	0.50	684	0.50	122	0.50	231	0.50

{cloc} 📦 metrics for tdigest

Code of Conduct

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.