ASOF Joins, OLS Regression, and extra summarizers

Since sparklyr.flint, a sparklyr extension for leveraging Flint time sequence functionalities via sparklyr, was introduced in September, we have now made a lot of enhancements to it, and have efficiently submitted sparklyr.flint 0.2 to CRAN.

On this weblog put up, we spotlight the next new options and enhancements from sparklyr.flint 0.2:

ASOF Joins

For these unfamiliar with the time period, ASOF joins are temporal be a part of operations primarily based on inexact matching of timestamps. Throughout the context of Apache Spark, a be a part of operation, loosely talking, matches data from two information frames (let’s name them left and proper) primarily based on some standards. A temporal be a part of implies matching data in left and proper primarily based on timestamps, and with inexact matching of timestamps permitted, it’s sometimes helpful to affix left and proper alongside one of many following temporal instructions:

1. Wanting behind: if a report from left has timestamp t, then it will get matched with ones from proper having the newest timestamp lower than or equal to t.
2. Wanting forward: if a report from left has timestamp t, then it will get matched with ones from proper having the smallest timestamp higher than or equal to (or alternatively, strictly higher than) t.

Nevertheless, oftentimes it’s not helpful to think about two timestamps as “matching” if they’re too far aside. Subsequently, an extra constraint on the utmost period of time to look behind or look forward is often additionally a part of an ASOF be a part of operation.

In sparklyr.flint 0.2, all ASOF be a part of functionalities of Flint are accessible by way of the asof_join() technique. For instance, given 2 timeseries RDDs left and proper:

library(sparklyr)
library(sparklyr.flint)

sc <- spark_connect(grasp = "native")
left <- copy_to(sc, tibble::tibble(t = seq(10), u = seq(10))) %>%
  from_sdf(is_sorted = TRUE, time_unit = "SECONDS", time_column = "t")
proper <- copy_to(sc, tibble::tibble(t = seq(10) + 1, v = seq(10) + 1L)) %>%
  from_sdf(is_sorted = TRUE, time_unit = "SECONDS", time_column = "t")

The next prints the results of matching every report from left with the newest report(s) from proper which are at most 1 second behind.

print(asof_join(left, proper, tol = "1s", course = ">=") %>% to_sdf())

## # Supply: spark<?> [?? x 3]
##    time                    u     v
##    <dttm>              <int> <int>
##  1 1970-01-01 00:00:01     1    NA
##  2 1970-01-01 00:00:02     2     2
##  3 1970-01-01 00:00:03     3     3
##  4 1970-01-01 00:00:04     4     4
##  5 1970-01-01 00:00:05     5     5
##  6 1970-01-01 00:00:06     6     6
##  7 1970-01-01 00:00:07     7     7
##  8 1970-01-01 00:00:08     8     8
##  9 1970-01-01 00:00:09     9     9
## 10 1970-01-01 00:00:10    10    10

Whereas if we alter the temporal course to “<”, then every report from left will probably be matched with any report(s) from proper that’s strictly sooner or later and is at most 1 second forward of the present report from left:

print(asof_join(left, proper, tol = "1s", course = "<") %>% to_sdf())

## # Supply: spark<?> [?? x 3]
##    time                    u     v
##    <dttm>              <int> <int>
##  1 1970-01-01 00:00:01     1     2
##  2 1970-01-01 00:00:02     2     3
##  3 1970-01-01 00:00:03     3     4
##  4 1970-01-01 00:00:04     4     5
##  5 1970-01-01 00:00:05     5     6
##  6 1970-01-01 00:00:06     6     7
##  7 1970-01-01 00:00:07     7     8
##  8 1970-01-01 00:00:08     8     9
##  9 1970-01-01 00:00:09     9    10
## 10 1970-01-01 00:00:10    10    11

Discover no matter which temporal course is chosen, an outer-left be a part of is at all times carried out (i.e., all timestamp values and u values of left from above will at all times be current within the output, and the v column within the output will comprise NA each time there isn’t a report from proper that meets the matching standards).

OLS Regression

You is perhaps questioning whether or not the model of this performance in Flint is kind of equivalent to lm() in R. Seems it has way more to supply than lm() does. An OLS regression in Flint will compute helpful metrics similar to Akaike information criterion and Bayesian information criterion, each of that are helpful for mannequin choice functions, and the calculations of each are parallelized by Flint to completely make the most of computational energy obtainable in a Spark cluster. As well as, Flint helps ignoring regressors which are fixed or practically fixed, which turns into helpful when an intercept time period is included. To see why that is the case, we have to briefly study the objective of the OLS regression, which is to seek out some column vector of coefficients (mathbf{beta}) that minimizes (|mathbf{y} – mathbf{X} mathbf{beta}|^2), the place (mathbf{y}) is the column vector of response variables, and (mathbf{X}) is a matrix consisting of columns of regressors plus a complete column of (1)s representing the intercept phrases. The answer to this drawback is (mathbf{beta} = (mathbf{X}^intercalmathbf{X})^{-1}mathbf{X}^intercalmathbf{y}), assuming the Gram matrix (mathbf{X}^intercalmathbf{X}) is non-singular. Nevertheless, if (mathbf{X}) incorporates a column of all (1)s of intercept phrases, and one other column fashioned by a regressor that’s fixed (or practically so), then columns of (mathbf{X}) will probably be linearly dependent (or practically so) and (mathbf{X}^intercalmathbf{X}) will probably be singular (or practically so), which presents a difficulty computation-wise. Nevertheless, if a regressor is fixed, then it basically performs the identical function because the intercept phrases do. So merely excluding such a relentless regressor in (mathbf{X}) solves the issue. Additionally, talking of inverting the Gram matrix, readers remembering the idea of “situation quantity” from numerical evaluation should be pondering to themselves how computing (mathbf{beta} = (mathbf{X}^intercalmathbf{X})^{-1}mathbf{X}^intercalmathbf{y}) may very well be numerically unstable if (mathbf{X}^intercalmathbf{X}) has a big situation quantity. This is the reason Flint additionally outputs the situation variety of the Gram matrix within the OLS regression consequence, in order that one can sanity-check the underlying quadratic minimization drawback being solved is well-conditioned.

So, to summarize, the OLS regression performance applied in Flint not solely outputs the answer to the issue, but additionally calculates helpful metrics that assist information scientists assess the sanity and predictive high quality of the ensuing mannequin.

To see OLS regression in motion with sparklyr.flint, one can run the next instance:

mtcars_sdf <- copy_to(sc, mtcars, overwrite = TRUE) %>%
  dplyr::mutate(time = 0L)
mtcars_ts <- from_sdf(mtcars_sdf, is_sorted = TRUE, time_unit = "SECONDS")
mannequin <- ols_regression(mtcars_ts, mpg ~ hp + wt) %>% to_sdf()

print(mannequin %>% dplyr::choose(akaikeIC, bayesIC, cond))

## # Supply: spark<?> [?? x 3]
##   akaikeIC bayesIC    cond
##      <dbl>   <dbl>   <dbl>
## 1     155.    159. 345403.

# ^ output says situation variety of the Gram matrix was inside motive

and procure (mathbf{beta}), the vector of optimum coefficients, with the next:

print(mannequin %>% dplyr::pull(beta))

## [[1]]
## [1] -0.03177295 -3.87783074

Further Summarizers

The EWMA (Exponential Weighted Transferring Common), EMA half-life, and the standardized second summarizers (particularly, skewness and kurtosis) together with a couple of others which had been lacking in sparklyr.flint 0.1 are actually absolutely supported in sparklyr.flint 0.2.

Higher Integration With sparklyr

Whereas sparklyr.flint 0.1 included a accumulate() technique for exporting information from a Flint time-series RDD to an R information body, it didn’t have an analogous technique for extracting the underlying Spark information body from a Flint time-series RDD. This was clearly an oversight. In sparklyr.flint 0.2, one can name to_sdf() on a timeseries RDD to get again a Spark information body that’s usable in sparklyr (e.g., as proven by mannequin %>% to_sdf() %>% dplyr::choose(...) examples from above). One also can get to the underlying Spark information body JVM object reference by calling spark_dataframe() on a Flint time-series RDD (that is often pointless in overwhelming majority of sparklyr use instances although).

Conclusion

Now we have introduced a lot of new options and enhancements launched in sparklyr.flint 0.2 and deep-dived into a few of them on this weblog put up. We hope you might be as enthusiastic about them as we’re.

Thanks for studying!

Acknowledgement

The creator wish to thank Mara (@batpigandme), Sigrid (@skeydan), and Javier (@javierluraschi) for his or her implausible editorial inputs on this weblog put up!