ASOF Joins, OLS Regression, and extra summarizers

Since sparklyr.flint, a sparklyr extension for leveraging Flint time sequence functionalities by sparklyr, was launched in September, we’ve got made quite a few enhancements to it, and have efficiently submitted sparklyr.flint 0.2 to CRAN.

On this weblog submit, 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 part of operations primarily based on inexact matching of timestamps. Inside the context of Apache Spark, a be part of operation, loosely talking, matches data from two knowledge frames (let’s name them left and proper) primarily based on some standards. A temporal be part of implies matching data in left and proper primarily based on timestamps, and with inexact matching of timestamps permitted, it’s usually 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 latest 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 larger than or equal to (or alternatively, strictly larger than) t.

Nonetheless, oftentimes it’s not helpful to contemplate two timestamps as “matching” if they’re too far aside. Due to this fact, an extra constraint on the utmost period of time to look behind or look forward is normally additionally a part of an ASOF be part of operation.

In sparklyr.flint 0.2, all ASOF be part of functionalities of Flint are accessible by way of the asof_join() methodology. 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 latest report(s) from proper which might be at most 1 second behind.

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

## # Supply: spark> [?? x 3]
##    time                    u     v
##                   
##  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 modify the temporal route to “<”, then every report from left shall 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", route = "<") %>% to_sdf())

## # Supply: spark> [?? x 3]
##    time                    u     v
##                   
##  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 route is chosen, an outer-left be 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 include NA at any time when there is no such thing as a report from proper that meets the matching standards).

OLS Regression

You could be questioning whether or not the model of this performance in Flint is kind of similar to lm() in R. Seems it has far more to supply than lm() does. An OLS regression in Flint will compute helpful metrics akin to Akaike data criterion and Bayesian data 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 accessible in a Spark cluster. As well as, Flint helps ignoring regressors which might be fixed or almost fixed, which turns into helpful when an intercept time period is included. To see why that is the case, we have to briefly look at the aim 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 whole column of (1)s representing the intercept phrases. The answer to this downside is (mathbf{beta} = (mathbf{X}^intercalmathbf{X})^{-1}mathbf{X}^intercalmathbf{y}), assuming the Gram matrix (mathbf{X}^intercalmathbf{X}) is non-singular. Nonetheless, if (mathbf{X}) accommodates a column of all (1)s of intercept phrases, and one other column shaped by a regressor that’s fixed (or almost so), then columns of (mathbf{X}) shall be linearly dependent (or almost so) and (mathbf{X}^intercalmathbf{X}) shall be singular (or almost so), which presents a problem computation-wise. Nonetheless, if a regressor is fixed, then it primarily performs the identical position 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 have to be pondering to themselves how computing (mathbf{beta} = (mathbf{X}^intercalmathbf{X})^{-1}mathbf{X}^intercalmathbf{y}) might be numerically unstable if (mathbf{X}^intercalmathbf{X}) has a big situation quantity. That is why 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 downside 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 knowledge 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
##            
## 1     155.    159. 345403.

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

and acquire (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 Shifting Common), EMA half-life, and the standardized second summarizers (particularly, skewness and kurtosis) together with a number of others which have 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() methodology for exporting knowledge from a Flint time-series RDD to an R knowledge body, it didn’t have an identical methodology for extracting the underlying Spark knowledge 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 knowledge 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 knowledge body JVM object reference by calling spark_dataframe() on a Flint time-series RDD (that is normally pointless in overwhelming majority of sparklyr use instances although).

Conclusion

We now have offered quite a few new options and enhancements launched in sparklyr.flint 0.2 and deep-dived into a few of them on this weblog submit. We hope you’re 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 incredible editorial inputs on this weblog submit!