Machine Learning with PySpark through MLlib

Tasks

1. Split data intro train and test

2. Formulate three pipelines, train and evaluate them:

   a. Feature selection with the UnivariateFeatureSelector and the fpr strategy (least conservative).

   b. Same, with the fwe strategy (most conservative).

   c. Same, but doing PCA and using 3 components.

3. Formulate, train and evaluate another pipeline that uses features obtained from two sources:

   a. Feature selection with the fpr

   b. The 3 components from PCA.

4. Can you determine how many features are selected by fpr and fwe?

Requirements

import findspark
findspark.init()

from pyspark.sql import SparkSession

spark = SparkSession.builder.appName('Intro to Spark').master("local[*]").getOrCreate()
sc = spark.sparkContext

import numpy as np
from pyspark.sql.functions import col
from pyspark.ml.feature import VectorAssembler, Imputer, PCA
from pyspark.ml.evaluation import RegressionEvaluator
from pyspark.ml.regression import LinearRegression, DecisionTreeRegressor
from pyspark.ml import Pipeline
from pyspark.ml.tuning import ParamGridBuilder, TrainValidationSplit, CrossValidator
from pyspark.ml.feature import StandardScaler, UnivariateFeatureSelector

Data preparation for SparkML

Reading the data

First of all we read the data:

data = spark.read.csv(path='wind_available_second.csv.gz', header=True, inferSchema=True) 

data.show(5)

+-------+----+-----+---+----+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+-----------------+------------------+-----------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+-----------------+-----------------+------------------+------------------+-------------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| energy|year|month|day|hour|       p54_162_1|       p54_162_2|       p54_162_3|       p54_162_4|       p54_162_5|       p54_162_6|       p54_162_7|       p54_162_8|       p54_162_9|      p54_162_10|      p54_162_11|      p54_162_12|      p54_162_13|      p54_162_14|      p54_162_15|      p54_162_16|      p54_162_17|      p54_162_18|      p54_162_19|      p54_162_20|      p54_162_21|      p54_162_22|      p54_162_23|      p54_162_24|      p54_162_25|       p55_162_1|       p55_162_2|       p55_162_3|       p55_162_4|       p55_162_5|       p55_162_6|       p55_162_7|       p55_162_8|       p55_162_9|      p55_162_10|      p55_162_11|      p55_162_12|      p55_162_13|      p55_162_14|      p55_162_15|      p55_162_16|      p55_162_17|      p55_162_18|      p55_162_19|      p55_162_20|      p55_162_21|      p55_162_22|      p55_162_23|      p55_162_24|      p55_162_25|          cape_1|          cape_2|          cape_3|          cape_4|          cape_5|          cape_6|          cape_7|          cape_8|          cape_9|         cape_10|         cape_11|         cape_12|         cape_13|         cape_14|         cape_15|         cape_16|         cape_17|         cape_18|         cape_19|         cape_20|         cape_21|         cape_22|         cape_23|         cape_24|         cape_25|       p59_162_1|       p59_162_2|       p59_162_3|       p59_162_4|       p59_162_5|       p59_162_6|       p59_162_7|       p59_162_8|       p59_162_9|      p59_162_10|      p59_162_11|      p59_162_12|      p59_162_13|      p59_162_14|      p59_162_15|      p59_162_16|      p59_162_17|      p59_162_18|      p59_162_19|      p59_162_20|      p59_162_21|      p59_162_22|      p59_162_23|      p59_162_24|      p59_162_25|        lai_lv_1|        lai_lv_2|        lai_lv_3|        lai_lv_4|        lai_lv_5|        lai_lv_6|        lai_lv_7|        lai_lv_8|        lai_lv_9|       lai_lv_10|       lai_lv_11|       lai_lv_12|       lai_lv_13|       lai_lv_14|       lai_lv_15|       lai_lv_16|       lai_lv_17|       lai_lv_18|       lai_lv_19|       lai_lv_20|       lai_lv_21|       lai_lv_22|       lai_lv_23|       lai_lv_24|       lai_lv_25|        lai_hv_1|        lai_hv_2|        lai_hv_3|        lai_hv_4|        lai_hv_5|        lai_hv_6|        lai_hv_7|        lai_hv_8|        lai_hv_9|       lai_hv_10|       lai_hv_11|       lai_hv_12|       lai_hv_13|       lai_hv_14|       lai_hv_15|       lai_hv_16|       lai_hv_17|       lai_hv_18|       lai_hv_19|       lai_hv_20|       lai_hv_21|       lai_hv_22|       lai_hv_23|       lai_hv_24|       lai_hv_25|            u10n_1|            u10n_2|            u10n_3|            u10n_4|            u10n_5|           u10n_6|            u10n_7|            u10n_8|            u10n_9|           u10n_10|           u10n_11|           u10n_12|           u10n_13|           u10n_14|           u10n_15|           u10n_16|           u10n_17|           u10n_18|           u10n_19|          u10n_20|           u10n_21|           u10n_22|           u10n_23|          u10n_24|           u10n_25|           v10n_1|            v10n_2|            v10n_3|           v10n_4|            v10n_5|            v10n_6|            v10n_7|            v10n_8|            v10n_9|           v10n_10|           v10n_11|           v10n_12|          v10n_13|           v10n_14|           v10n_15|           v10n_16|           v10n_17|          v10n_18|           v10n_19|           v10n_20|           v10n_21|           v10n_22|           v10n_23|          v10n_24|           v10n_25|            sp_1|            sp_2|            sp_3|            sp_4|            sp_5|            sp_6|            sp_7|            sp_8|            sp_9|           sp_10|           sp_11|           sp_12|           sp_13|           sp_14|           sp_15|           sp_16|           sp_17|           sp_18|           sp_19|           sp_20|           sp_21|           sp_22|           sp_23|           sp_24|           sp_25|          stl1_1|          stl1_2|          stl1_3|          stl1_4|          stl1_5|          stl1_6|          stl1_7|          stl1_8|          stl1_9|         stl1_10|         stl1_11|         stl1_12|         stl1_13|         stl1_14|         stl1_15|         stl1_16|         stl1_17|         stl1_18|         stl1_19|         stl1_20|         stl1_21|         stl1_22|         stl1_23|         stl1_24|         stl1_25|            u10_1|             u10_2|             u10_3|             u10_4|             u10_5|            u10_6|             u10_7|             u10_8|             u10_9|            u10_10|           u10_11|            u10_12|            u10_13|            u10_14|           u10_15|           u10_16|            u10_17|            u10_18|            u10_19|            u10_20|           u10_21|           u10_22|            u10_23|            u10_24|            u10_25|            v10_1|            v10_2|             v10_3|             v10_4|            v10_5|            v10_6|             v10_7|             v10_8|            v10_9|            v10_10|           v10_11|            v10_12|            v10_13|            v10_14|            v10_15|            v10_16|           v10_17|           v10_18|            v10_19|           v10_20|            v10_21|            v10_22|            v10_23|            v10_24|           v10_25|           t2m_1|           t2m_2|           t2m_3|           t2m_4|           t2m_5|           t2m_6|           t2m_7|           t2m_8|           t2m_9|          t2m_10|          t2m_11|          t2m_12|          t2m_13|          t2m_14|          t2m_15|          t2m_16|          t2m_17|          t2m_18|          t2m_19|          t2m_20|          t2m_21|          t2m_22|          t2m_23|          t2m_24|          t2m_25|          stl2_1|          stl2_2|          stl2_3|          stl2_4|          stl2_5|          stl2_6|          stl2_7|          stl2_8|          stl2_9|         stl2_10|         stl2_11|         stl2_12|         stl2_13|         stl2_14|         stl2_15|         stl2_16|         stl2_17|         stl2_18|         stl2_19|         stl2_20|         stl2_21|         stl2_22|         stl2_23|         stl2_24|         stl2_25|          stl3_1|          stl3_2|          stl3_3|          stl3_4|          stl3_5|          stl3_6|          stl3_7|          stl3_8|          stl3_9|         stl3_10|         stl3_11|         stl3_12|         stl3_13|         stl3_14|         stl3_15|         stl3_16|         stl3_17|         stl3_18|         stl3_19|         stl3_20|         stl3_21|         stl3_22|         stl3_23|         stl3_24|         stl3_25|             iews_1|             iews_2|             iews_3|             iews_4|             iews_5|             iews_6|             iews_7|             iews_8|             iews_9|            iews_10|            iews_11|            iews_12|            iews_13|            iews_14|            iews_15|            iews_16|            iews_17|            iews_18|            iews_19|            iews_20|            iews_21|            iews_22|            iews_23|            iews_24|            iews_25|             inss_1|             inss_2|             inss_3|             inss_4|             inss_5|             inss_6|             inss_7|             inss_8|             inss_9|            inss_10|            inss_11|            inss_12|            inss_13|            inss_14|            inss_15|            inss_16|            inss_17|            inss_18|            inss_19|            inss_20|            inss_21|            inss_22|            inss_23|            inss_24|            inss_25|          stl4_1|          stl4_2|          stl4_3|          stl4_4|          stl4_5|          stl4_6|          stl4_7|          stl4_8|          stl4_9|         stl4_10|         stl4_11|         stl4_12|         stl4_13|         stl4_14|         stl4_15|         stl4_16|         stl4_17|         stl4_18|         stl4_19|         stl4_20|         stl4_21|         stl4_22|         stl4_23|         stl4_24|         stl4_25|            fsr_1|            fsr_2|            fsr_3|            fsr_4|            fsr_5|            fsr_6|            fsr_7|            fsr_8|            fsr_9|           fsr_10|           fsr_11|           fsr_12|           fsr_13|           fsr_14|           fsr_15|           fsr_16|           fsr_17|           fsr_18|           fsr_19|           fsr_20|           fsr_21|           fsr_22|           fsr_23|           fsr_24|           fsr_25|           flsr_1|           flsr_2|           flsr_3|           flsr_4|           flsr_5|           flsr_6|           flsr_7|           flsr_8|           flsr_9|          flsr_10|          flsr_11|          flsr_12|          flsr_13|          flsr_14|          flsr_15|          flsr_16|          flsr_17|          flsr_18|          flsr_19|          flsr_20|          flsr_21|          flsr_22|          flsr_23|          flsr_24|          flsr_25|           u100_1|           u100_2|           u100_3|           u100_4|           u100_5|           u100_6|           u100_7|           u100_8|           u100_9|          u100_10|          u100_11|          u100_12|          u100_13|          u100_14|          u100_15|          u100_16|          u100_17|          u100_18|          u100_19|          u100_20|          u100_21|          u100_22|          u100_23|          u100_24|          u100_25|           v100_1|           v100_2|           v100_3|           v100_4|            v100_5|           v100_6|           v100_7|           v100_8|           v100_9|          v100_10|          v100_11|          v100_12|          v100_13|          v100_14|          v100_15|          v100_16|          v100_17|          v100_18|          v100_19|           v100_20|          v100_21|          v100_22|          v100_23|           v100_24|          v100_25|
+-------+----+-----+---+----+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+-----------------+------------------+-----------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+-----------------+-----------------+------------------+------------------+-------------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| 402.71|2005|    1|  2|  18|2534969.63189538|2526863.84970931|   2518753.54925|2510647.76706392|2502537.46660461|2531111.02655151|2522720.59315154|2514330.15975158|2505939.72635161|2497549.29295164|2528052.15557048|2519435.80850869|2510823.97972014|2502212.15093159|2493595.80386981|2525567.10529046|2516770.02729922|2507977.46758122|            NULL|2490387.82987197|2522309.43028703|2513281.92036073|2504254.41043444|2495226.90050814|2486199.39058184|9.44171895697496|            NULL|9.36651451737241|9.32857353883419|9.29063256029596| 9.3475440281033|9.30689297966949|9.26624193123568|9.22491336532797|9.18426231689416|9.27369462344854|9.22965598764525|9.18629486931585|9.14293375098645|9.09957263265705|9.21271805079783|9.16732438004674|9.12193070929565|9.07653703854456|9.03114336779347|9.14361126846035|9.09347497539198|9.04266116484972|8.99252487178135|            NULL|12.5802680787972|            NULL|13.1865460584982|13.4896850483487|13.7928240381993|            NULL|13.1486536847669|13.3760079271547|13.6033621695426|13.8307164119306|13.2244384322296|13.3760079271547|  13.52757742208|            NULL| 13.868608785662|13.4517926746173|13.5654697958114|            NULL|13.7549316644679| 13.868608785662|            NULL|13.1865460584982|13.3002231796922|13.4139003008861|  13.52757742208| 1400898.4880033|1405015.39028333|1408953.29681205|1413070.19909208|1417008.10562081|1389442.75991974|1393022.67494585|            NULL|1400361.50074938| 1403941.4157755|1380313.97660315|1383535.90012665|            NULL|1390158.74292496|1393559.66219977|1372796.15504831|1375839.08282051|1378882.01059271| 1381924.9383649| 1384967.8661371| 1365994.3164987|1368679.25276828|1371364.18903787|1373870.12955615|1376555.06582573|2.26952305148312| 2.2136081616507|2.15769327181829|2.10177838198587|2.04586349215346|2.37892061189892|2.32031197386597|2.26170333583303|2.20309469780008|2.14448605976713|            NULL|2.40483813099336| 2.3441111084532|2.28335793301789|2.22260475758258|2.53596874727948|2.47348948076422|2.41101021424895|2.34853094773369|2.28605168121842|2.54062396261632|            NULL|2.41940529359236|2.35880903552795|2.29821277746355|            NULL|2.24295759590331|2.23950522239152|2.23606402160953|2.23261164809773|2.35467372128996| 2.3510649295608|2.34744496510182|2.34383617337266| 2.3402273816435|2.44046911351359|2.43672624902669|2.43298338453979|            NULL|2.42548648283617| 2.5101310838892|2.50627649210418|2.50242190031916|2.49856730853415|2.49472388947894|2.53751544465754| 2.5318173524536|2.52611926024966|2.52042116804572|            NULL|-0.974206320564559|-0.875138235872909|-0.776070151181259|-0.676632409457178|-0.577564324765528|             NULL|-0.864048524899963|-0.765719754273176|-0.667390983646389|-0.569062213019602|-0.953505526748393|-0.855546413154038|-0.757587299559682|-0.659997842997758|-0.562038729403403|-0.946112386099763|-0.848522929537839|-0.751303130008346|-0.653713673446422|-0.55649387391693|-0.948330328294352|-0.852589156894586|-0.756478328462388|-0.66036750003019|-0.564256671597992|-2.49717269175828| -2.35288377637882|              NULL| -2.0650013138868| -1.92106008264079| -2.34766851437715| -2.19851202112947|  -2.0493555278818| -1.90019903463412| -1.75069485725299| -2.22910822487259| -2.07577952202358|-1.92279850330801|   -1.769469800459| -1.61614109760998| -2.13314740404191| -1.97634185985846|-1.81988399980844| -1.66307845562499| -1.50662059557497|              NULL| -1.93670586864579| -1.77711885139477|             NULL|  -1.4575971327593|100691.101044989|100414.200563075|100137.300081161|            NULL| 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1.2807859808137|   1.3820219437348| 1.48291001674895| 1.05048286241587|              NULL|  1.25121533872334| 1.35140763192361|  1.45194781503082| 1.02787001846442|              NULL|  1.22755882505106|  1.32740322834438|   1.4272476316377|  1.00977974330326| 1.10892836678269| 1.20842488016906|  1.30792139355544| 1.40741790694181| 0.970120293911487|  1.06439845869368|  1.15867662347587|  1.25295478825807| 1.34688506313332| 281.51242070785| 281.33754874039| 281.16267677293| 280.98780480547| 280.81293283801|281.394090676536|281.212806736936|281.030939890777|280.849655951177|280.668372011577|281.300242720666|281.113712622042|280.926599616859|280.740069518235|280.553539419612|281.223881961541| 281.03327151701| 280.84207816592|280.651467721389|  280.4602743703|281.167340025396| 280.96856888905|            NULL|280.571609522916|280.373421293128|280.764031992713|            NULL|280.480238085531|            NULL|280.196444178349|280.499183455357| 280.35342009976|280.207270103963|280.061506748367| 279.91535675257|280.289624466674|280.140381349273|279.991138231872|279.842281754671| 279.69303863727|            NULL|            NULL|279.815990221036|279.664040622231|279.512091023426| 279.99732447508|            NULL|279.686079113661|279.530263112851|279.374833752242|282.146488413982|281.994916344297|            NULL|281.691772204928|            NULL|            NULL|281.792451462894|281.636453931321| 281.48017980838|281.324182276807| 281.79162168879|            NULL|281.472435250075|281.312565439349|            NULL|            NULL|            NULL|281.339118210681|281.176482486275|281.013846761869|281.565093358367|281.398308763441|281.231800759883|281.065016164956|280.898508161398|    -0.259765876716| -0.259683236389943| -0.259683236389943| -0.259600596063885|               NULL| -0.268773672256306|  -0.26860839160419| -0.268525751278132| -0.268443110952074| -0.268360470626016| -0.275798099971223| -0.275715459645165| 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NULL|284.524606519108|284.802402941239|284.719334470088|284.636265998936|284.553004345293|284.469935874141|284.761061888155|284.677220687038|284.593379485922|284.509538284806| 284.42569708369|284.745414106379|284.659834262844|284.574254419308|            NULL|284.402901549746|             NULL|0.356263425237389|0.371848097877157|0.387432770516925|0.403017443156693|0.357097077860021|0.373432699489224|0.389768321118427|0.406100634602302|0.422436256231505| 0.37010470528935|0.387035793077576|             NULL|  0.4208946605087|0.437825748296926|0.380667613321356|             NULL|0.415492459188229|0.432906536194329| 0.45032061320043|0.385203080565916|0.402385587399063| 0.41956809423221|0.436750601065357|0.453936416043832|-6.40830526179772|-6.37050439138021| -6.3327035209627|-6.29487947404586|-6.25707860362835|-6.20574265759844|-6.16580954924199|-6.12587644088554| -6.0859433325291|             NULL|-6.04519904669588|-6.00359723038722|-5.96199541407856|-5.92037042127056|-5.87874542846256|             NULL|-5.87190836115835|-5.82891595488951|-5.78592354862067|-5.74295431885117|-5.85130445324838|-5.80859016497157|-5.76587587669477| -5.7231847649173| -5.6804704766405|-4.92247748921025|-4.83459173781154|-4.74670598641284|-4.65882023501414|-4.57093448361544|-4.79483389789308|-4.70223998124088|-4.60912293511607|-4.51652901846386|             NULL| -4.6938699096791|             NULL|-4.50083513428552|-4.40405618185243|-4.30727722941933|-4.61173858247912|-4.51182085321036|-4.41242625341421|-4.31250852414545| -4.2131139243493|-4.53954671525876|-4.44224463335305|-4.34441942197474|-4.24711734006903|-4.14929212869071|  1.3193756575776|  1.4351244464219|  1.5503743180729|  1.6661231069172|              NULL|   1.292933046333|  1.4086818351773|  1.5239317068283| 1.63918157847931| 1.75443145013031|             NULL| 1.38722839586564| 1.50247826751664| 1.61772813916765| 1.73347692801195| 1.25501533964262| 1.37026521129363| 1.48551508294463| 1.60076495459564|  1.71601482624664| 1.21061170943942|  1.3193756575776| 1.42813960571578|  1.53640463666066| 1.64516858479884|
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NULL|2.04429431844441|2.37737759108502|2.31874280015692|2.26010800922883|2.20144706540558|2.14281227447748|2.46399597982448|2.40321665149401|2.34243732316355|2.28165799483309|2.22087866650262|2.53432111488498|2.47181569547457|2.40931027606415|2.34677870375858|2.28427328434817|2.53900248311698|2.47838007215742|2.41773150830271|2.35710909734315|2.29648668638359|2.24609713298039|2.24252185944066|2.23894658590093|2.23537131236121|2.23180721155129|2.35434971212542|            NULL|2.34686398315162|2.34310994593491|  2.339367081448|2.44013393161924| 2.4362569943746|2.43236888440014|            NULL|2.42460383718105|2.50977355653523|2.50578489199247|2.50179622744971|2.49779639017714|2.49380772563438|2.53718026276319|2.53135927053133|2.52551593283984|2.51968376787816|2.51384043018667| -1.40448710631486| -1.38711322579058|  -1.3697393452663| -1.35199580770958|  -1.3346219271853|             NULL| -1.16531900633166| -1.14720581174252|  -1.1294622741858| -1.11134907959666| 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NULL|99129.0170162361|100051.934059939|99776.0483301352|99500.2894443448|99224.5305585545|98948.6448287504|99939.8039518258|99656.3075811996|99372.8112105733|99089.3148399471|98805.8184693208|99848.8567940007|99559.0182226893|            NULL|98979.5947680939|98689.7561967825|99727.8476049281|99430.0178607534|99132.1881165787| 98834.358372404|98536.5286282293|280.357317794938|280.231072054853|280.104319303764|279.977566552676|279.850813801587|280.073391632499|            NULL|279.813294987264|279.683500170149|            NULL|279.848278746565|            NULL|279.583111991287|279.450275108146|279.317945236009|279.665247773992|279.530382846834| 279.39602493068|279.261160003521|279.126295076362|279.557761441069|279.418333414871|279.278398377669|279.138970351471|278.999542325273|-2.62706775804115| -2.57520659668803| -2.52334543533492| -2.47111646432681|  -2.4192553029737|-2.47553018018665| -2.42109435124863| -2.36665852231061| -2.31222269337259| -2.25778686443456|-2.35562423266101| 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277.12138560493|277.415170510263|277.291594319925|277.168018129586|277.044441939248|            NULL|            NULL|277.176178821401|277.043276126132|            NULL|276.778053642151| 281.32543356387|281.172324044464|281.019214525057|280.866491645852|280.713382126445| 281.08764984055|280.930287278937|280.772538077125|280.615175515513|  280.4574263137|280.899356062896|280.738127099279|280.576898135661|280.416055812245|280.254826848627| 280.74663318369|280.582311098469|280.418375653448|280.254053568226|280.090118123205|280.641853689349|280.473278561922|280.304703434495|280.136128307067| 279.96755317964| 282.14538204851|281.994916344297|281.844174048717|281.693431753137|281.542689457556|281.947342628995|281.792451462894|281.637283705425|281.482115947956|281.326948190487|            NULL|281.631751878064|            NULL|            NULL|281.155738133672|281.663283294021|281.501477343719|281.339947984785|281.178418625851|281.016889266918|281.564540175631|281.398861946177|281.233460308091|            NULL|280.902103849182|-0.0479587210297409| -0.052173377658691|-0.0563053939615833|-0.0604374102644756|-0.0646520668934257|-0.0477934403776251| -0.052173377658691| -0.056470674613699|-0.0607679715687069| -0.065065268523715|-0.0477108000515672|-0.0520907373326331|-0.0565533149397568|-0.0610158925468806|-0.0654784701540042|-0.0475455193994516|-0.0520907373326331|-0.0566359552658147|-0.0612638135250541|-0.0658090314582356|-0.0491156855945507|-0.0536609035277322|-0.0582061214609138|-0.0628339797201531|               NULL| 0.0308736806502811|  0.035711366686826| 0.0405490527233709| 0.0453186023368659|               NULL| 0.0312824991885806| 0.0362564580712254| 0.0412985533769201| 0.0462725122595649| 0.0512464711422096| 0.0315550448807803| 0.0367334130325749| 0.0418436447613195| 0.0470220129131141| 0.0521322446418587|         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      NULL|0.419435768419093|0.436684438158798|0.453933107898504|-6.41029844074064|-6.37799040066583|-6.34570553709037| -6.3134206735149|             NULL|             NULL|-6.18031803782652|-6.14606317180746|-6.11180830578841|-6.07755343976936|             NULL|-6.02366807881245|-5.98786038733787|-5.95205269586328|-5.91622182788936|-5.93358102589225|-5.89649862695417|-5.85941622801608|  -5.822333829078|             NULL|-5.87160706666698|-5.83468690322425|-5.79776673978152|-5.76082339983946|-5.72390323639673|-3.74020488110866|-3.68527628648447|-3.63034769186028|-3.57541909723609|-3.52049050261191|             NULL|-3.55554017727686|-3.49747280581701|-3.43992856382976|-3.38186119236991|-3.51264356052274|             NULL|-3.39232378182213|-3.33268702194444|-3.27252713259414|-3.43103536279537|-3.36930608502723|-3.30705367778649|-3.24532440001835|             NULL|             NULL|-3.32013191460177|-3.26206454314191|-3.20347404220945|-3.14540667074959| 2.01885756257634| 2.10616807140286| 2.19397749742267| 2.28128800624919|  2.36859851507571| 1.98642794501221| 2.07274061945214| 2.15905329389207|   2.245365968332| 2.33167864277193|  1.9604842509609|             NULL| 2.13111393106758| 2.21692768831422| 2.30224252836756| 1.93903081164924|             NULL|             NULL| 2.19397749742267|  2.27879342028272| 1.87367265932767| 1.95300049306148|   2.031829409602|  2.11115724333581| 2.18998615987632|
+-------+----+-----+---+----+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+-----------------+------------------+-----------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+-----------------+------------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+------------------+-----------------+-----------------+------------------+------------------+-----------------+-----------------+------------------+------------------+-----------------+------------------+-----------------+------------------+------------------+------------------+------------------+------------------+-----------------+-----------------+------------------+-----------------+------------------+------------------+------------------+------------------+-----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+-------------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+------------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+-----------------+------------------+-----------------+-----------------+-----------------+------------------+-----------------+
only showing top 5 rows

Train-Test split

Now, we perform a train-test split.

Our split will not be random but years bases, following the same arguments given in the previous assignment (since we have the same data).

# Usual step in Spark ML: rename the response as 'label'
data = data.withColumnRenamed('energy', "label")

# Split the data in train-test
response = 'label'
predictors = [x for x in data.columns if x not in [response, 'year', 'month', 'day', 'hour']]

# Predefine train-test split
train_years = [2005, 2006, 2007]
test_years = [2008, 2009]

data_train = data.filter(col('year').isin(train_years))
data_test = data.filter(col('year').isin(test_years))

# Predefine train_train (train2) - train_validate (validate) split
train2_years = [2006, 2007]
validate_years = [2005]

data_train2 = data.filter(col('year').isin(train2_years))
data_validate = data.filter(col('year').isin(validate_years))

Pipelines definition

• Pipelines of the assignment:

  • Pipeline 0: imputer (mean), assembler, Linear Regression

  • Pipeline 1: imputer (mean), assembler, feature selector (fpr), Linear Regression

  • Pipeline 2: imputer (mean), assembler, feature selector (fwe), Linear Regression

  • Pipeline 3: imputer (mean), assembler, pca (k=3), Linear Regression

  • Pipeline 4: imputer (mean), assembler, feature selector (fpr) + pca (k=3), Linear Regression

• Extra pipeline:

  • Pipeline 5: imputer (not fixed), assembler, scaler, pca (not fixed), decision tree

The idea of including the extra pipeline is to show (and learn) how to do HPO in Spark.

This is the reason why we use decision trees (which has hyperparamiters) and imputation and pca without fixing the imputation method nor the number of components in pca, for being able of doing HPO on the hyperparameters of these three pipelines elements.

The following cells define the mentioned pipelines:

# Define an imputer for missing values imputation.
imputer = Imputer(inputCols=predictors, outputCols=predictors, strategy='mean')
# Define a assembler to create a new column 'features' whose i-th row is vector with the i-th column of the data on which the assembler is applied.
# This new column is necessary to apply ML model on data in Spark.
assembler = VectorAssembler(inputCols=predictors, outputCol='features', handleInvalid='keep')
# Define a feature selection method.
selector = UnivariateFeatureSelector(featuresCol="features", outputCol="selectedFeatures",
                                     labelCol="label", selectionMode="fpr")
selector.setFeatureType("continuous").setLabelType("continuous").setSelectionThreshold(0.5)
# Define a ML model, in this case Linear Regression model, on both the 'features' (predictors) and 'label' (response) columns.
model = LinearRegression(featuresCol="selectedFeatures", labelCol='label')
# Define the pipeline using the above elements.
pipeline1 = Pipeline(stages=[imputer, assembler, selector, model])

imputer = Imputer(inputCols=predictors, outputCols=predictors, strategy='mean')
assembler = VectorAssembler(inputCols=predictors, outputCol='features', handleInvalid='keep')
selector = UnivariateFeatureSelector(featuresCol="features", outputCol="selectedFeatures",
                                     labelCol="label", selectionMode="fwe")
selector.setFeatureType("continuous").setLabelType("continuous").setSelectionThreshold(0.5)
model = LinearRegression(featuresCol="selectedFeatures", labelCol='label')
pipeline2 = Pipeline(stages=[imputer, assembler, selector, model])

imputer = Imputer(inputCols=predictors, outputCols=predictors, strategy='mean')
assembler = VectorAssembler(inputCols=predictors, outputCol='features', handleInvalid='keep')
scaler = StandardScaler(inputCol="features", outputCol="scaledFeatures", withStd=True, withMean=True)
pca = PCA(inputCol="scaledFeatures",  outputCol="pcaFeatures", k=3)
model = LinearRegression(featuresCol="pcaFeatures", labelCol='label')
pipeline3 = Pipeline(stages=[imputer, assembler, scaler, pca, model])

imputer = Imputer(inputCols=predictors, outputCols=predictors, strategy='mean')  
assembler = VectorAssembler(inputCols=predictors, outputCol="features", handleInvalid='keep')
selector = UnivariateFeatureSelector(featuresCol="features", outputCol="selectedFeatures",
                                     labelCol="label", selectionMode="fpr")
selector.setFeatureType("continuous").setLabelType("continuous").setSelectionThreshold(0.5)
scaler = StandardScaler(inputCol="features", outputCol="scaledFeatures", withStd=True, withMean=True)
pca = PCA(k=3, inputCol="scaledFeatures", outputCol="pcaFeatures")
combinedAssembler = VectorAssembler(inputCols=["selectedFeatures", "pcaFeatures"], outputCol="combinedFeatures", handleInvalid='keep')
model = LinearRegression(featuresCol="combinedFeatures", labelCol='label')
pipeline4 = Pipeline(stages=[imputer, assembler, selector, scaler, pca, combinedAssembler, model])

imputer = Imputer(inputCols=predictors, outputCols=predictors) # strategy not fixed
assembler = VectorAssembler(inputCols=predictors, outputCol='features', handleInvalid='keep')
scaler = StandardScaler(inputCol="features", outputCol="scaledFeatures", withStd=True, withMean=True)
pca = PCA(inputCol="scaledFeatures", outputCol="pcaFeatures") # k not fixed
model = DecisionTreeRegressor(featuresCol="pcaFeatures", labelCol='label')
pipeline5 = Pipeline(stages=[imputer, assembler, scaler, pca, model])

imputer = Imputer(inputCols=predictors, outputCols=predictors, strategy='mean')
assembler = VectorAssembler(inputCols=predictors, outputCol='features', handleInvalid='keep')
model = LinearRegression(featuresCol="features", labelCol='label')
pipeline0 = Pipeline(stages=[imputer, assembler, model])

Pipelines evaluation

We are going to evaluate the pipelines using train-train and train-validate by three ways:

• The predefine split

• Random simple validation

• k-fold,

The idea, again, is to make the project more enriching and productive.

Despite this, to select the best pipeline among the first four (the extra pipeline will not be compared), we will only take into account the results for the predefine split.

In addition, we will use MAE as validation metric, following the approach used in the previous project.

evaluator = RegressionEvaluator(labelCol="label", predictionCol="prediction", metricName="mae")

Pipeline 1

Predefine split

# Fit the pipeline
pipeline1_fitted = pipeline1.fit(data_train2)
# Apply the pipeline to the test data.
validate_predictions_pipeline1 = pipeline1_fitted.transform(data_validate).select(['label', 'prediction'])
# This action generates a new data set on which the transformers of the pipeline has been applied (imputation and assembler, in this case).
# After that the fitted model (Linear Regression) is used to make predictions for the resulting new data (using 'features' and 'label' columns).
# Then a column 'prediction' with the model predictions is added.

validate_predictions_pipeline1.show(3)

+-------+------------------+
|  label|        prediction|
+-------+------------------+
| 402.71|144.15834636166255|
|  696.8|188.89930250890757|
|1591.15| 751.1438624302173|
+-------+------------------+
only showing top 3 rows

MAE_pipeline1_predef_split = evaluator.evaluate(validate_predictions_pipeline1)
MAE_pipeline1_predef_split

450.58502952096546

data

DataFrame[label: double, year: int, month: int, day: int, hour: int, p54_162_1: double, p54_162_2: double, p54_162_3: double, p54_162_4: double, p54_162_5: double, p54_162_6: double, p54_162_7: double, p54_162_8: double, p54_162_9: double, p54_162_10: double, p54_162_11: double, p54_162_12: double, p54_162_13: double, p54_162_14: double, p54_162_15: double, p54_162_16: double, p54_162_17: double, p54_162_18: double, p54_162_19: double, p54_162_20: double, p54_162_21: double, p54_162_22: double, p54_162_23: double, p54_162_24: double, p54_162_25: double, p55_162_1: double, p55_162_2: double, p55_162_3: double, p55_162_4: double, p55_162_5: double, p55_162_6: double, p55_162_7: double, p55_162_8: double, p55_162_9: double, p55_162_10: double, p55_162_11: double, p55_162_12: double, p55_162_13: double, p55_162_14: double, p55_162_15: double, p55_162_16: double, p55_162_17: double, p55_162_18: double, p55_162_19: double, p55_162_20: double, p55_162_21: double, p55_162_22: double, p55_162_23: double, p55_162_24: double, p55_162_25: double, cape_1: double, cape_2: double, cape_3: double, cape_4: double, cape_5: double, cape_6: double, cape_7: double, cape_8: double, cape_9: double, cape_10: double, cape_11: double, cape_12: double, cape_13: double, cape_14: double, cape_15: double, cape_16: double, cape_17: double, cape_18: double, cape_19: double, cape_20: double, cape_21: double, cape_22: double, cape_23: double, cape_24: double, cape_25: double, p59_162_1: double, p59_162_2: double, p59_162_3: double, p59_162_4: double, p59_162_5: double, p59_162_6: double, p59_162_7: double, p59_162_8: double, p59_162_9: double, p59_162_10: double, p59_162_11: double, p59_162_12: double, p59_162_13: double, p59_162_14: double, p59_162_15: double, p59_162_16: double, p59_162_17: double, p59_162_18: double, p59_162_19: double, p59_162_20: double, p59_162_21: double, p59_162_22: double, p59_162_23: double, p59_162_24: double, p59_162_25: double, lai_lv_1: double, lai_lv_2: double, lai_lv_3: double, lai_lv_4: double, lai_lv_5: double, lai_lv_6: double, lai_lv_7: double, lai_lv_8: double, lai_lv_9: double, lai_lv_10: double, lai_lv_11: double, lai_lv_12: double, lai_lv_13: double, lai_lv_14: double, lai_lv_15: double, lai_lv_16: double, lai_lv_17: double, lai_lv_18: double, lai_lv_19: double, lai_lv_20: double, lai_lv_21: double, lai_lv_22: double, lai_lv_23: double, lai_lv_24: double, lai_lv_25: double, lai_hv_1: double, lai_hv_2: double, lai_hv_3: double, lai_hv_4: double, lai_hv_5: double, lai_hv_6: double, lai_hv_7: double, lai_hv_8: double, lai_hv_9: double, lai_hv_10: double, lai_hv_11: double, lai_hv_12: double, lai_hv_13: double, lai_hv_14: double, lai_hv_15: double, lai_hv_16: double, lai_hv_17: double, lai_hv_18: double, lai_hv_19: double, lai_hv_20: double, lai_hv_21: double, lai_hv_22: double, lai_hv_23: double, lai_hv_24: double, lai_hv_25: double, u10n_1: double, u10n_2: double, u10n_3: double, u10n_4: double, u10n_5: double, u10n_6: double, u10n_7: double, u10n_8: double, u10n_9: double, u10n_10: double, u10n_11: double, u10n_12: double, u10n_13: double, u10n_14: double, u10n_15: double, u10n_16: double, u10n_17: double, u10n_18: double, u10n_19: double, u10n_20: double, u10n_21: double, u10n_22: double, u10n_23: double, u10n_24: double, u10n_25: double, v10n_1: double, v10n_2: double, v10n_3: double, v10n_4: double, v10n_5: double, v10n_6: double, v10n_7: double, v10n_8: double, v10n_9: double, v10n_10: double, v10n_11: double, v10n_12: double, v10n_13: double, v10n_14: double, v10n_15: double, v10n_16: double, v10n_17: double, v10n_18: double, v10n_19: double, v10n_20: double, v10n_21: double, v10n_22: double, v10n_23: double, v10n_24: double, v10n_25: double, sp_1: double, sp_2: double, sp_3: double, sp_4: double, sp_5: double, sp_6: double, sp_7: double, sp_8: double, sp_9: double, sp_10: double, sp_11: double, sp_12: double, sp_13: double, sp_14: double, sp_15: double, sp_16: double, sp_17: double, sp_18: double, sp_19: double, sp_20: double, sp_21: double, sp_22: double, sp_23: double, sp_24: double, sp_25: double, stl1_1: double, stl1_2: double, stl1_3: double, stl1_4: double, stl1_5: double, stl1_6: double, stl1_7: double, stl1_8: double, stl1_9: double, stl1_10: double, stl1_11: double, stl1_12: double, stl1_13: double, stl1_14: double, stl1_15: double, stl1_16: double, stl1_17: double, stl1_18: double, stl1_19: double, stl1_20: double, stl1_21: double, stl1_22: double, stl1_23: double, stl1_24: double, stl1_25: double, u10_1: double, u10_2: double, u10_3: double, u10_4: double, u10_5: double, u10_6: double, u10_7: double, u10_8: double, u10_9: double, u10_10: double, u10_11: double, u10_12: double, u10_13: double, u10_14: double, u10_15: double, u10_16: double, u10_17: double, u10_18: double, u10_19: double, u10_20: double, u10_21: double, u10_22: double, u10_23: double, u10_24: double, u10_25: double, v10_1: double, v10_2: double, v10_3: double, v10_4: double, v10_5: double, v10_6: double, v10_7: double, v10_8: double, v10_9: double, v10_10: double, v10_11: double, v10_12: double, v10_13: double, v10_14: double, v10_15: double, v10_16: double, v10_17: double, v10_18: double, v10_19: double, v10_20: double, v10_21: double, v10_22: double, v10_23: double, v10_24: double, v10_25: double, t2m_1: double, t2m_2: double, t2m_3: double, t2m_4: double, t2m_5: double, t2m_6: double, t2m_7: double, t2m_8: double, t2m_9: double, t2m_10: double, t2m_11: double, t2m_12: double, t2m_13: double, t2m_14: double, t2m_15: double, t2m_16: double, t2m_17: double, t2m_18: double, t2m_19: double, t2m_20: double, t2m_21: double, t2m_22: double, t2m_23: double, t2m_24: double, t2m_25: double, stl2_1: double, stl2_2: double, stl2_3: double, stl2_4: double, stl2_5: double, stl2_6: double, stl2_7: double, stl2_8: double, stl2_9: double, stl2_10: double, stl2_11: double, stl2_12: double, stl2_13: double, stl2_14: double, stl2_15: double, stl2_16: double, stl2_17: double, stl2_18: double, stl2_19: double, stl2_20: double, stl2_21: double, stl2_22: double, stl2_23: double, stl2_24: double, stl2_25: double, stl3_1: double, stl3_2: double, stl3_3: double, stl3_4: double, stl3_5: double, stl3_6: double, stl3_7: double, stl3_8: double, stl3_9: double, stl3_10: double, stl3_11: double, stl3_12: double, stl3_13: double, stl3_14: double, stl3_15: double, stl3_16: double, stl3_17: double, stl3_18: double, stl3_19: double, stl3_20: double, stl3_21: double, stl3_22: double, stl3_23: double, stl3_24: double, stl3_25: double, iews_1: double, iews_2: double, iews_3: double, iews_4: double, iews_5: double, iews_6: double, iews_7: double, iews_8: double, iews_9: double, iews_10: double, iews_11: double, iews_12: double, iews_13: double, iews_14: double, iews_15: double, iews_16: double, iews_17: double, iews_18: double, iews_19: double, iews_20: double, iews_21: double, iews_22: double, iews_23: double, iews_24: double, iews_25: double, inss_1: double, inss_2: double, inss_3: double, inss_4: double, inss_5: double, inss_6: double, inss_7: double, inss_8: double, inss_9: double, inss_10: double, inss_11: double, inss_12: double, inss_13: double, inss_14: double, inss_15: double, inss_16: double, inss_17: double, inss_18: double, inss_19: double, inss_20: double, inss_21: double, inss_22: double, inss_23: double, inss_24: double, inss_25: double, stl4_1: double, stl4_2: double, stl4_3: double, stl4_4: double, stl4_5: double, stl4_6: double, stl4_7: double, stl4_8: double, stl4_9: double, stl4_10: double, stl4_11: double, stl4_12: double, stl4_13: double, stl4_14: double, stl4_15: double, stl4_16: double, stl4_17: double, stl4_18: double, stl4_19: double, stl4_20: double, stl4_21: double, stl4_22: double, stl4_23: double, stl4_24: double, stl4_25: double, fsr_1: double, fsr_2: double, fsr_3: double, fsr_4: double, fsr_5: double, fsr_6: double, fsr_7: double, fsr_8: double, fsr_9: double, fsr_10: double, fsr_11: double, fsr_12: double, fsr_13: double, fsr_14: double, fsr_15: double, fsr_16: double, fsr_17: double, fsr_18: double, fsr_19: double, fsr_20: double, fsr_21: double, fsr_22: double, fsr_23: double, fsr_24: double, fsr_25: double, flsr_1: double, flsr_2: double, flsr_3: double, flsr_4: double, flsr_5: double, flsr_6: double, flsr_7: double, flsr_8: double, flsr_9: double, flsr_10: double, flsr_11: double, flsr_12: double, flsr_13: double, flsr_14: double, flsr_15: double, flsr_16: double, flsr_17: double, flsr_18: double, flsr_19: double, flsr_20: double, flsr_21: double, flsr_22: double, flsr_23: double, flsr_24: double, flsr_25: double, u100_1: double, u100_2: double, u100_3: double, u100_4: double, u100_5: double, u100_6: double, u100_7: double, u100_8: double, u100_9: double, u100_10: double, u100_11: double, u100_12: double, u100_13: double, u100_14: double, u100_15: double, u100_16: double, u100_17: double, u100_18: double, u100_19: double, u100_20: double, u100_21: double, u100_22: double, u100_23: double, u100_24: double, u100_25: double, v100_1: double, v100_2: double, v100_3: double, v100_4: double, v100_5: double, v100_6: double, v100_7: double, v100_8: double, v100_9: double, v100_10: double, v100_11: double, v100_12: double, v100_13: double, v100_14: double, v100_15: double, v100_16: double, v100_17: double, v100_18: double, v100_19: double, v100_20: double, v100_21: double, v100_22: double, v100_23: double, v100_24: double, v100_25: double]

The number of selected features with this pipeline (fpr selector) is 544 out of 555.

len(pipeline1_fitted.stages[2].selectedFeatures)

544

Random simple validation

pipeline1_sv = TrainValidationSplit(estimator=pipeline1,
                              evaluator=RegressionEvaluator(metricName="mae"),
                              estimatorParamMaps=ParamGridBuilder().build(),
                              trainRatio=0.75)

pipeline1_sv_fitted = pipeline1_sv.fit(data_train)

MAE_pipeline1_sv = pipeline1_sv_fitted.validationMetrics[0]
MAE_pipeline1_sv

428.04922049265014

k-fold cv

pipeline1_kfold = CrossValidator(estimator=pipeline1, 
                                 evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                 numFolds=3,
                                 estimatorParamMaps=ParamGridBuilder().build()
                                )

pipeline1_kfold_fitted = pipeline1_kfold.fit(data_train)

MAE_pipeline1_kfold = pipeline1_kfold_fitted.avgMetrics[0]
MAE_pipeline1_kfold

432.9321541656756

Pipeline 2

Predefine split

pipeline2_fitted = pipeline2.fit(data_train2)
validate_predictions_pipeline2 = pipeline2_fitted.transform(data_validate).select(['label', 'prediction'])
MAE_pipeline2_predef_split = evaluator.evaluate(validate_predictions_pipeline2)
MAE_pipeline2_predef_split

447.7850861127979

The number of selected features with this pipeline (fwe selector) is 496 out of 555.

len(pipeline2_fitted.stages[2].selectedFeatures)

496

Random simple validation

pipeline2_sv = TrainValidationSplit(estimator=pipeline2,
                              evaluator=RegressionEvaluator(metricName="mae"),
                              estimatorParamMaps=ParamGridBuilder().build(),
                              trainRatio=0.75)

pipeline2_sv_fitted = pipeline2_sv.fit(data_train)
MAE_pipeline2_sv = pipeline2_sv_fitted.validationMetrics[0]
MAE_pipeline2_sv

420.96574222724604

k-fold cv

pipeline2_kfold = CrossValidator(estimator=pipeline2, 
                                 evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                 numFolds=3,
                                 estimatorParamMaps=ParamGridBuilder().build()
                                )

pipeline2_kfold_fitted = pipeline2_kfold.fit(data_train)
MAE_pipeline2_kfold = pipeline2_kfold_fitted.avgMetrics[0]
MAE_pipeline2_kfold

428.8867064566628

Pipeline 3

Predefine split

pipeline3_fitted = pipeline3.fit(data_train2)
validate_predictions_pipeline3 = pipeline3_fitted.transform(data_validate).select(['label', 'prediction'])
MAE_pipeline3_predef_split = evaluator.evaluate(validate_predictions_pipeline3)
MAE_pipeline3_predef_split

515.1934949236103

Random simple validation

pipeline3_sv = TrainValidationSplit(estimator=pipeline3,
                              evaluator=RegressionEvaluator(metricName="mae"),
                              estimatorParamMaps=ParamGridBuilder().build(),
                              trainRatio=0.75)

pipeline3_sv_fitted = pipeline3_sv.fit(data_train)
MAE_pipeline3_sv = pipeline3_sv_fitted.validationMetrics[0]
MAE_pipeline3_sv

505.81672893381335

k-fold cv

pipeline3_kfold = CrossValidator(estimator=pipeline3, 
                                 evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                 numFolds=3,
                                 estimatorParamMaps=ParamGridBuilder().build()
                                )

pipeline3_kfold_fitted = pipeline3_kfold.fit(data_train)
MAE_pipeline3_kfold = pipeline3_kfold_fitted.avgMetrics[0]
MAE_pipeline3_kfold

500.1136347904351

Pipeline 4

Predefine split

pipeline4_fitted = pipeline4.fit(data_train2)
validate_predictions_pipeline4 = pipeline4_fitted.transform(data_validate).select(['label', 'prediction'])
MAE_pipeline4_predef_split = evaluator.evaluate(validate_predictions_pipeline4)
MAE_pipeline4_predef_split

451.70349096551405

Random simple validation

pipeline4_sv = TrainValidationSplit(estimator=pipeline4,
                              evaluator=RegressionEvaluator(metricName="mae"),
                              estimatorParamMaps=ParamGridBuilder().build(),
                              trainRatio=0.75)

pipeline4_sv_fitted = pipeline4_sv.fit(data_train)
MAE_pipeline4_sv = pipeline4_sv_fitted.validationMetrics[0]
MAE_pipeline4_sv

428.3733104604351

k-fold cv

pipeline4_kfold = CrossValidator(estimator=pipeline4, 
                                 evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                 numFolds=3,
                                 estimatorParamMaps=ParamGridBuilder().build()
                                )

pipeline4_kfold_fitted = pipeline4_kfold.fit(data_train)
MAE_pipeline4_kfold = pipeline4_kfold_fitted.avgMetrics[0]
MAE_pipeline4_kfold

433.057891066047

Pipeline 5 (extra)

Using predefine split

Apache Spark’s MLlib doesn’t natively support predefined splits for HPO like scikit-learn does with its PredefinedSplit.

This is the reason why we cannot compare the extra pipeline with the others by predefine split.

Using random simple validation

paramGrid = ParamGridBuilder() \
    .addGrid(imputer.strategy, ['mean', 'median']) \
    .addGrid(pca.k, [3, 10]) \
    .addGrid(pipeline5.getStages()[-1].maxDepth, [2, 6]) \
    .addGrid(pipeline5.getStages()[-1].maxBins, [20, 40]) \
    .addGrid(pipeline5.getStages()[-1].minInstancesPerNode, [2, 10]) \
    .build()

pipeline5_HPO_sv = TrainValidationSplit(estimator=pipeline5,
                              evaluator=RegressionEvaluator(metricName="mae"),
                              estimatorParamMaps=paramGrid,
                              trainRatio=0.75)

pipeline5_HPO_sv_fitted = pipeline5_HPO_sv.fit(data_train)

final_model_pipeline5_sv = pipeline5_HPO_sv_fitted.bestModel
# Time: 5.20 mins

final_model_pipeline5_sv_params = {param.name: value for param, value in final_model_pipeline5_sv.stages[-1].extractParamMap().items()}
final_model_pipeline5_sv_params

{'cacheNodeIds': False,
 'checkpointInterval': 10,
 'featuresCol': 'pcaFeatures',
 'impurity': 'variance',
 'labelCol': 'label',
 'leafCol': '',
 'maxBins': 40,
 'maxDepth': 6,
 'maxMemoryInMB': 256,
 'minInfoGain': 0.0,
 'minInstancesPerNode': 10,
 'minWeightFractionPerNode': 0.0,
 'predictionCol': 'prediction',
 'seed': 3529065940959987723}

final_model_pipeline5_sv_MAE = min(pipeline5_HPO_sv_fitted.validationMetrics)
final_model_pipeline5_sv_MAE

366.0861391472056

Using k-fold cv

paramGrid = ParamGridBuilder() \
    .addGrid(imputer.strategy, ['mean', 'median']) \
    .addGrid(pca.k, [3, 10]) \
    .addGrid(pipeline5.getStages()[-1].maxDepth, [2, 6]) \
    .addGrid(pipeline5.getStages()[-1].maxBins, [20, 40]) \
    .addGrid(pipeline5.getStages()[-1].minInstancesPerNode, [2, 10]) \
    .build()

pipeline5_HPO_kfold = CrossValidator(estimator=pipeline5, 
                                     evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                     numFolds=2,
                                    estimatorParamMaps=paramGrid
                                )

pipeline5_HPO_kfold_fitted = pipeline5_HPO_kfold.fit(data_train)

final_model_pipeline5_kfold = pipeline5_HPO_kfold_fitted.bestModel
# Time: 8.26 mins

final_model_pipeline5_kfold_imputer_strategy = final_model_pipeline5_kfold.stages[0].getStrategy()
final_model_pipeline5_kfold_imputer_strategy

'median'

final_model_pipeline5_kfold_pca_n_components = final_model_pipeline5_kfold.stages[3].getK()
final_model_pipeline5_kfold_pca_n_components

3

final_model_pipeline5_kfold_params = {param.name: value for param, value in final_model_pipeline5_kfold.stages[-1].extractParamMap().items()}
final_model_pipeline5_kfold_params

{'cacheNodeIds': False,
 'checkpointInterval': 10,
 'featuresCol': 'pcaFeatures',
 'impurity': 'variance',
 'labelCol': 'label',
 'leafCol': '',
 'maxBins': 40,
 'maxDepth': 6,
 'maxMemoryInMB': 256,
 'minInfoGain': 0.0,
 'minInstancesPerNode': 10,
 'minWeightFractionPerNode': 0.0,
 'predictionCol': 'prediction',
 'seed': 3529065940959987723}

final_model_pipeline5_kfold_MAE = min(pipeline5_HPO_kfold_fitted.avgMetrics)
final_model_pipeline5_kfold_MAE

368.84319998691024

Now we can update the pipeline taking into account the HPO results and compute the MAE again, to check that it is the same that the one we have just obtained:

imputer = Imputer(inputCols=predictors, outputCols=predictors, strategy=final_model_pipeline5_kfold_imputer_strategy)  
assembler = VectorAssembler(inputCols=predictors, outputCol='features', handleInvalid='keep')
scaler = StandardScaler(inputCol="features", outputCol="scaledFeatures", withStd=True, withMean=True)
pca = PCA(inputCol="scaledFeatures", outputCol="pcaFeatures", k=final_model_pipeline5_kfold_pca_n_components)  
model = DecisionTreeRegressor(featuresCol="pcaFeatures", labelCol='label', 
                              maxDepth=final_model_pipeline5_kfold_params['maxDepth'],
                              maxBins=final_model_pipeline5_kfold_params['maxBins'],
                              minInstancesPerNode=final_model_pipeline5_kfold_params['minInstancesPerNode'])
pipeline5_final = Pipeline(stages=[imputer, assembler, scaler, pca, model])

pipeline5_final_kfold = CrossValidator(estimator=pipeline5_final, 
                                     evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                     numFolds=2,
                                     estimatorParamMaps=ParamGridBuilder().build()
                                    )
pipeline5_final_kfold_fitted = pipeline5_final_kfold.fit(data_train)
pipeline5_final_kfold_MAE = min(pipeline5_final_kfold_fitted.avgMetrics)
pipeline5_final_kfold_MAE

383.82841469017933

Pipeline 0

Predefine split

pipeline0_fitted = pipeline0.fit(data_train2)
validate_predictions_pipeline0 = pipeline0_fitted.transform(data_validate).select(['label', 'prediction'])
MAE_pipeline0_predef_split = evaluator.evaluate(validate_predictions_pipeline0)
MAE_pipeline0_predef_split

452.3205499585219

Random simple validation

pipeline0_sv = TrainValidationSplit(estimator=pipeline0,
                              evaluator=RegressionEvaluator(metricName="mae"),
                              estimatorParamMaps=ParamGridBuilder().build(),
                              trainRatio=0.75)

pipeline0_sv_fitted = pipeline0_sv.fit(data_train)
MAE_pipeline0_sv = pipeline0_sv_fitted.validationMetrics[0]
MAE_pipeline0_sv

426.48961804895526

k-fold cv

pipeline0_kfold = CrossValidator(estimator=pipeline0, 
                                 evaluator=RegressionEvaluator(labelCol="label", 
                                                               predictionCol="prediction", 
                                                               metricName="mae"),
                                 numFolds=3,
                                 estimatorParamMaps=ParamGridBuilder().build()
                                )

pipeline0_kfold_fitted = pipeline0_kfold.fit(data_train)
MAE_pipeline0_kfold = pipeline0_kfold_fitted.avgMetrics[0]
MAE_pipeline0_kfold

434.6859310337352

Pipelines comparison

In this section we are going to compare the different pipelines (from 0 to 4) according to their validation MAE computed by the predefined split.

MAE_arr = np.array([MAE_pipeline0_predef_split, MAE_pipeline1_predef_split, MAE_pipeline2_predef_split, 
                    MAE_pipeline3_predef_split, MAE_pipeline4_predef_split])

MAE_arr

array([452.32054996, 450.58502952, 447.78508611, 515.19349492,
       451.70349097])

pipelines_indices_sorted = np.argsort(MAE_arr)
pipelines_indices_sorted

array([2, 1, 4, 0, 3])

pipelines_indices_sorted[0]

2

Therefore, the “best” pipeline between the five compared is the pipeline 2: [imputer (mean), assembler, feature selector (fwe), Linear Regression. This will be consider the final pipeline.

Again, we want to highlight that we have excluded the extra pipeline (pipeline 5) of the comparison, because it couldn`t be evaluated with the predefine split, and this is the validation method we have choose to evaluate all the pipelines.

Estimation of future performance for the final pipeline

In this section we are going to estimate the future performance of the final pipeline (pipeline 2).

pipeline2_fitted = pipeline2.fit(data_train)
test_predictions_pipeline2 = pipeline2_fitted.transform(data_test).select(['label', 'prediction'])
MAE_future_performance_pipeline2_predef_split = evaluator.evaluate(test_predictions_pipeline2)
MAE_future_performance_pipeline2_predef_split

412.9088216020078

The estimation of future performance of the final pipeline in terms of MAE is 412.91.

Conclusions

We can conclude several things from this project:

• Spark provide a simple and powerful way for carrying out Machine Learning tasks.

• Pipelines are one of the most powerful tools provided by Spark to perform Machine Learning tasks. Thanks to this project and the previous one, is pretty clear that pipelines are key element in any Machine Learning project, so, any good Data Scientist should know how to use them to make their ML projects much more efficient and robust.

• Feature selection is an important step in every Machine Learning pipeline since it can lead to better prediction performance.