Accelerate Linear Model Fitting on GPU
This example shows how you can accelerate regression model fitting by running functions on a graphical processing unit (GPU). The example compares the time required to fit a model on a central processing unit (CPU) with the time required to fit the same model on a GPU. Using a GPU requires Parallel Computing Toolbox™ and a supported GPU device. For information about supported devices, see GPU Computing Requirements (Parallel Computing Toolbox).
Create a table of airline sample data from the file airlinesmall.csv by using the readtable function. Remove table rows corresponding to canceled flights, and convert UniqueCarrier to a categorical variable using the categorical function.
A = readtable("airlinesmall.csv");
A = A(A.Cancelled~=1,:);
A.UniqueCarrier = categorical(A.UniqueCarrier)A=121171×29 table
Year Month DayofMonth DayOfWeek DepTime CRSDepTime ArrTime CRSArrTime UniqueCarrier FlightNum TailNum ActualElapsedTime CRSElapsedTime AirTime ArrDelay DepDelay Origin Dest Distance TaxiIn TaxiOut Cancelled CancellationCode Diverted CarrierDelay WeatherDelay NASDelay SecurityDelay LateAircraftDelay
____ _____ __________ _________ _______ __________ _______ __________ _____________ _________ _______ _________________ ______________ _______ ________ ________ _______ _______ ________ ______ _______ _________ ________________ ________ ____________ ____________ ________ _____________ _________________
1987 10 21 3 642 630 735 727 PS 1503 {'NA'} 53 57 {'NA'} 8 12 {'LAX'} {'SJC'} 308 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 26 1 1021 1020 1124 1116 PS 1550 {'NA'} 63 56 {'NA'} 8 1 {'SJC'} {'BUR'} 296 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 23 5 2055 2035 2218 2157 PS 1589 {'NA'} 83 82 {'NA'} 21 20 {'SAN'} {'SMF'} 480 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 23 5 1332 1320 1431 1418 PS 1655 {'NA'} 59 58 {'NA'} 13 12 {'BUR'} {'SJC'} 296 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 22 4 629 630 746 742 PS 1702 {'NA'} 77 72 {'NA'} 4 -1 {'SMF'} {'LAX'} 373 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 28 3 1446 1343 1547 1448 PS 1729 {'NA'} 61 65 {'NA'} 59 63 {'LAX'} {'SJC'} 308 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 8 4 928 930 1052 1049 PS 1763 {'NA'} 84 79 {'NA'} 3 -2 {'SAN'} {'SFO'} 447 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 10 6 859 900 1134 1123 PS 1800 {'NA'} 155 143 {'NA'} 11 -1 {'SEA'} {'LAX'} 954 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 20 2 1833 1830 1929 1926 PS 1831 {'NA'} 56 56 {'NA'} 3 3 {'LAX'} {'SJC'} 308 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 15 4 1041 1040 1157 1155 PS 1864 {'NA'} 76 75 {'NA'} 2 1 {'SFO'} {'LAS'} 414 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 15 4 1608 1553 1656 1640 PS 1907 {'NA'} 48 47 {'NA'} 16 15 {'LAX'} {'FAT'} 209 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 21 3 949 940 1055 1052 PS 1939 {'NA'} 66 72 {'NA'} 3 9 {'LGB'} {'SFO'} 354 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 22 4 1902 1847 2030 1951 PS 1973 {'NA'} 88 64 {'NA'} 39 15 {'LAX'} {'OAK'} 337 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 16 5 1910 1838 2052 1955 TW 19 {'NA'} 162 137 {'NA'} 57 32 {'STL'} {'DEN'} 770 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 2 5 1130 1133 1237 1237 TW 59 {'NA'} 187 184 {'NA'} 0 -3 {'STL'} {'PHX'} 1262 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
1987 10 30 5 1400 1400 1920 1934 TW 102 {'NA'} 200 214 {'NA'} -14 0 {'SNA'} {'STL'} 1570 {'NA'} {'NA'} 0 {'NA'} 0 {'NA'} {'NA'} {'NA'} {'NA'} {'NA'}
⋮
The table A contains data for 12,1171 flights. The table variables Year, Month, and DayofMonth contain data for the year, month, and day that each flight departed, respectively. ArrDelay contains the delay in minutes between each flight's scheduled and actual arrival time. UniqueCarrier contains data for the airline that operated each flight.
Measure Time to Fit Linear Model on CPU
Measure the time required to fit a linear regression model on a CPU to the predictor variables Year, Month, DayofMonth, and UniqueCarrier, and the response variable ArrDelay. This example uses an Intel® Xeon® W-2133 CPU @ 3.60 GHz.
Create a second table from the table A variables Year, Month, DayofMonth, UniqueCarrier, and ArrDelay.
tblCPU = table(A.Year,A.Month,A.DayofMonth,A.UniqueCarrier,A.ArrDelay, ... VariableNames=["Year" "Month" "DayofMonth" "UniqueCarrier" "ArrDelay"])
tblCPU=121171×5 table
Year Month DayofMonth UniqueCarrier ArrDelay
____ _____ __________ _____________ ________
1987 10 21 PS 8
1987 10 26 PS 8
1987 10 23 PS 21
1987 10 23 PS 13
1987 10 22 PS 4
1987 10 28 PS 59
1987 10 8 PS 3
1987 10 10 PS 11
1987 10 20 PS 3
1987 10 15 PS 2
1987 10 15 PS 16
1987 10 21 PS 3
1987 10 22 PS 39
1987 10 16 TW 57
1987 10 2 TW 0
1987 10 30 TW -14
⋮
Create an anonymous function that uses the fitlm function to fit a linear regression model to the variables in tblCPU. Measure the time required to run the anonymous function by using the timeit function.
cpufit = @() fitlm(tblCPU,CategoricalVars=4); tcpu = timeit(cpufit)
tcpu = 0.3241
tcpu contains the time required to fit the linear regression model on the CPU.
Measure Time to Fit Linear Model on GPU
Verify that a GPU device is available by using the gpuDevice (Parallel Computing Toolbox) function.
gpuDevice
ans =
CUDADevice with properties:
Name: 'NVIDIA RTX A5000'
Index: 1 (of 2)
ComputeCapability: '8.6'
DriverModel: 'TCC'
TotalMemory: 25544294400 (25.54 GB)
AvailableMemory: 25120866304 (25.12 GB)
DeviceAvailable: true
DeviceSelected: true
Show all properties.
Create a third table from the table tblCPU variables. Copy the table's numeric and logical variables to GPU memory by using the gpuArray (Parallel Computing Toolbox) function.
tblGPU = tblCPU; for ii = 1:width(tblCPU) if isnumeric(tblCPU.(ii)) || islogical(tblCPU.(ii)) tblGPU.(ii) = gpuArray(tblCPU.(ii)); end end tblGPU
tblGPU=121171×5 table
Year Month DayofMonth UniqueCarrier ArrDelay
____ _____ __________ _____________ ________
1987 10 21 PS 8
1987 10 26 PS 8
1987 10 23 PS 21
1987 10 23 PS 13
1987 10 22 PS 4
1987 10 28 PS 59
1987 10 8 PS 3
1987 10 10 PS 11
1987 10 20 PS 3
1987 10 15 PS 2
1987 10 15 PS 16
1987 10 21 PS 3
1987 10 22 PS 39
1987 10 16 TW 57
1987 10 2 TW 0
1987 10 30 TW -14
⋮
The tblGPU table contains gpuArray objects, each representing an array stored in GPU memory.
When you pass gpuArray inputs to the fitlm function, it automatically runs on the GPU. Measure the time required to fit the regression model on the GPU by using the gputimeit (Parallel Computing Toolbox) function. This function is preferable to timeit, because it ensures that all operations on the GPU are complete before it records the time. The function also compensates for the overhead of working on a GPU.
gpufit = @() fitlm(tblGPU,CategoricalVars=4); tgpu = gputimeit(gpufit)
tgpu = 0.1006
tgpu contains the time required to fit the linear regression model on the GPU, which is over three times faster than on the CPU.
Determine Statistical Significance
To investigate the statistical significance of the linear regression model terms, fit the regression model on the GPU.
mdl = fitlm(tblGPU,CategoricalVars=4)
mdl =
Linear regression model:
ArrDelay ~ 1 + Year + Month + DayofMonth + UniqueCarrier
Estimated Coefficients:
Estimate SE tStat pValue
___________ _________ ________ __________
(Intercept) -178.2904 33.3585 -5.3447 9.0739e-08
Year 0.09144843 0.0166 5.5089 3.6173e-08
Month -0.07640735 0.0255798 -2.987 0.0028176
DayofMonth 0.03731819 0.0100045 3.7301 0.00019147
UniqueCarrier_AA 2.474112 1.38942 1.7807 0.074968
UniqueCarrier_AQ -4.028572 2.81772 -1.4297 0.1528
UniqueCarrier_AS 3.478428 1.47986 2.3505 0.018749
UniqueCarrier_B6 6.685668 1.73686 3.8493 0.00011853
UniqueCarrier_CO 2.622961 1.40944 1.861 0.062748
UniqueCarrier_DH 2.514483 1.79715 1.3991 0.16177
UniqueCarrier_DL 3.071577 1.38827 2.2125 0.026932
UniqueCarrier_EA 4.619557 1.73326 2.6652 0.0076942
UniqueCarrier_EV 4.831761 1.55067 3.1159 0.0018342
UniqueCarrier_F9 3.199074 2.15633 1.4836 0.13792
UniqueCarrier_FL 4.286813 1.60874 2.6647 0.0077066
UniqueCarrier_HA -6.75125 2.29837 -2.9374 0.0033104
UniqueCarrier_HP 3.2339 1.46058 2.2141 0.026822
UniqueCarrier_ML (1) -3.77572 3.92876 -0.96105 0.33653
UniqueCarrier_MQ 3.739103 1.44475 2.5881 0.009653
UniqueCarrier_NW 0.9346265 1.3994 0.66788 0.50421
UniqueCarrier_OH 2.552324 1.58129 1.6141 0.10651
UniqueCarrier_OO 0.6509585 1.46651 0.44388 0.65713
UniqueCarrier_PA (1) 1.653223 2.21609 0.74601 0.45566
UniqueCarrier_PI 7.609183 1.73962 4.3741 1.2206e-05
UniqueCarrier_PS 1.854016 3.65042 0.50789 0.61153
UniqueCarrier_TW 3.235745 1.46218 2.213 0.026902
UniqueCarrier_TZ -3.190202 2.48632 -1.2831 0.19946
UniqueCarrier_UA 3.933074 1.3927 2.8241 0.0047426
UniqueCarrier_US 2.40755 1.39284 1.7285 0.083898
UniqueCarrier_WN 0.7392784 1.38333 0.53442 0.59305
UniqueCarrier_XE 3.605406 1.49916 2.405 0.016176
UniqueCarrier_YV 7.036055 1.72275 4.0842 4.426e-05
Number of observations: 120866, Error degrees of freedom: 120834
Root Mean Squared Error: 30.5
R-squared: 0.00259, Adjusted R-Squared: 0.00233
F-statistic vs. constant model: 10.1, p-value = 2.38e-48
mdl contains the formula for the linear regression model and statistics about the estimated model coefficients. The table output contains a row for each continuous term and for each value in UniqueCarrier. You can determine if a term or value has a statistically significant effect on the arrival delay by comparing its p-value to the significance level of 0.05.
To determine whether UniqueCarrier contains a value that has a statistically significant effect on the arrival delay, perform an ANOVA with a 95% confidence level by using the function anova. When you pass gpuArray inputs to the anova function, it automatically runs on the GPU.
aov = anova(mdl)
aov=5×5 table
SumSq DF MeanSq F pValue
__________ __________ ______ ______ __________
Year 28309 1 28309 30.348 3.6173e-08
Month 8322.7 1 8322.7 8.9223 0.0028176
DayofMonth 12979 1 12979 13.914 0.00019147
UniqueCarrier 2.4305e+05 28 8680.5 9.3059 1.6331e-39
Error 1.1271e+08 1.2083e+05 932.79
aov contains the results of the ANOVA. The p-value in the row corresponding to UniqueCarrier is smaller than the significance level of 0.05, indicating that at least one value in UniqueCarrier has a statistically significant effect on the arrival delay.
See Also
gpuDevice (Parallel Computing Toolbox) | gputimeit (Parallel Computing Toolbox) | timeit | fitlm | anova
Related Topics
- Analyze and Model Data on GPU
- Measure and Improve GPU Performance (Parallel Computing Toolbox)
- Run MATLAB Functions on a GPU (Parallel Computing Toolbox)
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