Is there a way to use Minimize() or a similar function to solve for this expression: expr1 = expr((a:A+b:B+c:C)=:Target); using the following table: ABCTarget10003050000150099990029997300100590050999950009501000500450050999902014820010008001000300000

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Optimization of linear expression using columns to solve for variables

aserino

Is there a way to use Minimize() or a similar function to solve for this expression:

expr1 = expr((a:A+b:B+c:C)=:Target);

using the following table:

A	B	C	Target
10	0	0	30
500	0	0	1500
9999	0	0	29997
30	0	100	590
0	50	9999	500095
0	1000	500	4500
50	9999	0	20148
200	100	0	800
10	0	0	30
0	0	0	0

Accepted answers

Dan_Obermiller

I'm not sure what you are really trying to do, but this looks like a regression problem to me:

Find values of a, b, and c such that the difference between (a*A + b*B + c*C) (which I will call predicted value) and Target is as small as possible. In the regression context that would be minimize the sum of squared errors where an error = Target - Predicted Value.

You can do this interactively with Fit Model, which I did. The script from going that is down below. The result is:

Fit Model(
	Y( :Target ),
	Effects( :A, :B, :C ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run(
		:Target << {Summary of Fit( 1 ), Analysis of Variance( 1 ),
		Parameter Estimates( 1 ), Scaled Estimates( 0 ),
		Plot Actual by Predicted( 1 ), Plot Regression( 0 ),
		Plot Residual by Predicted( 1 ), Plot Studentized Residuals( 0 ),
		Plot Effect Leverage( 1 ), Plot Residual by Normal Quantiles( 0 ),
		Box Cox Y Transformation( 0 )}
	)
);

All comments

aserino

Sorry, error with expression:

dt = Current Data Table;
expr1 = expr((a*dt:A+b*dt:B+c*dt:C)=:Target);

Looking to identify values for a, b, and c.

Dan_Obermiller

I'm not sure what you are really trying to do, but this looks like a regression problem to me:

You can do this interactively with Fit Model, which I did. The script from going that is down below. The result is:

Fit Model(
	Y( :Target ),
	Effects( :A, :B, :C ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run(
		:Target << {Summary of Fit( 1 ), Analysis of Variance( 1 ),
		Parameter Estimates( 1 ), Scaled Estimates( 0 ),
		Plot Actual by Predicted( 1 ), Plot Regression( 0 ),
		Plot Residual by Predicted( 1 ), Plot Studentized Residuals( 0 ),
		Plot Effect Leverage( 1 ), Plot Residual by Normal Quantiles( 0 ),
		Box Cox Y Transformation( 0 )}
	)
);

dale_lehman

I've had good luck with the nonlinear platform (even for linear optimization). You need to enter parameters in conjunction with columns and it will solve for those parameters.

aserino

Hi @Dan , thanks for the response. This seems promising for what I need, although how can you pull out the result that you mentioned?

Also, how would pull out those individual values for a, b, and c?

Thanks!

Dan_Obermiller

The results would be in the Parameter Estimates report. If you are trying to pull them out via JSL, look at the JMP Scripting Guide. Probably start with the section "Navigate JMP Reports".

ian_jmp

The phrasing of the original question perhaps suggests that a solution via JSL is required. If that's the case, an alternative avoiding the use of JMP Platforms is:

NamesDefaultToHere(1);

// Data table
dt = New Table( "Test",
	Add Rows( 10 ),
	New Column( "A",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Values( [10, 500, 9999, 30, 0, 0, 50, 200, 10, 0] )
	),
	New Column( "B",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Values( [0, 0, 0, 0, 50, 1000, 9999, 100, 0, 0] )
	),
	New Column( "C",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Values( [0, 0, 0, 100, 9999, 500, 0, 0, 0, 0] )
	),
	New Column( "Target",
		Numeric,
		"Continuous",
		Format( "Best", 12 ),
		Set Values( [30, 1500, 29997, 590, 500095, 4500, 20148, 800, 30, 0] )
	)
);

// Get values into vectors (could use table subscripting too)
Y = Column(dt, "Target") << getValues;
Avals = Column(dt, "A") << getValues;
Bvals = Column(dt, "B") << getValues;
Cvals = Column(dt, "C") << getValues;
X = Avals||Bvals||Cvals;

// Do the regression (see 'Help > Scripting Index' for more details of 'results')
results = LinearRegression(Y, X);
parameters = results[1];
Print(parameters);

But as @Dan_Obermiller points out, as stated it can be viewed as a regression problem, and it's generally not a good idea to do regression without a visual inspection of the data or the results.

aserino

While this method seems promising, I'm running into problems scaling it up... The log outputs:

Inputs have missing values.
[., ., ., ., ., ., ., ., ., ., .]

I'm attempting to eventually scale this up to a ~20 variable problem, where

X = [20x200] matrix

Y = [1x200] matrix

Y = M*X , where M is a matrix of 20 variables

Is this still possible with linear regression? Some online resources seem to suggest batch gradient descent.

Thanks

Dan_Obermiller

You might want to look at the free Statistical Thinking for Industrial Problem Solving course (or just Statistical Thinking course for short) that is available from the Learn JMP tab. Look at the regression section. That will show you how regression works and how to do it in JMP. Regression can handle a problem of this size.

Have your X columns entered into a JMP table. You will have 20 X columns and 200 rows. Put your Y column in as well so that your table has a total of 21 columns. From there you can use any of the JSL code if you want to use JMP scripting. Alternatively, you can use Fit Model. Specify your Y. Highlight all of your X's and click Add. Then click Run Model.