Dear All,

The goal is to achieve the highest accuracy for a specific combination of the input variables. For example, I only evaluated three different combinations of the input, while we have other combinations like y=f(x1,x4), y=f(x3,x4,x5), y=f(x3), and so on.

As you know evaluation of all possible combinations is time-consuming. Is there any way to get the best combination of inputs?

Any help would be greatly appreciated.

y = {7.56, 3.79, 2.85, 8.47, 1.37, 5.16, 3.83, 6.58, 6.14, 5.82};
x1 = {1.7, 0.67, 0.5, 7.9, 5.5, 0.81, 6.9, 4.6, 8.2, 8.1};
x2 = {9.02, 0.85, 1.09, 3.37, 8.64, 6.72, 0.62, 7.12, 7.42, 2.03};
x3 = {2.69, 2.04, 3.12, 2.09, 0.89, 7.82, 7.56, 2.24, 7.25, 3.44};
x4 = {6.01, 2.73, 5.35, 7.33, 9.38, 9.94, 1.19, 5.05, 9.39, 8.86};
x5 = {0.84, 2.31, 4.42, 4.18, 8.46, 3.02, 9.09, 6.14, 4.10, 7.15};

(*Scenario 1 : y=f(x1) *)

tuples1 = Thread[Rule[Transpose[{x1}], y]];

train = Take[tuples1, 7];

test = Take[tuples1, -3];

cfunc = Predict[train, Method ->  NeuralNetwork  , 
   PerformanceGoal ->  Quality  ];

predictOnTrained = Map[cfunc, train[[All, 1]]];

predictOnTest = Map[cfunc, test[[All, 1]]];

actualOnTrained = train[[All, 2]];

actualOnTest = test[[All, 2]];

RootMeanSquare[actualOnTest - predictOnTest];

Correlation[actualOnTest, predictOnTest];

(*Scenario 2 : y=f(x1,x2) *)

tuples2 = Thread[Rule[Transpose[{x1, x2}], y]];

train = Take[tuples2, 7];

test = Take[tuples2, -3];

cfunc = Predict[train, Method ->  NeuralNetwork  , 
   PerformanceGoal ->  Quality  ];

predictOnTrained = Map[cfunc, train[[All, 1]]];

predictOnTest = Map[cfunc, test[[All, 1]]];

actualOnTrained = train[[All, 2]];

actualOnTest = test[[All, 2]];

RootMeanSquare[actualOnTest - predictOnTest]

Correlation[actualOnTest, predictOnTest]

(*Scenario 3 : y=f(x1,x2,x3) *)

tuples3 = Thread[Rule[Transpose[{x1, x2, x3}], y]];

train = Take[tuples3, 7];

test = Take[tuples3, -3];

cfunc = Predict[train, Method ->  NeuralNetwork  , 
   PerformanceGoal ->  Quality  ];

predictOnTrained = Map[cfunc, train[[All, 1]]];

predictOnTest = Map[cfunc, test[[All, 1]]];

actualOnTrained = train[[All, 2]];

actualOnTest = test[[All, 2]];

RootMeanSquare[actualOnTest - predictOnTest]

Correlation[actualOnTest, predictOnTest]