Construct a mathematical formula

[adan]

Hello,
I have been thinking of it for a long time, and I would appreciate suggestions from math experts.

I am working on a simulation of human agents. I want to set up a formula that defines the consumption probability (0,1), which consists of X, a value between 0 and 1, and two positive and negative integer values (0,1). The idea is to combine these variables. If positive influence is high, consumption should increase if negative influence is high, consumption should decrease. X represents personal belief without any influence.
The X and the influences variables are computed differently.

I thought of a weighted sum but that doesn't give the expected output.

Thank you!

 

[pbuk]

I thought of a weighted sum but that doesn't give the expected output.

A weighted sum is the obvious first choice; what do you mean 'doesn't give the expected output'?

Did you set the weights manually - if so have you fully explored how your model responds to adjusting the weights?

If you have a sample 'expected output' have you tried fitting the weights using linear regression? Have you tried different optimisation functions (e.g. mean absolute error (MAE) as well as mean squared error (MSE))?

If this is still not working for you then this may be due to the inherent limitation of linearity of the model. To break through this you could consider using a neural net (a weighted sum is essentially a neural net with no hidden layers and a single neuron with a linear activation function in the output layer). However this is probably overkill for such a simple model with only 3 inputs.

 

[fresh_42]

Consider a portfolio of at least two stocks, take the consumption as the expectation value of returns, and the influences as the covariances.

 

[adan]

A weighted sum is the obvious first choice; what do you mean 'doesn't give the expected output'?

Did you set the weights manually - if so have you fully explored how your model responds to adjusting the weights?

If you have a sample 'expected output' have you tried fitting the weights using linear regression? Have you tried different optimisation functions (e.g. mean absolute error (MAE) as well as mean squared error (MSE))?

If this is still not working for you then this may be due to the inherent limitation of linearity of the model. To break through this you could consider using a neural net (a weighted sum is essentially a neural net with no hidden layers and a single neuron with a linear activation function in the output layer). However this is probably overkill for such a simple model with only 3 inputs.

Thank you @pbuk, for your answer!. I noticed that the weighted sum doesn't give what I expect. I don't have data but just some intuition. For example consumption = w1*X +w2 * Infpositive - w2 * infnegative.
I assume w1 should not be too small(> 0.5). I found that using the weighted sum can't enforce the positive effect. I use a negative weight w2 to achieve the negative influence.