Hi, I wonder if someone could give me some guidance on this problem please. I'm not a mathematician and I'm not even sure what the title of this problem should be - curve fitting, regression, function minimization?
It started with something fairly simple, least squares fitting with 3 variables and 6 or more equations. I know how to cast that problem in matrix form and get the answer, but now I need to do something slightly more difficult. If I call the variables X, Y and Z, it turns out that X is much more important than the other two variables, so I want solution where the variance in X is smaller than the other variances. How do I do that? In my head I'm picturing the problem geometrically. In the standard least squares approach I see the cost/loss function being spherical i.e. the same in all directions. What I need is a cost function that is more like an ellipse, but I don't know how to do that. I suppose the least squares algorithm doesn't really implement a cost function as such - effectively there is a cost function, but it is an innate feature of the algorithm and so can't be modified. Perhaps I need a whole new approach? I hope that makes some sense to someone!
Any advice appreciated, many thanks
Nick
It started with something fairly simple, least squares fitting with 3 variables and 6 or more equations. I know how to cast that problem in matrix form and get the answer, but now I need to do something slightly more difficult. If I call the variables X, Y and Z, it turns out that X is much more important than the other two variables, so I want solution where the variance in X is smaller than the other variances. How do I do that? In my head I'm picturing the problem geometrically. In the standard least squares approach I see the cost/loss function being spherical i.e. the same in all directions. What I need is a cost function that is more like an ellipse, but I don't know how to do that. I suppose the least squares algorithm doesn't really implement a cost function as such - effectively there is a cost function, but it is an innate feature of the algorithm and so can't be modified. Perhaps I need a whole new approach? I hope that makes some sense to someone!
Any advice appreciated, many thanks
Nick
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