Hi everyone, I am wondering whether it is possible to use a custom distance metric with a gaussian process in Stan. I have a classification problem, and the idea is that items which are close together should be assigned to the same class. However, the way of calculating the distance between two ite…

[image] Matias_Guzman_Naranjo: My worry was that there would be something fundamentally wrong about passing precomputed distances, but I guess not? You can use pre-computed distance matrix (it’s just not supported by cov_exp_quad)

Will the posterior parameters by in any way physically meaningful in your model? I.e. will they correspond to some theoretic generative assumption? If not, there are many very good clustering algorithms that work directly off of an arbitrary distance matrix (I like affinity propagation for example). …

Thank you for your answer emiruz. Will the posterior parameters by in any way physically meaningful in your model? I.e. will they correspond to some theoretic generative assumption? I do not know exactly what the generative model should be, other than ‘similar items should belong to the same cla…

I guess I’m saying if what you want is a clustering algorithm and you don’t care for the values of the model parameters (rho,alpha,a) and you just want item classifications, then you’re better off using a state of the art clustering algorithm many of which work directly off of an arbitrary distance …

[image] Matias_Guzman_Naranjo: I am wondering whether it is possible to use a custom distance metric with a gaussian process in Stan. Yep. Here’s code for an ARD exponential quadratic from the user’s guide: functions { matrix L_cov_exp_quad_ARD(vector[] x, real alpha, vector …

Thanks for your answer! I am using a variation on Levenshtein’s distance, so I’m not sure this is implementable in Stan, or that it would sample in reasonable time. This won’t work, distance is defined implicitly in C++ for each covariance function. I don’t quite understand why I can’t pass the x…

[image] Matias_Guzman_Naranjo: I don’t quite understand why I can’t pass the The built in covariance functions compute the distance implicitly. It doesn’t really make sense to take a pre-computed distance, and then input it into a function that then takes the distance again, right? You can d…

Right. I guess a different way of asking the question is, if in your code above I replace sq_alpha * exp(-0.5 * dot_self((x[i] - x[j]) ./ rho)); with K[i,j] = sq_alpha * exp(-0.5 * D[i, j] ./ rho); where D is a matrix of precomputed distances, would the result be a reasonable thing? is this nons…

[image] Matias_Guzman_Naranjo: I am wondering whether it is possible to use a custom distance metric with a gaussian process in Stan. First it’s important to realize that not all combinations of a metric and a covariance function produce valid positive definite covariance matrix. I’m not fami…

Thank you Aki. The result is a definite covariance matrix, and the model does sample. My worry was that there would be something fundamentally wrong about passing precomputed distances, but I guess not?

Custom distance metric with gaussian process

Modeling

avehtari July 2, 2020, 12:45pm 11

You can use pre-computed distance matrix (it’s just not supported by cov_exp_quad)

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Custom distance metric with gaussian process

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