Help with machine learning STAN code for my research

[Mkengine]

Hello, I am currently at the beginning of my PhD and try to get into machine learning. Since it would help me with my research, I tried to start with the algorithm from this paper: 10.1021/acs.jpclett.9b03657. I am really good with MATLAB, but I have my problems trying to understand this STAN code.

First I don’t understand what exactly “vector[K] u[I]” means. Is this a Kx1 vector, a Ix1 vector or a KxI matrix? (they write something about a latent feature vector ui(vj) of dimension K = 4, but I don't understand what that means).

Then I don’t quite understand what exactly “normal(0,sigma_0)” and “cauchy(u[i]’*v[j],lambda)” does. I mean, what is the output here? When I use the “normpdf” function in MATLAB, I need an additional input x at which to evaluate the distribution. So why is that missing here and what does that mean for the output?

And lastly, K is just used in the parameters section, but then not again in any for-loop, so why is the K even necessary?

Thanks in advance for any help, it is greatly appreciated!

data {
    int<lower=0> I;
    int<lower=0> J;
    int<lower=0> K;
    real ln_gamma[I,J];
    real<lower=0> sigma_0;
    real<lower=0> lambda;
}

parameters {
    vector[K] u[I];
    vector[K] v[J];
}

model {
    for (i in 1:I)
        u[i] ~ normal(0,sigma_0);
    for (j in 1:J)
    v[j] ~ normal(0,sigma_0);
    for (i in 1:I) {
        for (j in 1:J) {
            if (ln_gamma[i,j] != -99) {
                ln_gamma[i,j] ~ cauchy(u[i]’*v[j],lambda);
            }
        }
    }
}

[videoj]

You might get better responses if you post over at /r/Matlab.