Constrained least squares

Modeling
1

Hi, I would like to carry out a L1-constrained least squared estimate, something like following equation:
capture-20180529-141940

I’ve tried following codes, but failed to generate HMC samples.

functions { 
} 
data { 
  int<lower=1> N;  // total number of observations 
  vector[N] Y;  // response variable 
  int<lower=1> K;  // number of population-level effects 
  matrix[N,K] X;  // population-level design matrix 
} 
transformed data { 
} 
parameters { 
  vector[K] w_signed;  // population-level effects 
  
} 
transformed parameters { 
  vector[K] w;
  real<lower=0, upper=1> w_limit;
  for(k in 1:K) {
    w[k] = fabs(w_signed[k]);
  }
  w_limit = sum(w);
} 
model { 
  
  vector[N] squared_error;
  
  for (n in 1:N){
    squared_error[n] = (Y[n] - X[n] * w)^2 ; 
  }
    
  target += -sum(squared_error); 
    
} 
  
generated quantities {
}

I’ve got following error message
“Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: validate transformed params: w_limit is 15.1066, but must be less than or equal to 1 (in ‘model35f645629433b_synth_ConstrainedLeastSquare_woV’ at line 18)”

Any suggestions?

2

Posting the error message

3

Sure, here it is,

Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: validate transformed params: w_limit is 15.1066, but must be less than or equal to 1 (in ‘model35f645629433b_synth_ConstrainedLeastSquare_woV’ at line 18)

4

The message is saying that the constraints you declared in the transformed parameters block are being violated. Taking a very quick glance at the code in transformed parameters, it looks like you have a sum that is not constrained to be less than 1, but you are assigning that value to a variable with a declared upper bound of 1.