@techreport{sou-sto-15-roblsq-bay-tr,
   number = {IC-15-06},
   author = {Gilc{\'e}lia Regi{\^a}ne de Souza and Jorge Stolfi},
   title = {Robust Least Squares by Iterative {Bayesian} Data Adjustment},
   month = sep,
   year = 2015,
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 9 pages},
   abstract = {We describe an efficient algorithm for robust multivariate weighted least squares approximation in the presence of outliers. The algorithm iteratively constructs a self-consistent probabilistic interpretation of the data; specifically, the mean and variance of the two populations (inliers and outliers), the least squares fitted approximation, and the probability that each data point is an inlier. An original feature of this algorithm is that, at each iteration, it adjusts the given sampled values according to the estimated probabilities, before re-computing the least squares approximation. This approach is more efficient than the more obvious alternative of including the probabilities in the matrix of the least squares system. The convergence of the method is demonstrated with empirical tests.},
  altkey = {TR-IC-15-06}
}