  We perform a parameter fit in the Standard Model Effective Field Theory
(SMEFT) with an emphasis on using regularized linear regression to tackle the
issue of the large number of parameters in the SMEFT. In regularized linear
regression a positive definite function of the parameters of interest is added
to the usual cost function. A cross-validation is performed to try to determine
the optimal value of the regularization parameter to use, but it selects the
Standard Model (SM) as the best model to explain the measurements. Nevertheless
as proof of principle of this technique we apply it to fitting Higgs boson
signal strengths in SMEFT, including the latest Run-2 results. Results are
presented in terms of the eigensystem of the covariance matrix of the least
squares estimators as it has a degree model-independent to it. We find several
results in this initial work: the SMEFT predicts the total width of the Higgs
boson to be consistent with the SM prediction; the ATLAS and CMS experiments at
the LHC are currently sensitive to non-resonant double Higgs boson production.
Constraints are derived on the viable parameter space for electroweak
baryogenesis in the SMEFT, reinforcing the notion that a first order phase
transition requires fairly low scale Beyond the SM physics. Finally, we study
which future experimental measurements would give the most improvement on the
global constraints on the Higgs sector of the SMEFT.
