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In this work, we test the robustness of the constancy of the Supernovaabsolute magnitude $M_B$ using Non-parametric Reconstruction Techniques (NRT).We isolate the luminosity distance parameter $d_L(z)$ from the Baryon AcousticOscillations (BAO) data set and cancel the expansion part from the observeddistance modulus $\mu(z)$. Consequently, the degeneracy between the absolutemagnitude and the Hubble constant $H_0$, is replaced by a degeneracy between$M_B$ and the sound horizon at drag epoch $r_d$. When imposing the $r_d$ value,this yields the $M_B(z) = M_B + \delta M_B(z)$ value from NRT. We perform therespective reconstructions using the model independent Artificial NeuralNetwork (ANN) technique and Gaussian processes (GP) regression. For the ANN weinfer $M_B = -19.22\pm0.20$, and for the GP we get $M_B = -19.25\pm0.39$ as amean for the full distribution when using the sound horizon from late timemeasurements. These estimations provide a $1\,\sigma$ possibility of a nuisanceparameter presence $\delta M_B(z)$ at higher redshifts. We also testeddifferent known nuisance models with the Markov Chain Monte Carlo (MCMC)technique which showed a strong preference for the constant model, but it wasnot possible not single out a best fit nuisance model.

On the Robustness of the Constancy of the Supernova Absolute Magnitude: Non-parametric Reconstruction \& Bayesian approaches