  This study is devoted to the inference problem of extracting the nuclear
matter properties directly from a set of mass-radius observations. We employ
Bayesian neural networks (BNNs), which is a probabilistic model capable of
estimating the uncertainties associated with its predictions. To simulate
different noise levels on the $M(R)$ observations, we create three different
sets of mock data. Our results show BNNs as an accurate and reliable tool for
predicting the nuclear matter properties whenever the true values are not
completely outside the training dataset statistics, i.e., if the model is not
heavily dependent on its extrapolating capacities. Using real mass-radius
pulsar data, the model predicted, for instance, $L_{\text{sym}}=39.80\pm17.52 $
MeV and $K_{\text{sym}}=-101.67\pm62.86 $ MeV ($2\sigma$ interval). Our study
provides a valuable inference framework when new NS data becomes available.
