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In the current work, we have implemented an extension of the standardGaussian Process formalism, namely the Multi-Task Gaussian Process with theability to perform a joint learning of several cosmological datasimultaneously. We have utilised the "low-redshift" expansion rate data fromSupernovae Type-Ia (SN), Baryon Acoustic Oscillations (BAO) and CosmicChronometers (CC) data in a joint analysis. We have tested several possiblemodels of covariance functions and find very consistent estimates forcosmologically relevant parameters. In the current formalism, we also findprovisions for heuristic arguments which allow us to select the best-suitedkernel for the reconstruction of expansion rate data. We also utilised ourmethod to account for systematics in CC data and find an estimate of $H_0 =68.52^{+0.94 + 2.51 (sys)}_{-0.94} $ $\textrm{km/s Mpc}^{-1}$ and acorresponding $r_d = 145.61^{+2.82}_{ - 2.82 - 4.3 (sys)} $ Mpc as our primaryresult. Subsequently, we find constraints on the present deceleration parameter$q_0 = -0.52 \pm 0.06$ and the transition redshift $z_T =0.64^{+0.12}_{-0.09}$. All the estimated cosmological parameters are found tobe in good agreement with the standard $\Lambda$CDM scenario. Including thelocal model-independent $H_0$ estimate to the analysis we find $H_0 = 71.40^{ +0.30 + 1.65 (sys)}_{- 0.30 } $ $\textrm{km/s Mpc}^{-1}$ and the corresponding$r_d = 141.29^{ + 1.31 }_{-1.31-2.63 (sys)}$ Mpc. Also, the constraints on $r_dH_0$ remain consistent throughout our analysis and also with themodel-dependent CMB estimate. Using the $\mathcal{O}m(z)$ diagnostic, we findthat the concordance model is very consistent within the redshift range $z\lesssim 2$ and mildly discrepant for $z \gtrsim 2$.

An improved model-independent assessment of the late-time cosmic expansion