  The spectral conductivity, i.e., the electrical conductivity as a function of
the Fermi energy, is a cornerstone in determining the thermoelectric transport
properties of electrons. However, the spectral conductivity depends on
sample-specific properties such as carrier concentrations, vacancies, charge
impurities, chemical compositions, and material microstructures, making it
difficult to relate the experimental result with the theoretical prediction
directly. Here, we propose a data-driven approach based on machine learning to
reconstruct the spectral conductivity and chemical potential from the
thermoelectric transport data. Using this machine learning method, we first
demonstrate that the spectral conductivity and temperature-dependent chemical
potentials can be recovered within a simple toy model. In a second step, we
apply our method to experimental data in doped one-dimensional telluride
Ta$_4$SiTe$_4$~[T. Inohara, \textit{et al.}, Appl. Phys. Lett. \textbf{110},
183901 (2017)] to reconstruct the spectral conductivity and chemical potential
for each sample. Furthermore, the thermal conductivity of electrons and the
maximal figure of merit $ZT$ are estimated from the reconstructed spectral
conductivity, which provides accurate estimates beyond the Wiedemann-Franz law.
Our study clarifies the connection between the thermoelectric transport
properties and the low-energy electronic states of real materials, and
establishes a promising route to incorporate experimental data into traditional
theory-driven workflows.
