  Spin qubits in quantum dots are a compelling platform for fault-tolerant
quantum computing due to the potential to fabricate dense two-dimensional
arrays with nearest neighbour couplings, a requirement to implement the surface
code. However, due to the proximity of the surface gate electrodes,
cross-coupling capacitances can be substantial, making it difficult to control
each quantum dot independently. Increasing the number of quantum dots increases
the complexity of the calibration process, which becomes impractical to do
heuristically. Inspired by recent demonstrations of industrial-grade silicon
quantum dot bilinear arrays, we develop a theoretical framework to mitigate the
effect of cross-capacitances in 2x2 arrays of quantum dots, that can be
directly extended to 2xN arrays. The method is based on extracting the
gradients in gate voltage space of different charge transitions in multiple
two-dimensional charge stability diagrams to determine the system's virtual
voltages. To automate the process, we train an ensemble of regression models to
extract the gradients from a Hough transformation of a stability diagram and
validate the algorithm on simulated and experimental data of a 2x2 quantum dot
array. Our method provides a completely automated tool to mitigate the effect
of cross capacitances, which could be used to study cross capacitance
variability across QDs in large bilinear arrays
