Deep Compressed Sensing for Learning Submodular Functions

The AI community has been paying attention to submodular functions due to their various applications (e.g., target search and 3D mapping). Learning submodular functions is a challenge since the number of a function's outcomes of N sets is <mml:semantics>2N</mml:semantics>. The state-of-the-art approach is based on compressed sensing techniques, which are to learn submodular functions in the Fourier domain and then recover the submodular functions in the spatial domain. However, the number of Fourier bases is relevant to the number of sets' sensing overlapping. To overcome this issue, this research proposed a submodular deep compressed sensing (SDCS) approach to learning submodular functions. The algorithm consists of learning autoencoder networks and Fourier coefficients. The learned networks can be applied to predict <mml:semantics>2N</mml:semantics> values of submodular functions. Experiments conducted with this approach demonstrate that the algorithm is more efficient than the benchmark approach.