Propose an architectural change to address the challenge of missing inputs in your classification task. Explain how this approach can be applied to improve the robustness and accuracy of your system.

Learn a probability distribution over all relevant variables and use marginalization to solve the classification task. This approach allows the model to handle cases with missing inputs by learning a set of functions, each corresponding to classifying x with a different subset of its inputs missing. At runtime, the model can efficiently select the correct function based on the available input data.