Estimating from No Data: Deriving a Continuous Score from Categories

A method is presented for deriving a continuous numerical score from categorical training data, such as patient outcomes. A standard classifier approach fails, so a low-capacity linear model is used as a bottleneck to generate the score. This score is then fed into a "category approximator head" which uses a dense layer and softmax to learn the thresholds between the original categories. The process involves extracting these thresholds from the trained model's weights and biases to create a meaningful, ordered scoring system, allowing for fine-grained predictions when only coarse labels are available.