We address the design of inference-oriented communication systems where multiple transmitters send partial inference values through noisy communication channels, and the receiver aggregates these channel outputs to obtain a reliable final inference. Since large data items are replaced by compact inference values, these systems lead to significant savings of communication resources. In particular, we present a principled framework to optimize communication-resource allocation for distributed boosting classifiers. Boosting classification algorithms make a final decision via a weighted vote from the outputs of multiple base classifiers. Since these base classifiers transmit their partial inference values over noisy channels, communication errors would degrade the final classification accuracy. We formulate communication resource allocation problems to maximize the final classification accuracy by taking into account the importance of base classifiers and the resource budget. To solve these problems rigorously, we formulate convex optimization problems to optimize: 1) transmit-power allocations and 2) transmit-rate allocations. This framework departs from classical communication-systems optimizations in seeking to maximize the classification accuracy rather than the reliability of the individual communicated bits. Results from numerical experiments demonstrate the benefits of our approach.