Edge-device co-inference, which concerns the cooperation between edge devices and an edge server for completing inference tasks over wireless networks, has been a promising technique for enabling various kinds of intelligent services at the network edge, e.g., auto-driving. In this paradigm, the concerned design objective of the network shifts from the traditional communication throughput to the effective and efficient execution of the inference task underpinned by the network, measured by, e.g., the inference accuracy and latency. In this paper, a task-oriented over-the-air computation scheme is proposed for a multidevice artificial intelligence system. Particularly, a novel tractable inference accuracy metric is proposed for classification tasks, which is called minimum pair-wise discriminant gain. Unlike prior work measuring the average of all class pairs in feature space, it measures the minimum distance of all class pairs. By maximizing the minimum pair-wise discriminant gain instead of its average counterpart, any pair of classes can be better separated in the feature space, and thus leading to a balanced and improved inference accuracy for all classes. Besides, this paper jointly optimizes the minimum discriminant gain of all feature elements instead of separately maximizing that of each element in the existing designs. As a result, the transmit power can be adaptively allocated to the feature elements according to their different contributions to the inference accuracy, opening an extra degree of freedom to improve inference performance. Extensive experiments are conducted using a concrete use case of human motion recognition to verify the superiority of the proposed design over the benchmarking scheme.