While neural network binary classifiers are often evaluated on metrics such as Accuracy and $F_1$-Score, they are commonly trained with a cross-entropy objective. How can this training-evaluation gap be addressed? While specific techniques have been adopted to optimize certain confusion matrix based metrics, it is challenging or impossible in some cases to generalize the techniques to other metrics. Adversarial learning approaches have also been proposed to optimize networks via confusion matrix based metrics, but they tend to be much slower than common training methods. In this work, we propose a unifying approach to training neural network binary classifiers that combines a differentiable approximation of the Heaviside function with a probabilistic view of the typical confusion matrix values using soft sets. Our theoretical analysis shows the benefit of using our method to optimize for a given evaluation metric, such as $F_1$-Score, with soft sets, and our extensive experiments show the effectiveness of our approach in several domains.

We study human perception of gaze rendered by popular semi-virtual robotic heads, which use a screen to render a robot's face. It is known that when these heads are stationary, the screen may induce the Mona Lisa gaze effect, which widens the robot's apparent cone of direct gaze. But how do people perceive gaze when the head can move as well? To study this question, we conducted a laboratory experiment that investigated human perception of robot gaze when a semi-virtual platform looked in different directions. We varied the way in which the robot conveyed gaze, using several behaviors involving 2D eye and head motion. Our results suggest that the interplay between these motions can regulate how wide users perceive the robot's cone of direct gaze. Also, our findings suggest that the location of observers can affect the perception of gaze by semi-virtual robotic heads. We discuss the implications of our findings for social interaction.