Learning acceptable windows of contingency

By learning a range of possible times over which the effect of an action can take place, a robot can reason more effectively about causal and contingent relationships in the world. However, learning these time windows in a noisy environment where random events interfere can pose a challenge. We present an algorithm for learning the interval [t1min , t1max ] of possible times during which a response to an action can take place, and implement the model on a physical robot for the domains of visual self-recognition and auditory social-partner recognition. The environment model that we use to justify our error bounds assumes that natural environments generate Poisson distributions of random events at all scales. From this assumption, we derive a lineartime algorithm, which we call Poisson threshold learning, for finding a threshold T that provides an arbitrarily small rate of background events λ(T ) if such a threshold exists for the specified error rate. We can then use this rate to calculate an expected number of false positives in our sample data and discard them. We implement the principles of our method using a motion detection module as our input stream in the visual domain, and sampled audio energy in the auditory domain. In this way, we find time windows for self-generated motion, self-generated audio, and verbal social responses. We also present data on the distributions of these events, showing that while our self-generated action had a normal distribution, the social events were better modeled by a Poisson process. Finally, we present several applications for which such simple classifiers could potentially prove useful, such as mirror selfrecognition and learning the meanings of the words “I” and “you.”