Quantum Inference on Bayesian Networks

Performing exact inference on Bayesian networks is known to be #P-hard. Typically approximate inference techniques are used instead to sample from the distribution on query variables given the values $e$ of evidence variables. Classically, a single unbiased sample is obtained from a Bayesian network on $n$ variables with at most $m$ parents per node in time $\mathcal{O}(nmP(e)^{-1})$, depending critically on $P(e)$, the probability the evidence might occur in the first place. By implementing a quantum version of rejection sampling, we obtain a square-root speedup, taking $\mathcal{O}(n2^mP(e)^{-\frac12})$ time per sample. We exploit the Bayesian network's graph structure to efficiently construct a quantum state, a q-sample, representing the intended classical distribution, and also to efficiently apply amplitude amplification, the source of our speedup. Thus, our speedup is notable as it is unrelativized -- we count primitive operations and require no blackbox oracle queries.Comment: 8 pages, 3 figures. Submitted to PR

An evaluation of the relationship between Gray’s revised RST and Eysenck’s PEN: distinguishing BIS and FFFS in Carver and White’s BIS/BAS scales

Recent revisions of Gray's Reinforcement Sensitivity Theory (RST) have important implications for self-report measures of approach and avoidance behaviours and how Gray's model relates to other personality models. In this paper, we examine the revised RST by comparing Carver and White's (1994) original one-factor solution of the BIS scale with two alternative two-factor solutions separating BIS-Anxiety and FFFS-Fear. We also examine the relationships between Eysenck's PEN and revised RST factors. Two hundred and twelve participants completed Carver and White's BIS/BAS scales and Eysenck's Personality Questionnaire-Revised. Confirmatory factor analyses of the original BIS scale showed that the hypothesized two-factor model of BIS-Anxiety and FFFS-Fear was the best fit to these data. Associations between the revised RST and Eysenck's PEN were examined using path analysis. In line with theoretical predictions, Psychoticism was related to revised BIS-Anxiety and BAS, Neuroticism to revised BIS-Anxiety and FFFS- Fear, and Extraversion to BAS and FFFS-Fear. Distinctions between BAS subscales and their associations to BIS, N and P were made in terms of past, present and future focus. Possible explanations for mixed findings in the literature and implications for future research are discussed

Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equation governing the system dynamics is obtained. The agents are considered to interact with one another implicitly via the reward of one agent depending on the choice of the other agents. The pairwise interaction model is adopted to describe this effect. As a specific example of systems with non-transitive interactions, a two agent and three agent systems of the rock-paper-scissors type are analyzed in detail, including the stability analysis and numerical simulation. Scale-free memory is demonstrated to cause complex dynamics of the systems at hand. In particular, it is shown that there can be simultaneously two modes of the system instability undergoing subcritical and supercritical bifurcation, with the latter one exhibiting anomalous oscillations with the amplitude and period growing with time. Besides, the instability onset via this supercritical mode may be regarded as "altruism self-organization". For the three agent system the instability dynamics is found to be rather irregular and can be composed of alternate fragments of oscillations different in their properties.Comment: 17 pages, 7 figur