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Gibbs Sampling with People

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 Added by Peter Harrison
 Publication date 2020
and research's language is English




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A core problem in cognitive science and machine learning is to understand how humans derive semantic representations from perceptual objects, such as color from an apple, pleasantness from a musical chord, or seriousness from a face. Markov Chain Monte Carlo with People (MCMCP) is a prominent method for studying such representations, in which participants are presented with binary choice trials constructed such that the decisions follow a Markov Chain Monte Carlo acceptance rule. However, while MCMCP has strong asymptotic properties, its binary choice paradigm generates relatively little information per trial, and its local proposal function makes it slow to explore the parameter space and find the modes of the distribution. Here we therefore generalize MCMCP to a continuous-sampling paradigm, where in each iteration the participant uses a slider to continuously manipulate a single stimulus dimension to optimize a given criterion such as pleasantness. We formulate both methods from a utility-theory perspective, and show that the new method can be interpreted as Gibbs Sampling with People (GSP). Further, we introduce an aggregation parameter to the transition step, and show that this parameter can be manipulated to flexibly shift between Gibbs sampling and deterministic optimization. In an initial study, we show GSP clearly outperforming MCMCP; we then show that GSP provides novel and interpretable results in three other domains, namely musical chords, vocal emotions, and faces. We validate these results through large-scale perceptual rating experiments. The final experiments use GSP to navigate the latent space of a state-of-the-art image synthesis network (StyleGAN), a promising approach for applying GSP to high-dimensional perceptual spaces. We conclude by discussing future cognitive applications and ethical implications.



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In their recent paper titled Large Associative Memory Problem in Neurobiology and Machine Learning [arXiv:2008.06996] the authors gave a biologically plausible microscopic theory from which one can recover many dense associative memory models discussed in the literature. We show that the layers of the recent MLP-mixer [arXiv:2105.01601] as well as the essentially equivalent model in [arXiv:2105.02723] are amongst them.

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