The Sense of Confidence during Probabilistic Learning: A Normative Account

PLoS Comput Biol. 2015 Jun 15;11(6):e1004305. doi: 10.1371/journal.pcbi.1004305. eCollection 2015 Jun.

Abstract

Learning in a stochastic environment consists of estimating a model from a limited amount of noisy data, and is therefore inherently uncertain. However, many classical models reduce the learning process to the updating of parameter estimates and neglect the fact that learning is also frequently accompanied by a variable "feeling of knowing" or confidence. The characteristics and the origin of these subjective confidence estimates thus remain largely unknown. Here we investigate whether, during learning, humans not only infer a model of their environment, but also derive an accurate sense of confidence from their inferences. In our experiment, humans estimated the transition probabilities between two visual or auditory stimuli in a changing environment, and reported their mean estimate and their confidence in this report. To formalize the link between both kinds of estimate and assess their accuracy in comparison to a normative reference, we derive the optimal inference strategy for our task. Our results indicate that subjects accurately track the likelihood that their inferences are correct. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We show that human performance matches several properties of the optimal probabilistic inference. In particular, subjective confidence is impacted by environmental uncertainty, both at the first level (uncertainty in stimulus occurrence given the inferred stochastic characteristics) and at the second level (uncertainty due to unexpected changes in these stochastic characteristics). Confidence also increases appropriately with the number of observations within stable periods. Our results support the idea that humans possess a quantitative sense of confidence in their inferences about abstract non-sensory parameters of the environment. This ability cannot be reduced to simple heuristics, it seems instead a core property of the learning process.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Adult
  • Algorithms
  • Computational Biology
  • Female
  • Humans
  • Learning / physiology*
  • Male
  • Models, Neurological*
  • Models, Statistical*
  • Task Performance and Analysis
  • Uncertainty*
  • Young Adult

Grant support

This work was supported by INSERM, CEA, Collège de France, Université Paris Sud. It received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 604102 (Human Brain Project). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.