Bayesian principles of learning : are we scientists from the cradle ?

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Contemporary cognitive science has refuted William James's (1890) view that the baby " assailed by eyes, ears, nose, skin and bowels, experiences all as a vast and noisy confusion ". This refutation took place in two stages.

Firstly, since the 1970s, hundreds of experiments have highlighted babies' multiple skills. From the very first year of life, they possess acore of fundamental knowledge, such as the concepts of object (Spelke, 1983), number (Mehler & Bever, 1967; Wynn, 1992) and space (Landau et al., 1981), as well as a range of relevant phonemes and rules that facilitate language learning (Chomsky, Gleitman, Mehler).

On this basis, the metaphor of the baby as scientist or detective developed. According to Gopnik, the child's observations are integrated into " intuitive theories of the physical, biological and psychological world. These theories, like scientific theories, are complex, coherent and abstract representations of the causal structure of the external world " (Gopnik & Schulz, 2004). Babies develop mental models of the world and evaluate their plausibility in relation to the observations they make. They would therefore have early skills for manipulating probabilities, evaluating numerous models in parallel, selecting relevant variables, eliminating variables of no interest, and spotting ambiguities or multiple interpretations.

These strong hypotheses gave rise to a new experimental movement aimed at testing the presence of probability intuition and inference skills in very young children. This research has been crowned with success. For example, as early as eight months of age, a baby is able to anticipate the approximate outcome of a random draw from an urn. Even more surprisingly, it is also able to infer, in the opposite direction, the likely contents of an urn after a few draws, which is the very foundation of Bayesian inference. At sixteen months, Laura Schulz's experiments show that he is already making a whole chain of hierarchical inferences from a very small set of observations. For example, if he fails to operate an object, he deduces from the precise circumstances of his failure whether it is his action or the object itself that is at fault (Gweon & Schulz, 2011). When a draw deviates from random sampling, it attributes a specific intention to the person drawing from the urn (Gweon, Tenenbaum, & Schulz, 2010).

From the second year of life, then, children seem to derive mental models from their observations, taking into account the intentions of those acting around them, and using Bayesian inferences to trace the hidden causes of their actions. The metaphor of a " detective " or a " cradle scientist " does not seem inappropriate. However, there's nothing mysterious about this shrewdness, as it can be modeled mathematically. Various algorithms can be used to approximate the rules of Bayesian inference, and could be used by the child (T. D. Ullman, Goodman, & Tenenbaum, 2012).

The Bayesian approach reconciles nativism and constructivism. Indeed, on the one hand, it requires us to postulate a large number of innate fundamental mechanisms (sense of probability, probabilistic reasoning with distributions, vocabulary of concepts of number, space, etc.). On the other hand, it demonstrates that, on this basis, by relying on a generic Bayesian inference mechanism, extremely abstract principles can be inferred from interactions with the outside world. Thus, even the notion of causality need not be postulated from the outset - the baby might discover that this hypothesis accounts, better than others, for what it observes (Goodman, Ullman, & Tenenbaum, 2011).