Children's imitation of causal action sequences is influenced by statistical and pedagogical evidence

Children are ubiquitous imitators, but how do they decide which actions to imitate? One possibility is that children rationally combine multiple sources of information about which actions are necessary to cause a particular outcome. For instance, children might learn from contingencies between action sequences and outcomes across repeated demonstrations, and they might also use information about the actor’s knowledge state and pedagogical intentions. We define a Bayesian model that predicts children will decide whether to imitate part or all of an action sequence based on both the pattern of statistical evidence and the demonstrator’s pedagogical stance. To test this prediction, we conducted an experiment in which preschool children watched an experimenter repeatedly perform sequences of varying actions followed by an outcome. Children’s imitation of sequences that produced the outcome increased, in some cases resulting in production of shorter sequences of actions that the children had never seen performed in isolation. A second experiment established that children interpret the same statistical evidence differently when it comes from a knowledgeable teacher versus a naïve demonstrator. In particular, in the pedagogical case children are more likely to “overimitate” by reproducing the entire demonstrated sequence. This behavior is consistent with our model’s predictions, and suggests that children attend to both statistical and pedagogical evidence in deciding which actions to imitate, rather than obligately imitating successful action sequences.     

Segmenting dynamic human action via statistical structure

Human social, cognitive, and linguistic functioning depends on skills for rapidly processing action. Identifying distinct acts within the dynamic motion flow is one basic component of action processing; for example, skill at segmenting action is foundational to action categorization, verb learning, and comprehension of novel action sequences. Yet little is currently known about mechanisms that may subserve action segmentation. The present research documents that adults can register statistical regularities providing clues to action segmentation. This finding provides new evidence that structural knowledge gained by mechanisms such as statistical learning can play a role in action segmentation, and highlights a striking parallel between processing of action and processing in other domains, such as language.     

Learning the form of causal relationships using hierarchical bayesian models

People learn quickly when reasoning about causal relationships, making inferences from limited data and avoiding spurious inferences. Efficient learning depends on abstract knowledge, which is often domain or context specific, and much of it must be learned. While such knowledge effects are well documented, little is known about exactly how we acquire knowledge that constrains learning. This work focuses on knowledge of the functional form of causal relationships; there are many kinds of relationships that can apply between causes and their effects, and knowledge of the form such a relationship takes is important in order to quickly identify the real causes of an observed effect. We developed a hierarchical Bayesian model of the acquisition of knowledge of the functional form of causal relationships and tested it in five experimental studies, considering disjunctive and conjunctive relationships, failure rates, and cross-domain effects. The Bayesian model accurately predicted human judgments and outperformed several alternative models.     

Sticking to the Evidence? A Behavioral and Computational Case Study of Micro‐Theory Change in the Domain of Magnetism

Constructing an intuitive theory from data confronts learners with a “chicken‐and‐egg” problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing neither to begin with? We explore how children can solve this chicken‐and‐egg problem in the domain of magnetism, drawing on perspectives from computational modeling and behavioral experiments. We present 4‐ and 5‐year‐olds with two different simplified magnet‐learning tasks. Children appropriately constrain their beliefs to two hypotheses following ambiguous but informative evidence. Following a critical intervention, they learn the correct theory. In the second study, children infer the correct number of categories given no information about the possible causal laws. Children's hypotheses in these tasks are explained as rational inferences within a Bayesian computational framework.     

Structure and strength in causal induction

We present a framework for the rational analysis of elemental causal induction-learning about the existence of a relationship between a single cause and effect-based upon causal graphical models. This framework makes precise the distinction between causal structure and causal strength: the difference between asking whether a causal relationship exists and asking how strong that causal relationship might be. We show that two leading rational models of elemental causal induction, DeltaP and causal power, both estimate causal strength, and we introduce a new rational model, causal support, that assesses causal structure. Causal support predicts several key phenomena of causal induction that cannot be accounted for by other rational models, which we explore through a series of experiments. These phenomena include the complex interaction between DeltaP and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Causal support also provides a better account of a number of existing datasets than either DeltaP or causal power.     

Error probabilities for inference of causal directions

A main message from the causal modelling literature in the last several decades is that under some plausible assumptions, there can be statistically consistent procedures for inferring (features of) the causal structure of a set of random variables from observational data. But whether we can control the error probabilities with a finite sample size depends on the kind of consistency the procedures can achieve. It has been shown that in general, under the standard causal Markov and Faithfulness assumptions, the procedures can only be pointwise but not uniformly consistent without substantial background knowledge. This implies the impossibility of choosing a finite sample size to control the worst case error probabilities. In this paper, I consider the simpler task of inferring causal directions when the skeleton of the causal structure is known, and establish a similarly negative result concerning the possibility of controlling error probabilities. Although the result is negative in form, it has an interesting positive implication for causal discovery methods.     

Bayes and blickets: effects of knowledge on causal induction in children and adults

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults' judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children's judgments (Experiments 3 and 5) agreed qualitatively with this account.     

Action understanding as inverse planning

Humans are adept at inferring the mental states underlying other agents’ actions, such as goals, beliefs, desires, emotions and other thoughts. We propose a computational framework based on Bayesian inverse planning for modeling human action understanding. The framework represents an intuitive theory of intentional agents’ behavior based on the principle of rationality: the expectation that agents will plan approximately rationally to achieve their goals, given their beliefs about the world. The mental states that caused an agent’s behavior are inferred by inverting this model of rational planning using Bayesian inference, integrating the likelihood of the observed actions with the prior over mental states. This approach formalizes in precise probabilistic terms the essence of previous qualitative approaches to action understanding based on an “intentional stance” [Dennett, D. C. (1987). The intentional stance. Cambridge, MA: MIT Press] or a “teleological stance” [Gergely, G., Nádasdy, Z., Csibra, G., & Biró, S. (1995). Taking the intentional stance at 12 months of age. Cognition, 56, 165-193]. In three psychophysical experiments using animated stimuli of agents moving in simple mazes, we assess how well different inverse planning models based on different goal priors can predict human goal inferences. The results provide quantitative evidence for an approximately rational inference mechanism in human goal inference within our simplified stimulus paradigm, and for the flexible nature of goal representations that human observers can adopt. We discuss the implications of our experimental results for human action understanding in real-world contexts, and suggest how our framework might be extended to capture other kinds of mental state inferences, such as inferences about beliefs, or inferring whether an entity is an intentional agent.     

Predictive coding: an account of the mirror neuron system

Is it possible to understand the intentions of other people by simply observing their actions? Many believe that this ability is made possible by the brain’s mirror neuron system through its direct link between action and observation. However, precisely how intentions can be inferred through action observation has provoked much debate. Here we suggest that the function of the mirror system can be understood within a predictive coding framework that appeals to the statistical approach known as empirical Bayes. Within this scheme the most likely cause of an observed action can be inferred by minimizing the prediction error at all levels of the cortical hierarchy that are engaged during action observation. This account identifies a precise role for the mirror system in our ability to infer intentions from actions and provides the outline of the underlying computational mechanisms.     

Do people reason rationally about causally related events? Markov violations,weak inferences,and failures of explaining away

Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X₁ → Y → X₂, common cause structures X₁ ← Y → X₂, and common effect structures X₁ → Y ← X₂, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative “explaining away” pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations.     

Statistical inference and sensitivity to sampling in 11-month-old infants

Research on initial conceptual knowledge and research on early statistical learning mechanisms have been, for the most part, two separate enterprises. We report a study with 11-month-old infants investigating whether they are sensitive to sampling conditions and whether they can integrate intentional information in a statistical inference task. Previous studies found that infants were able to make inferences from samples to populations, and vice versa [Xu, F., & Garcia, V. (2008). Intuitive statistics by 8-month-old infants. Proceedings of the National Academy of Sciences of the United States of America, 105, 5012-5015]. We found that when employing this statistical inference mechanism, infants are sensitive to whether a sample was randomly drawn from a population or not, and they take into account intentional information (e.g., explicitly expressed preference, visual access) when computing the relationship between samples and populations. Our results suggest that domain-specific knowledge is integrated with statistical inference mechanisms early in development.     

Seeking Confirmation Is Rational for Deterministic Hypotheses

The tendency to test outcomes that are predicted by our current theory (the confirmation bias) is one of the best‐known biases of human decision making. We prove that the confirmation bias is an optimal strategy for testing hypotheses when those hypotheses are deterministic, each making a single prediction about the next event in a sequence. Our proof applies for two normative standards commonly used for evaluating hypothesis testing: maximizing expected information gain and maximizing the probability of falsifying the current hypothesis. This analysis rests on two assumptions: (a) that people predict the next event in a sequence in a way that is consistent with Bayesian inference; and (b) when testing hypotheses, people test the hypothesis to which they assign highest posterior probability. We present four behavioral experiments that support these assumptions, showing that a simple Bayesian model can capture people's predictions about numerical sequences (Experiments 1 and 2), and that we can alter the hypotheses that people choose to test by manipulating the prior probability of those hypotheses (Experiments 3 and 4).     

Are People Successful at Learning Sequences of Actions on a Perceptual Matching Task?

We report the results of an experiment in which human subjects were trained to perform a perceptual matching task. Subjects were asked to manipulate comparison objects until they matched target objects using the fewest manipulations possible. An unusual feature of the experimental task is that efficient performance requires an understanding of the hidden or latent causal structure governing the relationships between actions and perceptual outcomes. We use two benchmarks to evaluate the quality of subjects' learning. One benchmark is based on optimal performance as calculated by a dynamic programming procedure. The other is based on an adaptive computational agent that uses a reinforcement-learning method known as Q-learning to learn to perform the task. Our analyses suggest that subjects were successful learners. In particular, they learned to perform the perceptual matching task in a near-optimal manner (i.e., using a small number of manipulations) at the end of training. Subjects were able to achieve near-optimal performance because they learned, at least partially, the causal structure underlying the task. In addition, subjects' performances were broadly consistent with those of model-based reinforcement-learning agents that built and used internal models of how their actions influenced the external environment. We hypothesize that people will achieve near-optimal performances on tasks requiring sequences of action-especially sensorimotor tasks with underlying latent causal structures-when they can detect the effects of their actions on the environment, and when they can represent and reason about these effects using an internal mental model.