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.     

The origins of probabilistic inference in human infants

Reasoning under uncertainty is the bread and butter of everyday life. Many areas of psychology, from cognitive, developmental, social, to clinical, are interested in how individuals make inferences and decisions with incomplete information. The ability to reason under uncertainty necessarily involves probability computations, be they exact calculations or estimations. What are the developmental origins of probabilistic reasoning? Recent work has begun to examine whether infants and toddlers can compute probabilities; however, previous experiments have confounded quantity and probability—in most cases young human learners could have relied on simple comparisons of absolute quantities, as opposed to proportions, to succeed in these tasks. We present four experiments providing evidence that infants younger than 12 months show sensitivity to probabilities based on proportions. Furthermore, infants use this sensitivity to make predictions and fulfill their own desires, providing the first demonstration that even preverbal learners use probabilistic information to navigate the world. These results provide strong evidence for a rich quantitative and statistical reasoning system in infants.     

Object individuation and object identity in infancy: the role of spatiotemporal information, object property information, and language.

Recent work on object individuation and object identity in infancy indicates that at least three sources of information may be used for object individuation and object identity: spatiotemporal information, object property information, and object kind information. Several experiments have shown that a major developmental change occurs between 10 and 12 months of age (Xu & Carey, 1996; Xu, Carey & Welch, in press; Van de Walle, Prevor & Carey, under review; Xu, Carey & Quint, in preparation): Infants at 10 months and younger readily use spatiotemporal information in object individuation and object identity tasks, but not until about 12 months of age are infants able to use object property or object kind information to do so. This paper proposes a two-part conjecture about the mechanism underlying this change. The first part borrows ideas from object-based attention and the distinction between "what" and "where" information in visual processing. The hypothesis is that (1) young infants encode object motion and location information separately from object property information; and (2) toward the end of the first year, infants integrate these two sources of information. The second part of the conjecture posits an important role for language. Infants may take distinct labels as referring to distinct kinds of objects from the onset of word learning, and infants use this information in solving the problem of object individuation and object identity. Evidence from human adults, infants, and non-human primates is reviewed to provide support for the conjecture.     

Perception Versus Knowledge of Cause and Effect in Children: When Seeing Is Believing

Recent research has shown that even infants have perceptual sensitivity to the causal structure of the world, and it is often claimed that causal knowledge supports many of preschoolers' impressive cognitive achievements. That older children nevertheless can encounter difficulties in causal-reasoning tasks is typically attributed to lack of domain knowledge. A different explanation, however, is that causal structure may appear at more than one level, in perception, as well as in underlying knowledge. Children may make some reasoning errors because they have difficulty coordinating these levels. This article reviews relevant evidence on physical causality: Even infants in their first year perceive the causal structure of simple collision events. This perceptual skill could support rapid causal learning without prior knowledge and thus helps us understand children's precocity preschoolers already reason with the assumption that causes and effects are linked by underlying physical mechanisms. However, what may promote early development may later become a hindrance: When perception and mechanism point to different causes, children may not realize that mechanism is superordinate. Although the components of competent causal reasoning are available early in development, much experience may be required before children learn how to integrate them.     

Intuitive probabilistic inference in capuchin monkeys

The ability to reason about probabilities has ecological relevance for many species. Recent research has shown that both preverbal infants and non-human great apes can make predictions about single-item samples randomly drawn from populations by reasoning about proportions. To further explore the evolutionary origins of this ability, we conducted the first investigation of probabilistic inference in a monkey species (capuchins; Sapajus spp.). Across four experiments, capuchins (N = 19) were presented with two populations of food items that differed in their relative distribution of preferred and non-preferred items, such that one population was more likely to yield a preferred item. In each trial, capuchins had to select between hidden single-item samples randomly drawn from each population. In Experiment 1 each population was homogeneous so reasoning about proportions was not required; Experiments 2–3 replicated previous probabilistic reasoning research with infants and apes; and Experiment 4 was a novel condition untested in other species, providing an important extension to previous work. Results revealed that at least some capuchins were able to make probabilistic inferences via reasoning about proportions as opposed to simpler quantity heuristics. Performance was relatively poor in Experiment 4, so the possibility remains that capuchins may use quantity-based heuristics in some situations, though further work is required to confirm this. Interestingly, performance was not at ceiling in Experiment 1, which did not involve reasoning about proportions, but did involve sampling. This suggests that the sampling task posed demands in addition to reasoning about proportions, possibly related to inhibitory control, working memory, and/or knowledge of object permanence.     

Universal Grammar, statistics or both?

Recent demonstrations of statistical learning in infants have reinvigorated the innateness versus learning debate in language acquisition. This article addresses these issues from both computational and developmental perspectives. First, I argue that statistical learning using transitional probabilities cannot reliably segment words when scaled to a realistic setting (e.g. child-directed English). To be successful, it must be constrained by knowledge of phonological structure. Then, turning to the bona fide theory of innateness--the Principles and Parameters framework--I argue that a full explanation of children's grammar development must abandon the domain-specific learning model of triggering, in favor of probabilistic learning mechanisms that might be domain-general but nevertheless operate in the domain-specific space of syntactic parameters.     

Everyday conditional reasoning: A working memory—dependent tradeoff between counterexample and likelihood use

Considerable evidence has revealed that working memory capacity is an important determinant of conditional reasoning performance. There are two accounts describing the conditional inference process, the probabilistic and the mental models accounts. According to the mental models account, reasoners retrieve and integrate counterexample information to attain a conclusion. According to the probabilistic account, reasoners base their judgments on probabilistic information. It can be assumed that reasoning according to the mental models process would require more working memory resources than would solving the inference on the basis of probabilistic information. By means of a verbal report study, we showed that participants with low working memory capacity more often use probabilistic information, whereas participants with higher working memory capacity are more likely to use counterexample information. Working memory capacity thus not only relates to reasoning performance, it also determines which process reasoners will engage in.     

More evidence for a dual-process model of conditional reasoning

Many studies have shown that the deductive inferences that people make have global properties that reflect the statistical information implicit in the premises. This suggests that such reasoning can be explained by a single, underlying probabilistic model. In contrast, the dual process model of conditional reasoning (Verschueren, Schaeken, & d'Ydewalle, 2005b) proposes that people can use either a logical, counterexample-based strategy or a probabilistic one. In two studies, we presented reasoners with sequences of affirmation-of-the-consequent inferences that differed with respect to the statistical properties of the premises, either explicitly or implicitly. As predicted by the dual-process model, an analysis of individual response patterns showed the presence of two distinct strategies, with use of the counterexample strategy being associated with higher levels of abstract-reasoning competence. Use of the counterexample strategy was facilitated by the explicit presentation of counterexample information. In a further study, we then examined explicitly probabilistic inferences. This study showed that although most reasoners made statistically appropriate inferences, the ability to make more-accurate inferences was associated with higher levels of abstract reasoning competence. These results show that deductive inferential reasoning cannot be explained by a single, unitary process and that any analysis of reasoning must consider individual differences in strategy use.     

Apes are intuitive statisticians

Inductive learning and reasoning, as we use it both in everyday life and in science, is characterized by flexible inferences based on statistical information: inferences from populations to samples and vice versa. Many forms of such statistical reasoning have been found to develop late in human ontogeny, depending on formal education and language, and to be fragile even in adults. New revolutionary research, however, suggests that even preverbal human infants make use of intuitive statistics. Here, we conducted the first investigation of such intuitive statistical reasoning with non-human primates. In a series of 7 experiments, Bonobos, Chimpanzees, Gorillas and Orangutans drew flexible statistical inferences from populations to samples. These inferences, furthermore, were truly based on statistical information regarding the relative frequency distributions in a population, and not on absolute frequencies. Intuitive statistics in its most basic form is thus an evolutionarily more ancient rather than a uniquely human capacity.     

A Logic For Inductive Probabilistic Reasoning

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone.     

Infants' ability to use object kind information for object individuation.

The present studies investigate infants reliance on object kind information in solving the problem of object individuation. Two experiments explored whether adults, 10- and 12-month-old infants could use their knowledge of ducks and cars to individuate an ambiguous array consisting of a toy duck perched on a toy car into two objects. A third experiment investigated whether 10-month-old infants could use their knowledge of cups and shoes to individuate an array consisting of a cup perched on a shoe into two objects. Ten-month-old infants failed to use object kind information alone to resolve the ambiguity with both pairs of objects. In contrast, infants this age succeeded in using spatiotemporal information to segment the array into two objects, i.e. they succeeded if shown that the duck moved independently relative to the car, or the cup relative to the shoe. Twelve-month-old infants, as well as adults, succeeded at object individuation on the basis of object kind information alone. These findings shed light on the developmental course of object individuation and provide converging evidence for the Object-first Hypothesis [Xu, F., Carey, S., 1996; Xu, F., 1997b]. Early on, infants may represent only one concept that provides criteria for individuation, namely physical object; kind concepts such as duck, car, cup, and shoe may be acquired later in the first year of life.     

统计认知理论及应用研究

长期以来大家认为人类认知尽管可以看成是非确定的推理计算过程,但它的知识表达、模型结构、及计算方法和概率统计理论在本质上是不同的,因此认知科学和概率统计方法存在巨大的鸿沟,过去两者基本上独立发展。近年来随着Bayesian概率统计模型研究的一系列突破性工作和认知过程本质的不断被发现和挖掘,两者的相关性和互补性逐渐突显出来。许多研究者认为认知是近似遵循概率统计推理原则的,一些研究工作显示两者的结合有可能对人工智能发展产生深远的影响。本文对当前统计认知理论及应用研究的现状进行系统的梳理,并结合自身的研究对它今后的发展提出自己的看法。     

Learning about Probability from Text and Tables: Do Color Coding and Labeling through an Interactive‐user Interface Help?

Learning from visual representations is enhanced when learners appropriately integrate corresponding visual and verbal information. This study examined the effects of two methods of promoting integration, color coding and labeling, on learning about probabilistic reasoning from a table and text. Undergraduate students (N = 98) were randomly assigned to learn about probabilistic reasoning from one of 4 computer‐based lessons generated from a 2 (color coding/no color coding) by 2 (labeling/no labeling) between‐subjects design. Learners added the labels or color coding at their own pace by clicking buttons in a computer‐based lesson. Participants' eye movements were recorded while viewing the lesson. Labeling was beneficial for learning, but color coding was not. In addition, labeling, but not color coding, increased attention to important information in the table and time with the lesson. Both labeling and color coding increased looks between the text and corresponding information in the table. The findings provide support for the multimedia principle, and they suggest that providing labeling enhances learning about probabilistic reasoning from text and tables. Copyright © 2016 John Wiley & Sons, Ltd.     

Brain responses reveal that infants' face discrimination is guided by statistical learning from distributional information

Infants' perception of faces becomes attuned to the environment during the first year of life. However, the mechanisms that underpin perceptual narrowing for faces are only poorly understood. Considering the developmental similarities seen in perceptual narrowing for faces and speech and the role that statistical learning has been shown to play for speech, the current study examined whether and how learning from distributional information impacts face identity discrimination. We familiarized 6.5‐month‐old infants with exemplars of female faces taken from a morphed continuum going from one identity to another. Using event‐related brain potentials (ERPs), we show that only infants who were familiarized with a bimodal frequency distribution, but not infants familiarized with a unimodal frequency distribution, discriminated between identities. These results are the first to demonstrate the influence of probabilistic information on infants' face identity discrimination, suggesting that statistical learning contributes to perceptual attunement for both faces and language.     

Data‐driven approaches to information access

This paper summarizes three lines of research that are motivated by the practical problem of helping users find information from external data sources, most notably computers. The application areas include information retrieval, text categorization, and question answering. A common theme in these applications is that practical information access problems can be solved by analyzing the statistical properties of words in large volumes of real world texts. The same statistical properties constrain human performance, thus we believe that solutions to practical information access problems can shed light on human knowledge representation and reasoning.     

The Role of Domain-Specific Knowledge in Generative Reasoning About Complicated Multileveled Phenomena

Promoting the ability to reason generatively about novel phenomena and problems students may encounter in their everyday lives is a major goal of science education. This goal proves to be a formidable challenge in domains, such as molecular genetics, for which the accumulated scientific understandings are daunting in both amount and complexity. To develop effective instruction that fosters generative reasoning we need to have a sound understanding of the types of knowledge in the domain that are critical for such reasoning. In this study I examined the ensemble of knowledge, both general and domain-specific, undergraduate students employed in reasoning about problems in genetics. I found that students initially formulate a solution in terms that are not domain specific and that serve as a frame–solution frame–that outlines and constrains a more specific and domain-appropriate explanation. This solution frame is then filled in with two powerful forms of domain-specific knowledge I term: domain-specific heuristics and domain-specific explanatory schemas. These knowledge forms embody understandings of central mechanisms and entities in molecular genetics. By invoking these domain-specific knowledge forms, students were able to reason about a variety of both familiar and novel genetics problems. I present a cognitive model that highlights the role of these powerful conceptual understandings in promoting generative reasoning in genetics.     

Décalage in infants' knowledge about occlusion and containment events: Converging evidence from action tasks

In the present research, 6-month-old infants consistently searched for a tall toy behind a tall as opposed to a short occluder. However, when the same toy was hidden inside a tall or a short container, only older, 7.5-month-old infants searched for the tall toy inside the tall container. These and control results (1) confirm previous violation-of-expectation (VOE) findings of a décalage in infants' reasoning about height information in occlusion and containment events; (2) cast doubt on the suggestion that VOE tasks overestimate infants' cognitive abilities; and (3) support recent proposals that infants use their physical knowledge to guide their actions when task demands do not overwhelm their limited processing resources.     

Comprehension of the representational mind in infancy

A broad array of infant studies are reviewed that appear to be consistent with the idea that belief understanding specifically, and mental attribution generally, emerge much earlier than previously acknowledged. We first examine existing false-belief research, which, while confirming that children under 4 years perform poorly on standard tests, suggests nevertheless that they have more implicit understanding of beliefs than they can express. After surveying theories that both favor and reject early development of theory of mind (TOM), we address two recent bodies of visual fixation research that provide support for the possibility of knowledge and belief attribution in infancy. The first indicates that infants of 13–15 months are sensitive to others’ false beliefs (and therefore have a representational TOM), the second, that by 12 months or younger infants have two antecedently related psychological understandings: (a) that when agents look they “see” and (b) that seeing plays a presumptive role in producing knowledge. This raises the broader question of whether “mentalism” might be part of core knowledge, which takes us to the earliest manifestation of psychological attribution, the construal of agentive behavior as intentional. Contrary to previous assumptions, recent studies indicate that infants of 3–9 months do not accord intentionality exclusively to humans or to self-propelled objects but rather to any entity that: (1) chooses flexibly among means and ends, (2) responds non-randomly to social overtures, and (3) reacts rationally to changing circumstances (i.e., that is not a mere automaton but is selectively and adaptively responsive to the environment). Other evidence is then examined which suggests that infants begin to construe these and other behaviors in mentalist rather than teleological terms much earlier than expected. Finally, the implications of this empirical record for domain-specific and domain-general theories of TOM are considered.     

Décalage in infants' knowledge about occlusion and containment events: converging evidence from action tasks

In the present research, 6-month-old infants consistently searched for a tall toy behind a tall as opposed to a short occluder. However, when the same toy was hidden inside a tall or a short container, only older, 7.5-month-old infants searched for the tall toy inside the tall container. These and control results (1) confirm previous violation-of-expectation (VOE) findings of a décalage in infants' reasoning about height information in occlusion and containment events; (2) cast doubt on the suggestion that VOE tasks overestimate infants' cognitive abilities; and (3) support recent proposals that infants use their physical knowledge to guide their actions when task demands do not overwhelm their limited processing resources.