Papers by Neil Bramley
Event timing and interventions are important and intertwined cues to causal structure, yet they h... more Event timing and interventions are important and intertwined cues to causal structure, yet they have typically been studied separately. We bring them together for the first time in an experiment where participants learn causal structure by performing interventions in continuous time. We contrast learning in acyclic and cyclic devices, with reliable and unreliable cause– effect delays. We show that successful learners use interventions to structure and simplify their interactions with the devices and that we can capture judgment patterns with heuristics based on online construction and testing of a single structural hypothesis.
How do people explore in order to gain rewards in uncertain dynamical systems? Within a reinforce... more How do people explore in order to gain rewards in uncertain dynamical systems? Within a reinforcement learning paradigm, control normally involves trading off between exploration (i.e. trying out actions in order to gain more knowledge about the system) and exploitation (i.e. using current knowledge of the system to maximize reward). We study a novel control task in which participants must steer a boat on a grid, aiming to follow a path of high reward whilst learning how their actions affect the boat's position. We find that participants explore strategically yet conservatively, exploring more when mistakes are less costly and practicing actions that will be required later on.
Higher-level cognition depends on the ability to learn models of the world. We can characterize t... more Higher-level cognition depends on the ability to learn models of the world. We can characterize this at the computational level as a structure-learning problem with the goal of best identifying the prevailing causal relationships among a set of relata. However, the computational cost of performing exact Bayesian inference over causal models grows rapidly as the number of relata increases. This implies that the cognitive processes underlying causal learning must be substantially approximate. A powerful class of approximations that focuses on the sequential absorption of successive inputs is captured by the Neurath's ship metaphor in philosophy of science, where theory change is cast as a stochastic and gradual process shaped as much by people's limited willingness to abandon their current theory when considering alternatives as by the ground truth they hope to approach. Inspired by this metaphor and by algorithms for approximating Bayesian inference in machine learning, we propose an algorithmic-level model of causal structure learning under which learners represent only a single global hypothesis that they update locally as they gather evidence. We propose a related scheme for understanding how, under these limitations, learners choose informative interventions that manipulate the causal system to help elucidate its workings. We find support for our approach in the analysis of 3 experiments.
Children between 5 and 8 years of age freely intervened on a three-variable causal system, with t... more Children between 5 and 8 years of age freely intervened on a three-variable causal system, with their task being to discover whether it was a common cause structure or one of two causal chains. From 6 or 7 years of age, children were able to use information from their interventions to correctly disambiguate the structure of a causal chain. We used a Bayesian model to examine children’s interventions on the system; this showed that with development children became more efficient in producing the interventions needed to disambiguate the causal structure and that the quality of interventions, as measured by their informativeness, improved developmentally. The latter measure was a significant predictor of children’s correct inferences about the causal structure. A second experiment showed that levels of performance were not reduced in a task where children did not select and carry out interventions themselves, indicating no advantage for self-directed learning. However, children’s performance was not related to intervention quality in these circumstances, suggesting that children learn in a different way when they carry out interventions themselves.
Causal models are key to flexible and efficient exploitation of the environment. However, learnin... more Causal models are key to flexible and efficient exploitation of the environment. However, learning causal structure is hard, with massive spaces of possible models, hard-to-compute marginals and the need to integrate diverse evidence over many instances. We report on two experiments in which participants learnt about probabilistic causal systems involving three and four variables from sequences of interventions. Participants were broadly successful, albeit exhibiting sequential dependence and floundering under high background noise. We capture their behavior with a simple model, based on the " Neu-rath's ship " metaphor for scientific progress, that neither maintains a probability distribution, nor computes exact likelihoods. " We are like sailors who on the open sea must reconstruct their ship but are never able to start afresh from the bottom. Where a beam is taken away a new one must at once be put there, and for this the rest of the ship is used as support. " (Quine, 1969, p3)
The timing and order in which a set of events occur strongly influences whether people judge them... more The timing and order in which a set of events occur strongly influences whether people judge them to be causally related. But what do people think particular temporal patterns of events tell them about causal structure? And how do they integrate multiple pieces of temporal evidence? We present a behavioral experiment that explores human causal structure induction from multiple temporal patterns of observations. We compare two simple Bayesian models that make no assumptions about delay lengths, assume that causes must precede their effects but differ in whether they assume simultaneous events can also be causally connected. We find that participants' judgments are in line with the model that rules out simultaneous causation. Variants of this model that assume people update their beliefs conservatively provide a close fit to participants' judgments. We discuss possible psychological bases for this conservative belief updating and how we plan to further explore how people learn about causal structure from time.
Journal of Experimental Psychology: Learning, Memory & Cognition
A large body of research has explored how the time between two events affects judgments of causal... more A large body of research has explored how the time between two events affects judgments of causal strength between them. In this paper, we extend this work in 4 experiments that explore the role of temporal information in causal structure induction with multiple variables. We distinguish two qualitatively different types of information: The order in which events occur, and the temporal intervals between those events. We focus on one-shot learning in Experiment 1. In Experiment 2, we explore how people integrate evidence from multiple observations of the same causal device. Participants’ judgments are well predicted by a Bayesian model that rules out causal structures that are inconsistent with the observed temporal order, and favors structures that imply similar intervals between causally connected components. In Experiments 3 and 4, we look more closely at participants’ sensitivity to exact event timings. Participants see three events that always occur in the same order, but the variability and correlation between the timings of the events is either more consistent with a chain or a fork structure. We show, for the first time, that even when order cues do not differentiate, people can still make accurate causal structure judgments on the basis of interval variability alone.
In this paper, we bring together research on active learning and intuitive physics to explore how... more In this paper, we bring together research on active learning and intuitive physics to explore how people learn about " microworlds " with continuous spatiotemporal dynamics. Participants interacted with objects in simple two-dimensional worlds governed by a physics simulator, with the goal of identifying latent physical properties such as mass, and forces of attraction or repulsion. We find an advantage for active learners over passive and yoked controls. Active participants spontaneously performed several kinds of " natural experiments " which reveal the objects' properties with varying success. While yoked participants' judgments were affected by the quality of the active participant they observed, they did not share the learning advantage, performing no better than passive controls overall. We discuss possible explanations for the divergence between active and yoked learners, and outline further steps to categorize and explore active learning in the wild. The great majority of research on human and machine learning has focused on passive situations, where evidence is fixed or preselected. Participants are typically invited to make judgments based on carefully pre-chosen evidence; and machine learning algorithms compete for predictive accuracy on pre-existing datasets. In contrast, Nature's successful learners are necessarily embedded in the world they must learn about and exploit. Thus, it is the norm for human learners to exert some degree of active control over the evidence they see. To understand human learning then, one must also understand the myriad decisions about where to attend, and what action to take, that control and manage the flow of incoming evidence. An effective active learner will be able to bootstrap their learning and improve the utility of the information they receive by tailoring it to resolving their subjective uncertainty. On this view, we can think of the little actions in everyday life as small experiments, ranging from the automatic (e.g. cocking one's head to better locate the origin of a sound), to the deliberate (lifting a suitcase to judge its weight; shaking a present to try and guess its contents; holding a pool cue to one eye, or spinning it, to gauge its straightness). A common element in these examples is that they create situations that bring into sharper relief the physical properties of interest. In this paper we explore this naturalistic type of learning by looking at how people learn about physical laws and properties , such as magnetism and object mass. The structure of the paper is as follows. We first survey the literatures on active learning and intuitive physics, then describe experiments that contrast passive learners with active and yoked learners. Finally , we look closely at the types of actions that active participants performed to reveal the microworlds' hidden physical properties.
Journal of Experimental Psychology: Learning, Memory, and Cognition, 2014
The timing and order in which a set of events occur strongly influences whether people judge them... more The timing and order in which a set of events occur strongly influences whether people judge them to be causally related. But what do people think particular temporal patterns of events tell them about causal structure? And how do they integrate multiple pieces of temporal evidence? We present a behavioral experiment that explores human causal structure induction from multiple temporal patterns of observations. We compare two simple Bayesian models that make no assumptions about de- lay lengths, assume that causes must precede their effects but differ in whether they assume simultaneous events can also be causally connected. We find that participants’ judgments are in line with the model that rules out simultaneous causation. Variants of this model that assume people update their beliefs conservatively provide a close fit to participants’ judgments. We discuss possible psychological bases for this conservative belief updating and how we plan to further explore how people learn about causal structure from time.
Conference Presentations by Neil Bramley
Causal structure induction is a highly important but relatively understudied aspect of human lear... more Causal structure induction is a highly important but relatively understudied aspect of human learning. A mathematical framework has been developed showing how intervening on a system can provide information about its causal structure (Pearl, 2000), but there is little consensus about what makes a chosen intervention more or less valuable to real learners. Common norms for choosing interventions in cognitive science include (1) classification error reduction (probability gain), and (2) information gain (reduction in Shannon entropy). We explore how each of these norms performs, when implemented in a stepwise (myopic) way, on a sequential causal learning task. In a variety of circumstances, stepwise information gain's performance is superior to that of stepwise probability gain, at the goal of reducing error. We explored this surprising result by testing a wider variety of information gain-like functions. A variety of information gain measures, based on expected reduction in Tsallis and Renyi entropy, performed as well as the standard information gain measure.
Existing studies on causal structure learning are largely restricted to single-shot interventions... more Existing studies on causal structure learning are largely restricted to single-shot interventions, usually in constrained or deterministic scenarios. However, real world causal learning is generally noisy, incremental and constrained only by prior beliefs. Here we describe experiments where participants were incentivised to infer the causal structure of a series of novel noisy systems of nodes through the free selection of multiple interventions. Participants’ sequences of intervention choices and online structure judgements are measured against those of an efficient Bayesian learner, which integrates information perfectly and intervenes to maximise expected utility. Successful participants were systematic and learned effectively, but chose markedly different intervention sequences to those of a Bayesian learner. Several simple intervention-attribution mechanisms were motivated by these patterns and fitted to individual participant’s data. Overall, we find evidence suggesting that causal structure learning is achieved by iteration of simple, action-selection and causal-attribution mechanisms.
Thesis Chapters by Neil Bramley
Humans are adept at constructing causal models of the world that can support prediction, explanat... more Humans are adept at constructing causal models of the world that can support prediction, explanation, simulation-based reasoning, planning and control. In this thesis I explore how people learn about the causal world interacting with it, and how they represent and modify their causal knowledge as they gather evidence. Over 10 experiments and modelling, I show that interventional and temporal cues, along with top-down hierarchical constraints, inform the gradual evolution and adaptation of increasingly rich causal representations.
Chapters 1 and 2 develop a rational analysis of the problems of learning and representing causal structure, and choosing interventions, that perturb the world in ways that reveal its structure.
Chapters 3--5 focus on structure learning over sequences of discrete trials, in which learners can intervene by setting variables within a causal system and observe the consequences. The second half of the thesis generalises beyond the discrete trial learning case, exploring interventional causal learning in situations where events occur in continuous time (Chapters 6 and 7); and in spatiotemporally rich physical ``microworlds'' (Chapter 8).
Throughout the experiments, I find that both children and adults are robust active causal learners, able to deal with noise and complexity even as normative judgment and intervention selection become radically intractable. To explain their success, I develop scalable process level accounts of both causal structure learning and intervention selection inspired by approximation algorithms in machine learning. I show that my models can better explain patterns of behaviour than a range of alternatives as well as shedding light on the source of common biases including confirmatory testing, anchoring effects and probability matching. Finally, I propose a close relationship between active learning and active aspects of cognition including thinking, decision making and executive control.
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Papers by Neil Bramley
Conference Presentations by Neil Bramley
Thesis Chapters by Neil Bramley
Chapters 1 and 2 develop a rational analysis of the problems of learning and representing causal structure, and choosing interventions, that perturb the world in ways that reveal its structure.
Chapters 3--5 focus on structure learning over sequences of discrete trials, in which learners can intervene by setting variables within a causal system and observe the consequences. The second half of the thesis generalises beyond the discrete trial learning case, exploring interventional causal learning in situations where events occur in continuous time (Chapters 6 and 7); and in spatiotemporally rich physical ``microworlds'' (Chapter 8).
Throughout the experiments, I find that both children and adults are robust active causal learners, able to deal with noise and complexity even as normative judgment and intervention selection become radically intractable. To explain their success, I develop scalable process level accounts of both causal structure learning and intervention selection inspired by approximation algorithms in machine learning. I show that my models can better explain patterns of behaviour than a range of alternatives as well as shedding light on the source of common biases including confirmatory testing, anchoring effects and probability matching. Finally, I propose a close relationship between active learning and active aspects of cognition including thinking, decision making and executive control.
Chapters 1 and 2 develop a rational analysis of the problems of learning and representing causal structure, and choosing interventions, that perturb the world in ways that reveal its structure.
Chapters 3--5 focus on structure learning over sequences of discrete trials, in which learners can intervene by setting variables within a causal system and observe the consequences. The second half of the thesis generalises beyond the discrete trial learning case, exploring interventional causal learning in situations where events occur in continuous time (Chapters 6 and 7); and in spatiotemporally rich physical ``microworlds'' (Chapter 8).
Throughout the experiments, I find that both children and adults are robust active causal learners, able to deal with noise and complexity even as normative judgment and intervention selection become radically intractable. To explain their success, I develop scalable process level accounts of both causal structure learning and intervention selection inspired by approximation algorithms in machine learning. I show that my models can better explain patterns of behaviour than a range of alternatives as well as shedding light on the source of common biases including confirmatory testing, anchoring effects and probability matching. Finally, I propose a close relationship between active learning and active aspects of cognition including thinking, decision making and executive control.