Biology subjects

Schulz, E.

Publications and source records attributed to Schulz, E..

51 records · Page 3Linked to original sources

bioRxiv2018

Learning list concepts through program induction

Humans master complex systems of interrelated concepts like mathematics and natural language. Previous work suggests learning these systems relies on iteratively and directly revising a language-like conceptual representation. We introduce and assess a novel concept learning paradigm called Marthas Magical Machines that captures complex relationships between concepts. We model human concept learning in this paradigm as a search in the space of term rewriting systems, previously developed as an abstract model of computation. Our model accurately predicts that participants learn some transformations more easily than others and that they learn harder concepts more easily using a bootstrapping curriculum focused on their compositional parts. Our results suggest that term rewriting systems may be a useful model of human conceptual representations.

animal behavior and cognition↗

bioRxiv2018

Structured priors in human forecasting

Forecasting is an increasingly important part of our daily lives. Many studies on how people produce forecasts frame their behavior as prone to systematic errors. Based on recent evidence on how people learn about functions, we propose that participants forecasts are not irrational but rather driven by structured priors, i.e. situationally induced expectations of structure derived from experience with the real world. To test this, we extract participants priors over various contexts using a free-form forecasting paradigm. Instead of exhibiting systematic biases, our results show that participants priors match well with structure found in real-world data. Moreover, given the same data set, structured priors induce predictably different posterior forecasts depending on the evoked situational context.

animal behavior and cognition↗

bioRxiv2018

Adaptive planning in human search

How do people plan ahead when searching for rewards? We investigate planning in a foraging task in which participants search for rewards on an infinite two-dimensional grid. Our results show that their search is best-described by a model which searches at least 3 steps ahead. Furthermore, participants do not seem to update their beliefs during planning, but rather treat their initial beliefs as given, a strategy similar to a heuristic called root-sampling. This planning algorithm corresponds well with participants behavior in test problems with restricted movement and varying degrees of information, outperforming more complex models. These results enrich our understanding of adaptive planning in complex environments.

animal behavior and cognition↗

bioRxiv2018

Active Function Learning

How do people actively explore to learn about functional relationships, that is, how continuous inputs map onto continuous outputs? We introduce a novel paradigm to investigate information search in continuous, multi-feature function learning scenarios. Participants either actively selected or passively observed information to learn about an underlying linear function. We develop and compare different variants of rule-based (linear regression) and non-parametric (Gaussian process regression) active learning approaches to model participants active learning behavior. Our results show that participants performance is best described by a rule-based model that attempts to efficiently learn linear functions with a focus on high and uncertain outcomes. These results advance our understanding of how people actively search for information to learn about functional relations in the environment.

animal behavior and cognition↗

bioRxiv2018

Connecting conceptual and spatial search via a model of generalization

The idea of a \"cognitive map\" was originally developed to explain planning and generalization in spatial domains through a representation of inferred relationships between experiences. Recently, new research has suggested similar principles may also govern the representation of more abstract, conceptual knowledge in the brain. We test whether the search for rewards in conceptual spaces follows similar computational principles as in spatial environments. Using a within-subject design, participants searched for both spatially and conceptually correlated rewards in multi-armed bandit tasks. We use a Gaussian Process model combining generalization with an optimistic sampling strategy to capture human search decisions and judgments in both domains, and to simulate human-level performance when specified with participant parameter estimates. In line with the notion of a domain-general generalization mechanism, parameter estimates correlate across spatial and conceptual search, yet some differences also emerged, with participants generalizing less and exploiting more in the conceptual domain.

animal behavior and cognition↗

bioRxiv2017

Active learning reveals underlying decision strategies

One key question is whether people rely on frugal heuristics or full-information strategies when making preference decisions. We propose a novel method, model-based active learning, to answer whether people conform more to a rank-based heuristic (Take-The-Best) or a weight-based full-information strategy (logistic regression). Our method eclipses traditional model comparison techniques by using information theory to characterize model predictions for how decision makers should actively sample information. These analyses capture how sampling affects learning and how learning affects decisions on subsequent trials. We develop and test model-based active learning algorithms for both Take-The-Best and logistic regression. Our findings reveal that people largely follow a weight-based learning strategy rather than a rank-based strategy, even in cases where their preference decisions are better predicted by the Take-The-Best heuristic. This finding suggests that people may have more refined knowledge than is revealed by their preference decisions, but which can be revealed by their information sampling behavior. We argue that model-based active learning is an effective and sensitive method for model selection that expands the basis for model comparison.

animal behavior and cognition↗

bioRxiv2017

Remembrance of Inferences Past

Bayesian models of cognition assume that people compute probability distributions over hypotheses. However, the required computations are frequently intractable or prohibitively expensive. Since people often encounter many closely related distributions, selective reuse of computations (amortized inference) is a computationally efficient use of the brains limited resources. We present three experiments that provide evidence for amortization in human probabilistic reasoning. When sequentially answering two related queries about natural scenes, participants responses to the second query systematically depend on the structure of the first query. This influence is sensitive to the content of the queries, only appearing when the queries are related. Using a cognitive load manipulation, we find evidence that people amortize summary statistics of previous inferences, rather than storing the entire distribution. These findings support the view that the brain trades off accuracy and computational cost, to make efficient use of its limited cognitive resources to approximate probabilistic inference.

animal behavior and cognition↗

bioRxiv2017

Generalization and search in risky environments

How do people pursue rewards in risky environments, where some outcomes should be avoided at all costs? We investigate how participant search for spatially correlated rewards in scenarios where one must avoid sampling rewards below a given threshold. This requires not only the balancing of exploration and exploitation, but also reasoning about how to avoid potentially risky areas of the search space. Within risky versions of the spatially correlated multi-armed bandit task, we show that participants behavior is aligned well with a Gaussian process function learning algorithm, which chooses points based on a safe optimization routine. Moreover, using leave-one-block-out cross-validation, we find that participants adapt their sampling behavior to the riskiness of the task, although the underlying function learning mechanism remains relatively unchanged. These results show that participants can adapt their search behavior to the adversity of the environment and enrich our understanding of adaptive behavior in the face of risk and uncertainty.

animal behavior and cognition↗

bioRxiv2017

Exploration and generalization in vast spaces

From foraging for food to learning complex games, many aspects of human behaviour can be framed as a search problem with a vast space of possible actions. Under finite search horizons, optimal solutions are generally unobtainable. Yet how do humans navigate vast problem spaces, which require intelligent exploration of unobserved actions? Using a variety of bandit tasks with up to 121 arms, we study how humans search for rewards under limited search horizons, where the spatial correlation of rewards (in both generated and natural environments) provides traction for generalization. Across a variety of diifferent probabilistic and heuristic models, we find evidence that Gaussian Process function learning--combined with an optimistic Upper Confidence Bound sampling strategy--provides a robust account of how people use generalization to guide search. Our modelling results and parameter estimates are recoverable, and can be used to simulate human-like performance, providing insights about human behaviour in complex environments.

animal behavior and cognition↗

bioRxiv2017

Amortized Hypothesis Generation

Bayesian models of cognition posit that people compute probability distributions over hypotheses, possibly by constructing a sample-based approximation. Since people encounter many closely related distributions, a computationally efficient strategy is to selectively reuse computations - either the samples themselves or some summary statistic. We refer to these reuse strategies as amortized inference. In two experiments, we present evidence consistent with amortization. When sequentially answering two related queries about natural scenes, we show that answers to the second query vary systematically depending on the structure of the first query. Using a cognitive load manipulation, we find evidence that people cache summary statistics rather than raw sample sets. These results enrich our notions of how the brain approximates probabilistic inference.

animal behavior and cognition↗

bioRxiv2017

Strategic exploration in human adaptive control

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 boats 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.

animal behavior and cognition↗

bioRxiv2017

Mapping the unknown: The spatially correlated multi-armed bandit

We introduce the spatially correlated multi-armed bandit as a task coupling function learning with the exploration-exploitation trade-off. Participants interacted with bi-variate reward functions on a two-dimensional grid, with the goal of either gaining the largest average score or finding the largest payoff. By providing an opportunity to learn the underlying reward function through spatial correlations, we model to what extent people form beliefs about unexplored payoffs and how that guides search behavior. Participants adapted to assigned payoff conditions, performed better in smooth than in rough environments, and--surprisingly--sometimes performed equally well in short as in long search horizons. Our modeling results indicate a preference for local search options, which when accounted for, still suggests participants were best-described as forming local inferences about unexplored regions, combined with a search strategy that directly traded off between exploiting high expected rewards and exploring to reduce uncertainty about the spatial structure of rewards.

animal behavior and cognition↗

bioRxiv2016

A tutorial on Gaussian process regression with a focus on exploration-exploitation scenarios

This tutorial introduces the reader to Gaussian process regression as an expressive tool to model, actively explore and exploit unknown functions. Gaussian process regression is a powerful, non-parametric Bayesian approach towards regression problems that can be utilized in exploration and exploitation scenarios. This tutorial aims to provide an accessible introduction to these techniques. We will introduce Gaussian processes which generate distributions over functions used for Bayesian non-parametric regression, and demonstrate their use in applications and didactic examples including simple regression problems, a demonstration of kernel-encoded prior assumptions and compositions, a pure exploration scenario within an optimal design framework, and a bandit-like exploration-exploitation scenario where the goal is to recommend movies. Beyond that, we describe a situation modelling risk-averse exploration in which an additional constraint (not to sample below a certain threshold) needs to be accounted for. Lastly, we summarize recent psychological experiments utilizing Gaussian processes. Software and literature pointers are also provided.

animal behavior and cognition↗

bioRxiv2016

Compositional Inductive Biases in Function Learning

How do people recognize and learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is achieved by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian regression using a grammar over Gaussian process kernels, and compare this approach with other structure learning approaches. Participants consistently chose compositional (over non-compositional) extrapolations and interpolations of functions. Experiments designed to elicit priors over functional patterns revealed an inductive bias for compositional structure. Compositional functions were perceived as subjectively more predictable than non-compositional functions, and exhibited other signatures of predictability, such as enhanced memorability and reduced numerosity. Taken together, these results support the view that the human intuitive theory of functions is inherently compositional.

animal behavior and cognition↗

bioRxiv2016

Putting bandits into context: How function learning supports decision making

We introduce the contextual multi-armed bandit task as a framework to investigate learning and decision making in uncertain environments. In this novel paradigm, participants repeatedly choose between multiple options in order to maximise their rewards. The options are described by a number of contextual features which are predictive of the rewards through initially unknown functions. From their experience with choosing options and observing the consequences of their decisions, participants can learn about the functional relation between contexts and rewards and improve their decision strategy over time. In three experiments, we explore participants behaviour in such learning environments. We predict participants behaviour by context-blind (mean-tracking, Kalman filter) and contextual (Gaussian process and linear regression) learning approaches combined with different choice strategies. Participants are mostly able to learn about the context-reward functions and their behaviour is best described by a Gaussian process learning strategy which generalizes previous experience to similar instances. In a relatively simple task with binary features, they seem to combine this learning with a \"probability of improvement\" decision strategy which focuses on alternatives that are expected to lead to an improvement upon a current favourite option. In a task with continuous features that are linearly related to the rewards, participants seem to more explicitly balance exploration and exploitation. Finally, in a difficult learning environment where the relation between features and rewards is non-linear, some participants are again well-described by a Gaussian process learning strategy, whereas others revert to context-blind strategies.

animal behavior and cognition↗