Generalization as diffusion: Human function learning on graphs
Charley M. Wu,Eric Schulz,Samuel J. Gershman +2 more
- 03 Feb 2019
- pp 3122-3128
TL;DR: In this article, the authors adapt a Bayesian framework for function learning to graph structures, and propose that people perform generalization by diffusing observed function values across the graph, and test the predictions of this model by asking participants to make predictions about passenger volume in virtual subway network.
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Abstract: From social networks to public transportation, graph structures are a ubiquitous feature of life. Yet little is known about how humans learn functions on graphs, where relationships are defined by the connectivity structure. We adapt a Bayesian framework for function learning to graph structures, and propose that people perform generalization by diffusing observed function values across the graph. We test the predictions of this model by asking participants to make predictions about passenger volume in a virtual subway network. The model captures both generalization and confidence judgments, and is a quantitatively superior account relative to several heuristic models. Our work suggests that people exploit graph structure to make generalizations about functions in complex discrete spaces.
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Figures
Figure 3: Results. a-b) Participant judgment errors and confidence estimates. Each dot is a single participant (averaged over each number of observed nodes), with Tukey boxplots and diamonds indicating group means. The dotted line in a) is a random baseline. c) Judgment error and confidence. Each colored dot is a participant (averaged over each confidence level), dashed line is a linear regression, with black dots and error bars indicating group means and 95% CI. We report the mixed-effects regression coefficient and Bayes Factor above. d) Cross-validated model comparison between the Gaussian Process with diffusion kernel (GP), d-nearest neighbors (dNN), and k-nearest neighbors (kNN). Each point is a single participant with a Tukey boxplot overlaid and diamonds indicating group means. Comparisons are for a Bayesian one-sample t-test, where the null hypothesis posits no difference between models and assumes a Cauchy prior with the scale set to √ 2/2. e) Parameter estimates, where each dot is the mean cross-validated estimate for each participant, with Tukey boxplots and diamonds indicating group means. f) GP uncertainty estimates (rank ordered within participant) and participant confidence judgments (Likert scale). Dotted line is a linear regression, with black dots and error bars indicating mean and 95% CI. We report the mixed-effects regression coefficient and Bayes factor (see text for details). 
Figure 1: Graph-structured function learning. a) An example of a graph structure, where nodes represent states and edges indicate the transition structure. b) A diffusion kernel is a similarity metric between nodes on a graph, allowing us to generalize to unobserved nodes based on the assumption that the correlation between function values decays as an exponential function of the distance between two nodes. The diffusion parameter (α) governs the rate of decay. c) Given some observations on the graph (colored nodes), we can use the diffusion kernel combined with the Gaussian Process framework to make predictions (d) about expected rewards (numbers in grey nodes) and the underlying uncertainty (size of halo) for each unobserved node. 
Figure 2: Screenshot from the Subway Prediction Experiment. Observed nodes (3, 5, or 7 randomly sampled nodes depending on the information condition) are shown with a numerical value and a corresponding color aid (darker indicates larger values). The target node is indicated by the dashed line, and dynamically changes color and displays a numerical value when participants move the top slider. Confidence judgments were used to compute a weighted error (i.e., more confident answers having a larger contribution), which was used to determine the performance contingent bonus.
Citations
A rational model of function learning
Thomas L. Griffiths,Michael L. Kalish,Chris Lucas +2 more
- 01 Jan 2009
TL;DR: In this paper, the authors present a rational model that transparently identifies the inductive biases that a process model should seek to capture, and they find that it explains several phenomena, including knowledge partitioning and iterated learning data.
Reinforcement learning with associative or discriminative generalization across states and actions: fMRI at 3 T and 7 T
Jaron T. Colas,Neil M. Dundon,Raphael T. Gerraty,Natalie Saragosa-Harris,Karol P. Szymula,Koranis Tanwisuth,J. Michael Tyszka,Camilla van Geen,Harang Ju,Arthur W. Toga,Joshua I. Gold,Danielle S. Bassett,Catherine A. Hartley,Daphna Shohamy,Scott T. Grafton,John P. O'Doherty +15 more
TL;DR: Factoring in generalization as a multidimensional process in value‐based learning, these findings shed light on complexities that, while challenging classic RL, can still be resolved within the bounds of its core computations.
8
Inference and search on graph-structured spaces
TL;DR: This work studies human behavior on structures with graph-correlated values and proposes a Bayesian model of function learning to describe and predict their behavior, finding that this model captures human predictions and sampling behavior better than several alternatives, generates human-like learning curves, and also captures participants’ confidence judgements.
Cognitive graphs: Representational substrates for planning.
Jungsun Yoo,Elizabeth R. Chrastil,Aaron M. Bornstein +2 more
TL;DR: Researchers review cognitive graphs, a framework combining cognitive psychology and computer science, to unify representations supporting planning, highlighting their creation, use, and impact on planning through structured sequences and compressed predictive representations.
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Learning to Learn Functions
Michael Y. Li,Frederick Callaway,Ryan P. Adams,Thomas L. Griffiths +3 more
TL;DR: In this article , the process of learning to learn functions is modeled as a form of hierarchical Bayesian inference about the Gaussian process hyperparameters, and it is shown that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter.
1
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