## Gaze Following as Goal Inference: A Bayesian Model

Citations: | 3 - 0 self |

### BibTeX

@MISC{Friesen_gazefollowing,

author = {Abram L. Friesen and Rajesh P. N. Rao},

title = {Gaze Following as Goal Inference: A Bayesian Model},

year = {}

}

### OpenURL

### Abstract

The ability to follow the gaze of another human plays a critical role in cognitive development. Infants as young as 12 months old have been shown to follow the gaze of adults. Recent experimental results indicate that gaze following is not merely an imitation of head movement. We propose that children learn a probabilistic model of the consequences of their movements, and later use this learned model of self as a surrogate for another human. We introduce a Bayesian model where gaze following occurs as a consequence of goal inference in a learned probabilistic graphical model. Bayesian inference over this learned model provides both an estimate of another’s fixation location and the appropriate action to follow their gaze. The model can be regarded as a probabilistic instantiation of Meltzoff’s “Like me ” hypothesis. We present simulation results based on a nonparametric Gaussian process implementation of the model, and compare the model’s performance to infant gaze following results.

### Citations

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(Show Context)
Citation Context ...n to follow gaze to an object (Moore, 1999). A second class of models supports the nativist view that infants have a built-in module for interpreting eye gaze in terms of visual experience in others (=-=Baron-Cohen, 1995-=-). A third class of models adopts the developmental view that gaze following behavior emerges from self-experience (Meltzoff & Brooks, 2007). Our model can be regarded as a Bayesian example of this la... |

256 | Unscented filtering and nonlinear estimation
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(Show Context)
Citation Context ...d use the 3 Technically, we use the formulas for multivariate inputs and outputs which can be found in (Deisenroth, 2010). 4 This is a standard approximation used in Gaussian filters such as the UKF (=-=Julier & Uhlmann, 2004-=-) and the GP-ADF (Deisenroth et al., 2009). 2459samples as “measurements” when we compute p(G,A|xi,xf ). These “measurements” act in the same way as the measured xf , above, and allow us to condition... |

91 |
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Citation Context ...ze following models, one class of models posits that young infants watch an adult’s head movement in space and are drawn to the correct hemi-field where they are attracted to a salient target object (=-=Butterworth & Jarrett, 1991-=-); over time, they learn to follow gaze to an object (Moore, 1999). A second class of models supports the nativist view that infants have a built-in module for interpreting eye gaze in terms of visual... |

62 |
Bayesian rationality: The probabilistic approach to human reasoning
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(Show Context)
Citation Context ...odels for cognition proposed in recent years and acknowledges the psychophysical and neurobiological evidence for Bayesian mechanisms in perception and action (e.g., (Rao, Olshausen, & Lewicki, 2002; =-=Oaksford & Chater, 2007-=-)). Within the realm of gaze following models, one class of models posits that young infants watch an adult’s head movement in space and are drawn to the correct hemi-field where they are attracted to... |

46 | Action Understanding as Inverse Planning
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(Show Context)
Citation Context ...ces of intentions and related actions. Related Work Our model is closely related to the goal-based imitation model of Verma and Rao (Verma & Rao, 2006) and the inverse planning model of Baker et al. (=-=Baker, Saxe, & Tenenbaum, 2009-=-). Unlike these previous models, which assume discrete state and action spaces, our model is based on a nonparametric model that allows learning and inference in continuous state and action spaces. Al... |

46 |
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(Show Context)
Citation Context ...s, as well as learn useful actions to perform on the object through imitation. It has been shown that children as young as 12 months old can follow the gaze of an adult and engage in joint attention (=-=Brooks & Meltzoff, 2002-=-). Recent results have shown that gaze following is not merely an imitation of head movement. For example, 14and 18-month olds do not follow the gaze of an adult who is wearing a blindfold, although t... |

44 | Probabilistic inference for solving discrete and continuous state markov decision processes
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(Show Context)
Citation Context ...odel is based on a nonparametric model that allows learning and inference in continuous state and action spaces. Also related to our approach are models for planning based on probabilistic inference (=-=Toussaint & Storkey, 2006-=-; Verma & Rao, 2007; Botvinick & An, 2009). Again, these models are restricted to discrete state and action spaces or assume knowledge of the dynamics of the world. Our model for gaze following joins ... |

34 |
Goal-based imitation as probabilistic inference over graphical models
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(Show Context)
Citation Context ...h a reinforcement-based paradigm that combines exploration of the goal-action-state space for training the transition GP with selection of data from successful trials for training the policy GP (see (=-=Verma & Rao, 2006-=-) for related ideas). After training, it is simple for the agent to fixate on a goal location. We assume that the agent knows its current state xi and the goal g. Given these, the agent uses its learn... |

31 | Propagation of Uncertainty in Bayesian Kernel Models—Application to Multiple-Step Ahead Forecasting - Quiñonero-Candela, Girard, et al. - 2003 |

31 | Bayesian monte carlo
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Citation Context ...observations of the starting and ending head poses, xi and xf , respectively. To accomplish this, the agent must be able to recover the inputs to each GP given the outputs. Fortunately, results from (=-=Rasmussen & Ghahramani, 2003-=-) allow us to estimate a distribution over the inputs given the outputs. As such, we can infer a distribution over actions given xi and xf and then use this to estimate a distribution over goals. Gaze... |

28 |
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(Show Context)
Citation Context ... wearing a blindfold (i.e., occlusion) and unlike 12-month olds, make the inference that the adult is not looking at an object. This observation is closely related to Meltzoff’s “Like me” hypothesis (=-=Meltzoff, 2005-=-) which states that self-experience plays an important role in making inferences about the internal states of others. In particular, in the case of the blindfold experiment, self-experience with own e... |

27 | Analytic moment-based Gaussian process filtering
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(Show Context)
Citation Context ...(µ,Σ) is uncertain. This corresponds to seeking ∫ p(h(x∗)|µ,Σ) = p(h(x∗)|x∗)p(x∗|µ,Σ)dx∗. (5) For the SE kernel, we can compute the mean µ∗ and variance σ 2 ∗ of equation 5 in closed form, following (=-=Deisenroth, Huber, & Hanebeck, 2009-=-; Quiñonero-Candela, Girard, Larsen, 2 We determine the hyperparameters, θ, of each GP by maximizing the marginal likelihood p(y|X,θ) with respect to the hyperparameters, which is equivalent to maximi... |

21 |
Efficient Reinforcement Learning using Gaussian Processes, volume 9
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Citation Context ... goal from observations of the current and final state, p(G|Xi = xi,Xf = xf ). This computation is similar to the filtering and smoothing computations used in Gaussian dynamical systems (reviewed in (=-=Deisenroth, 2010-=-)). To begin, we set Xi = xi and perform forward inference using our prior p(G = g). We obtain p(A|xi) = N (a|µa,Σa) and p(Xf |xi) ≈ N (xf |µxf ,Σxf ). Now, we approximate the joint p(A,Xf |xi) with a... |

15 | Self-experience as a mechanism for learning about others: A training study 2 Perspective-Taking 673 in social cognition
- Meltzoff, Brooks
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(Show Context)
Citation Context ...owed blindfold. On seeing an adult with a blindfold turn towards an object, most of the children who had had self-experience with blindfolds did not turn to the object while the other two groups did (=-=Meltzoff & Brooks, 2008-=-). These results suggest that (a) gaze following involves an inference of the underlying intention or goal of the head movement, and (b) self-experience plays a major role in learning the consequences... |

12 | Goaldirected decision making in prefrontal cortex: a computational framework
- Botvinick, An
- 2008
(Show Context)
Citation Context ...lows learning and inference in continuous state and action spaces. Also related to our approach are models for planning based on probabilistic inference (Toussaint & Storkey, 2006; Verma & Rao, 2007; =-=Botvinick & An, 2009-=-). Again, these models are restricted to discrete state and action spaces or assume knowledge of the dynamics of the world. Our model for gaze following joins the growing number of Bayesian models for... |

5 | Eyes wide shut: The importance of eyes in infant gazefollowing and understanding other minds
- Meltzoff, Brooks
- 2007
(Show Context)
Citation Context ...for interpreting eye gaze in terms of visual experience in others (Baron-Cohen, 1995). A third class of models adopts the developmental view that gaze following behavior emerges from self-experience (=-=Meltzoff & Brooks, 2007-=-). Our model can be regarded as a Bayesian example of this last class of models. 2461Summary and Conclusion This paper proposes a Bayesian framework for social interaction that postulates that (1) ch... |

5 |
Gaze following and the control of attention. In P. Rochat (Ed.), Early social cognition: Understanding others in the first months of life (pp
- Moore
- 1999
(Show Context)
Citation Context ...’s head movement in space and are drawn to the correct hemi-field where they are attracted to a salient target object (Butterworth & Jarrett, 1991); over time, they learn to follow gaze to an object (=-=Moore, 1999-=-). A second class of models supports the nativist view that infants have a built-in module for interpreting eye gaze in terms of visual experience in others (Baron-Cohen, 1995). A third class of model... |