Modeling Human Imitation as Probabilistic Inference and an Application in Robotics

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The “Like-Me” Hypothesis Self-experience allows infants to interpret the act of other Self-experience plays an important role in goal inference and imitation Meltzoff, Dev Sci, 2007  Meltzoff, Acta Psychologica, 2007 Computational Model: Probabilistic instantiation of “Like-me” hypothesis

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Computational Model : goal : action : start state : ﬁnal state Friesen & Rao, Cog Sci, 2011

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Computational Model: Gaze Following : desired ﬁxation location : head motor commands : start head pose : ﬁnal head pose Friesen & Rao, Cog Sci, 2011

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Computational Model: Gaze Following : desired ﬁxation location : head motor commands : start head pose : ﬁnal head pose Random Variables are Continuous Relations are Probabilistic Functions

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Probabilistic Functions: Gaussian Processes (GP) ‣ nonparametric ‣ probabilistic distribution over functions Effective with small numbers of training examples

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Modeling Relations Transition model: Learned from “Exploration” or “Body Babbling”

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Modeling Relations Policy model: Learned from “Rejection sampling” “Planning via Probabilistic Inference” (Verma & Rao, NIPS, 2005)

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Goal-directed Planning G A B Xi Xf Given goal and start state, infer action. Closed form solutions.

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Goal Inference G A B Xi Xf Given start state and ﬁnal state, infer goal. Approximate via Bayesian Monte Carlo.

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Gaze Following Gm Am Bm Xm i Xm f A G B Xi X f change of coords. Given: mentor start state, mentor ﬁnal state, start state  Infer: mentor goal, action OTHER SELF Infer goal

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Model Simulation 0 200 400 600 −600 −400 −200 0 200 400 x position (cm) y position (cm) Agent Mentor true fixation points inferred fixation points 500 -500 500 100

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Model Performance 0 200 400 600 −600 −400 −200 0 200 400 x position (cm) y position (cm) Agent Mentor true fixation points inferred fixation points

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Blindfold Self-Experience Task Gm Am Bm Xm i Xm f A G B Xi X f change of coords.

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Blindfold Self-Experience Task Baseline Window Opaque 0 1 2 3 4 Looking Score (a) Computational Model (b) Infant Data AGENT (simulation results) INFANT (actual behavior data) Friesen & Rao, Cog Sci, 2011

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Computational Model: Robotic Tabletop Manipulation : desired tabletop position : control commands : start object location : ﬁnal object location Random Variables are Discrete Relations are Probability Tables

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Robotic Tabletop Manipulation Task Chung et al, Tech report, 2014

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Learning: Transition Model Transition model:

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Learning: Policy Model Policy model:

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Goal-Based Imitation and Action Selection Step1: Goal-Inference Step II: Action-Inference Step III:  Final State Prediction Gm Am Bm Xm i Xm f A G B Xi X f change of coords.

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Learned Transition Model Place Right Place Off-table Push Right Push Off-table Place Right Place Off-table Push Right Push Off-table

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Learned Transition Model Place Right Place Off-table Push Right Push Off-table Place Right Place Off-table Push Right Push Off-table

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Learned Transition Model Place Right Place Off-table Push Right Push Off-table Place Right Place Off-table Push Right Push Off-table

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Goal Inference Goal ✴MAP Prediction

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Action Inference Place Left Place Right Place Off Push Left Push Right Push Off Place Left Place Right Place Off Push Left Push Right Push Off Goal ✴MAP Prediction Demonstration: Xi = LEFT, Xf = RIGHT

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Final State Prediction

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Imitation Results

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A Bayesian Developmental Approach to Goal-Based Imitation Learning Michael Jae-Yoon Chung, Abram L. Friesen,  Dieter Fox, Andrew N. Meltzoff, and Rajesh P.N. Rao University of Washington HRI2015 Workshop Cognition: A Bridge between robotics and interaction

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Imitation Learning in Humans Not mere trajectory following. Imitation based on goal inference. Demonstration Goal-based imitation Infants above 1.5 years of age can imitate action even from an unsuccessful demonstration (Meltzoff & Brook 1998)

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Another Example: Gaze Following and Blindfolds 12 month olds Meltzoff & Brooks, Dev Psych Blind fold experience no training after training

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The “Like-Me” Hypothesis Self-experience allows infants to interpret the act of others. Self-experience plays an important role in goal inference and imitation. Computational Model: Probabilistic instantiation of “Like-me” hypothesis. Meltzoff, Dev Sci, 2007 Metlzoff, Acta Psychologica, 2007

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Model Performance 0 10 20 30 40 0 0.05 0.1 0.15 0.2 gaze error (degrees) p(error) −40 −20 0 0 0.05 0.1 0.15 0.2 gaze error (degrees) p(error) −40 −20 0 0 0.05 0.1 0.15 0.2 gaze error (degrees) p(error) (a) Forward Inference (b) Reverse Inference (c) Gaze Following