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27
StateSpace Inference and Learning with Gaussian Processes
"... Statespace inference and learning with Gaussian processes (GPs) is an unsolved problem. We propose a new, general methodology for inference and learning in nonlinear statespace models that are described probabilistically by nonparametric GP models. We apply the expectation maximization algorithm ..."
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Statespace inference and learning with Gaussian processes (GPs) is an unsolved problem. We propose a new, general methodology for inference and learning in nonlinear statespace models that are described probabilistically by nonparametric GP models. We apply the expectation maximization algorithm to iterate between inference in the latent statespace and learning the parameters of the underlying GP dynamics model. Inference (filtering and smoothing) in linear dynamical systems (LDS) and nonlinear dynamical systems (NLDS) is frequently used in many areas, such as signal processing, state estimation, control, and finance/econometric models. Inference aims to estimate the state of a system from a stream of noisy measurements. Imagine tracking the location of a car based on odometer and GPS sensors, both of which are noisy. Sequential measurements from both sensors are combined to overcome the noise in the system and to obtain an accurate estimate of the system state. Even when the full state is only partially measured, it can still be inferred; in the car example the engine temperature is unobserved, but can be inferred via the nonlinear relationship from acceleration. To exploit this relationship appropriately, inference techniques in nonlinear models are required; they play an important role in many practical applications. LDS and NLDS belong to a class of models known as statespace models. A statespace model assumes that there exists a time sequence of latent states xt that evolve over time according to a Markovian process specified by a transition function f. The latent states are observed indirectly in y t through a measurement
Efficient Reinforcement Learning for Motor Control
"... Abstract — Artificial learners often require many more trials than humans or animals when learning motor control tasks in the absence of expert knowledge. We implement two key ingredients of biological learning systems, generalization and incorporation of uncertainty into the decisionmaking process ..."
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Cited by 6 (1 self)
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Abstract — Artificial learners often require many more trials than humans or animals when learning motor control tasks in the absence of expert knowledge. We implement two key ingredients of biological learning systems, generalization and incorporation of uncertainty into the decisionmaking process, to speed up artificial learning. We present a coherent and fully Bayesian framework that allows for efficient artificial learning in the absence of expert knowledge. The success of our learning framework is demonstrated on challenging nonlinear control problems in simulation and in hardware. I.
Probabilistic Modeling of Human Movements for Intention Inference
 In Proceedings of Robotics: Science and Systems (R:SS). 99
, 2012
"... Abstract—Inference of human intention may be an essential step towards understanding human actions and is hence important for realizing efficient humanrobot interaction. In this paper, we propose the IntentionDriven Dynamics Model (IDDM), a latent variable model for inferring unknown human intenti ..."
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Cited by 5 (1 self)
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Abstract—Inference of human intention may be an essential step towards understanding human actions and is hence important for realizing efficient humanrobot interaction. In this paper, we propose the IntentionDriven Dynamics Model (IDDM), a latent variable model for inferring unknown human intentions. We train the model based on observed human movements/actions. We introduce an efficient approximate inference algorithm to infer the human’s intention from an ongoing movement. We verify the feasibility of the IDDM in two scenarios, i.e., target inference in robot table tennis and action recognition for interactive humanoid robots. In both tasks, the IDDM achieves substantial improvements over stateoftheart regression and classification. I.
Gaze Following as Goal Inference: A Bayesian Model
"... 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 childr ..."
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Cited by 4 (1 self)
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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.
Active Sequential Learning with Tactile Feedback
"... We consider the problem of tactile discrimination, with the goal of estimating an underlying state parameter in a sequential setting. If the data is continuous and highdimensional, collecting enough representative data samples becomes difficult. We present a framework that uses active learning to he ..."
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We consider the problem of tactile discrimination, with the goal of estimating an underlying state parameter in a sequential setting. If the data is continuous and highdimensional, collecting enough representative data samples becomes difficult. We present a framework that uses active learning to help with the sequential gathering of data samples, using informationtheoretic criteria to find optimal actions at each time step. We consider two approaches to recursively update the state parameter belief: an analytical Gaussian approximation and a Monte Carlo sampling method. We show how both active frameworks improve convergence, demonstrating results on a real robotic handarm system that estimates the viscosity of liquids from tactile feedback data. 1
Expectation Propagation in Gaussian Process Dynamical Systems
"... Rich and complex timeseries data, such as those generated from engineering systems, financial markets, videos, or neural recordings are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we ..."
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Rich and complex timeseries data, such as those generated from engineering systems, financial markets, videos, or neural recordings are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian process dynamical systems as a rich model class that is appropriate for such an analysis. We present a new approximate messagepassing algorithm for Bayesian state estimation and inference in Gaussian process dynamical systems, a nonparametric probabilistic generalization of commonly used statespace models. We derive our messagepassing algorithm using Expectation Propagation provide a unifying perspective on message passing in general statespace models. We show that existing Gaussian filters and smoothers appear as special cases within our inference framework, and that these existing approaches can be improved upon using iterated message passing. Using both synthetic and realworld data, we demonstrate that iterated message passing can improve inference in a wide range of tasks in Bayesian state estimation, thus leading to improved predictions and more effective decision making. 1
SIGMA POINT METHODS IN OPTIMAL SMOOTHING OF NONLINEAR STOCHASTIC STATE SPACE MODELS
"... In this article, we shall show how the sigmapoint based approximations that have previously been used in optimal filtering can also be used in optimal smoothing. In particular, we shall consider unscented transformation, GaussHermite quadrature and central differences based optimal smoothers. We b ..."
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In this article, we shall show how the sigmapoint based approximations that have previously been used in optimal filtering can also be used in optimal smoothing. In particular, we shall consider unscented transformation, GaussHermite quadrature and central differences based optimal smoothers. We briefly present the smoother equations and compare performance of different methods in simulated scenarios. 1.
Probabilistic Movement Modeling for Intention Inference in HumanRobot Interaction
"... Intention inference can be an essential step toward efficient humanrobot interaction. For this purpose, we propose the IntentionDriven Dynamics Model (IDDM) to probabilistically model the generative process of movements that are directed by the intention. The IDDM allows to infer the intention from ..."
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Intention inference can be an essential step toward efficient humanrobot interaction. For this purpose, we propose the IntentionDriven Dynamics Model (IDDM) to probabilistically model the generative process of movements that are directed by the intention. The IDDM allows to infer the intention from observed movements using Bayes ’ theorem. The IDDM simultaneously finds a latent state representation of noisy and highdimensional observations, and models the intentiondriven dynamics in the latent states. As most robotics applications are subject to realtime constraints, we develop an efficient online algorithm that allows for realtime intention inference. Two humanrobot interaction scenarios, i.e., target prediction for robot table tennis and action recognition for interactive humanoid robots, are used to evaluate the performance of our inference algorithm. In both intention inference tasks, the proposed algorithm achieves substantial improvements over support vector machines and Gaussian processes. 1
System Identification in Gaussian Process Dynamical Systems
"... Inference and learning in linear dynamical systems have long been studied in signal processing, machine learning, and system theory for tracking, localization, and control. In the linear Gaussian case, closed form solutions to inference and learning, also called system identification, are known as t ..."
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Inference and learning in linear dynamical systems have long been studied in signal processing, machine learning, and system theory for tracking, localization, and control. In the linear Gaussian case, closed form solutions to inference and learning, also called system identification, are known as the Kalman Filter. For nonlinear dynamical systems (NLDSs), inference and system identification typically require approximations, such as the Extended Kalman Filter (EKF). We consider the case of the NLDS being given by the statespace formulation xt = f(xt−1) + ɛt ∈ R M, y t = g(xt) + νt ∈ R D, (1) where the latent state x evolves according to a Markovian process. At each time instance t, we obtain a measurement y t which depends on the latent state xt. The terms ɛ and ν denote Gaussian system noise and Gaussian measurement noise, respectively. Assume for a moment that the transition function f: R M → R M and the measurement function g: R M → R D in Eq. (1) are known and a sequence Y = y 1,..., y T of measurements has been obtained. Then, inference aims to determine a posterior distribution over the latent state sequence X: = x1:T. The requirement for inference in latent space is that the transition function f and the measurement function g are known.
Multimodal nonlinear filtering using GaussHermite Quadrature
"... Abstract. In many filtering problems the exact posterior state distribution is not tractable and is therefore approximated using simpler parametric forms, such as single Gaussian distributions. In nonlinear filtering problems the posterior state distribution can, however, take complex shapes and eve ..."
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Abstract. In many filtering problems the exact posterior state distribution is not tractable and is therefore approximated using simpler parametric forms, such as single Gaussian distributions. In nonlinear filtering problems the posterior state distribution can, however, take complex shapes and even become multimodal so that single Gaussians are no longer sufficient. A standard solution to this problem is to use a bank of independent filters that individually represent the posterior with a single Gaussian and jointly form a mixture of Gaussians representation. Unfortunately, since the filters are optimized separately and interactions between the components consequently not taken into account, the resulting representation is typically poor. As an alternative we therefore propose to directly optimize the full approximating mixture distribution by minimizing the KL divergence to the true state posterior. For this purpose we describe a deterministic sampling approach that allows us to perform the intractable minimization approximately and at reasonable computational cost. We find that the proposed method models multimodal posterior distributions noticeably better than banks of independent filters even when the latter are allowed many more mixture components. We demonstrate the importance of accurately representing the posterior with a tractable number of components in an active learning scenario where we report faster convergence, both in terms of number of observations processed and in terms of computation time, and more reliable convergence on up to tendimensional problems. 1