Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for a task and the optimality of human behavior is evaluated by comparing observed and predicted trajectories. Here, we introduce inverse optimal control with signal-dependent noise, which allows inferring the cost function from observed behavior. To do so, we formalize the problem as a partially observable Markov decision process and distinguish between the agent's and the experimenter's inference problems. Specifically, we derive a probabilistic formulation of the evolution of states and belief states and an approximation to the propagation equation in the linear-quadratic Gaussian problem with signal-dependent noise. We extend the model to the case of partial observability of state variables from the point of view of the experimenter. We show the feasibility of the approach through validation on synthetic data and application to experimental data. Our approach enables recovering the costs and benefits implicit in human sequential sensorimotor behavior, thereby reconciling normative and descriptive approaches in a computational framework.

Table 1 provides an overview of the notation used in this paper. In this section we will consider first the more general case where the state is partially observable, and derive the equations for a fully-observable state as a special case afterwards. Eq. (18) gives directly the formula for the approximation of p(x If not stated otherwise, we used 100 trajectories to determine the MLEs. In this section we will provide additional results for the reaching and random problems. Figure 1 shows the RMSEs of our method in comparison to the two baselines described in Section 4.1. Evaluation of the proposed inverse optimal control method in terms of RMSE of the maximum-likelihood parameter estimates.

Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for a task and the optimality of human behavior is evaluated by comparing observed and predicted trajectories. Here, we introduce inverse optimal control with signal-dependent noise, which allows inferring the cost function from observed behavior. To do so, we formalize the problem as a partially observable Markov decision process and distinguish between the agent's and the experimenter's inference problems. Specifically, we derive a probabilistic formulation of the evolution of states and belief states and an approximation to the propagation equation in the linear-quadratic Gaussian problem with signal-dependent noise.

Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for a task and the optimality of human behavior is evaluated by comparing observed and predicted trajectories. Here, we introduce inverse optimal control with signal-dependent noise, which allows inferring the cost function from observed behavior. To do so, we formalize the problem as a partially observable Markov decision process and distinguish between the agent's and the experimenter's inference problems. Specifically, we derive a probabilistic formulation of the evolution of states and belief states and an approximation to the propagation equation in the linear-quadratic Gaussian problem with signal-dependent noise.

Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for a task and the optimality of human behavior is evaluated by comparing observed and predicted trajectories. Here, we introduce inverse optimal control with signal-dependent noise, which allows inferring the cost function from observed behavior. To do so, we formalize the problem as a partially observable Markov decision process and distinguish between the agent's and the experimenter's inference problems. Specifically, we derive a probabilistic formulation of the evolution of states and belief states and an approximation to the propagation equation in the linear-quadratic Gaussian problem with signal-dependent noise. We extend the model to the case of partial observability of state variables from the point of view of the experimenter. We show the feasibility of the approach through validation on synthetic data and application to experimental data. Our approach enables recovering the costs and benefits implicit in human sequential sensorimotor behavior, thereby reconciling normative and descriptive approaches in a computational framework.

Generative adversarial networks (GANs) are neural networks that learn data distributions through adversarial training. In intensive studies, recent GANs have shown promising results for reproducing training data. However, in spite of noise, they reproduce data with fidelity. As an alternative, we propose a novel family of GANs called noise-robust GANs (NR-GANs), which can learn a clean image generator even when training data are noisy. In particular, NR-GANs can solve this problem without having complete noise information (e.g., the noise distribution type, noise amount, or signal-noise relation). To achieve this, we introduce a noise generator and train it along with a clean image generator. As it is difficult to generate an image and a noise separately without constraints, we propose distribution and transformation constraints that encourage the noise generator to capture only the noise-specific components. In particular, considering such constraints under different assumptions, we devise two variants of NR-GANs for signal-independent noise and three variants of NR-GANs for signal-dependent noise. On three benchmark datasets, we demonstrate the effectiveness of NR-GANs in noise robust image generation. Furthermore, we show the applicability of NR-GANs in image denoising.