In the absence of explicit or tractable likelihoods, Bayesians often resort to approximate Bayesian computation (ABC) for inference. Our work bridges ABC with deep neural implicit samplers based on generative adversarial networks (GANs) and adversarial variational Bayes. Both ABC and GANs compare aspects of observed and fake data to simulate from posteriors and likelihoods, respectively. We develop a Bayesian GAN (B-GAN) sampler that directly targets the posterior by solving an adversarial optimization problem. B-GAN is driven by a deterministic mapping learned on the ABC reference by conditional GANs. Once the mapping has been trained, iid posterior samples are obtained by filtering noise at a negligible additional cost. We propose two post-processing local refinements using (1) data-driven proposals with importance reweighting, and (2) variational Bayes. We support our findings with frequentist-Bayesian results, showing that the typical total variation distance between the true and approximate posteriors converges to zero for certain neural network generators and discriminators. Our findings on simulated data show highly competitive performance relative to some of the most recent likelihood-free posterior simulators.

To address the force/position control challenges in transitioning from free-space motion to tasks involving environmental contact, this paper proposes an Adaptive Dynamic Programming (ADP)-based finite-time optimal backstepping force/position control method for Reconfigurable Robot Manipulators (RRMs), which ensures rapid convergence of state errors under external constraints while maintaining system stability. By integrating robust control, the proposed method enhances both convergence speed and robustness against uncertainties. Furthermore, the parameters related to robustness are optimized using a cooperative game-theoretic approach based on Pareto optimality. A Lyapunov-based analysis demonstrates the closed-loop system’s Semi-Global Practical Finite-time Stability (SGPFS). Experimental validation confirms the effectiveness of the proposed control method.

Major challenges of controlling human-robot collaboration (HRC)-oriented modular robot manipulators (MRMs) include the estimation of human motion intention while cooperating with a robot and performance optimization. This article proposes a cooperative game-based approximate optimal control method of MRMs for HRC tasks. A harmonic drive compliance model-based human motion intention estimation method is developed using robot position measurements only, which forms the basis of the MRM dynamic model. Based on the cooperative differential game strategy, the optimal control problem of HRC-oriented MRM systems is transformed into a cooperative game problem of multiple subsystems. By taking advantage of the adaptive dynamic programming (ADP) algorithm, a joint cost function identifier is developed via the critic neural networks, which is implemented for solving the parametric Hamilton-Jacobi-Bellman (HJB) equation and Pareto optimal solutions. The trajectory tracking error under the HRC task of the closed-loop MRM system is proved to be ultimately uniformly bounded (UUB) by the Lyapunov theory. Finally, experiment results are presented, which reveal the advantage of the proposed method.

Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution through an accept/reject mechanism which compares summary statistics of real and simulated data. To obviate the need for summary statistics, we directly compare empirical distributions with a Kullback-Leibler (KL) divergence estimator obtained via contrastive learning. In particular, we blend flexible machine learning classifiers within ABC to automate fake/real data comparisons. We consider the traditional accept/reject kernel as well as an exponential weighting scheme which does not require the ABC acceptance threshold. Our theoretical results show that the rate at which our ABC posterior distributions concentrate around the true parameter depends on the estimation error of the classifier. We derive limiting posterior shape results and find that, with a properly scaled exponential kernel, asymptotic normality holds. We demonstrate the usefulness of our approach on simulated examples as well as real data in the context of stock volatility estimation.

Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering infinite dimensional objects (curves or densities). Despite the impressive array of available theoretical results, the literature has been largely silent about uncertainty quantification for deep learning. This paper takes a step forward in this important direction by taking a Bayesian point of view. We study Gaussian approximability of certain aspects of posterior distributions of sparse deep ReLU architectures in non-parametric regression. Building on tools from Bayesian non-parametrics, we provide semi-parametric Bernstein-von Mises theorems for linear and quadratic functionals, which guarantee that implied Bayesian credible regions have valid frequentist coverage. Our results provide new theoretical justifications for (Bayesian) deep learning with ReLU activation functions, highlighting their inferential potential.