Subsampling Error in Stochastic Gradient Langevin Diffusions

The Stochastic Gradient Langevin Dynamics (SGLD) are popularly used to approximate Bayesian posterior distributions in statistical learning procedures with large-scale data. As opposed to many usual Markov chain Monte Carlo (MCMC) algorithms, SGLD is not stationary with respect to the posterior distribution; two sources of error appear: The first error is introduced by an Euler--Maruyama discretisation of a Langevin diffusion process, the second error comes from the data subsampling that enables its use in large-scale data settings. In this work, we consider an idealised version of SGLD to analyse the method's pure subsampling error that we then see as a best-case error for diffusion-based subsampling MCMC methods. Indeed, we introduce and study the Stochastic Gradient Langevin Diffusion (SGLDiff), a continuous-time Markov process that follows the Langevin diffusion corresponding to a data subset and switches this data subset after exponential waiting times. There, we show that the Wasserstein distance between the posterior and the limiting distribution of SGLDiff is bounded above by a fractional power of the mean waiting time. Importantly, this fractional power does not depend on the dimension of the state space. We bring our results into context with other analyses of SGLD

Bundling of Digital Goods in the Presence of Piracy

The efficacy of bundling is well-known in the context of digital goods with zero marginal cost. However, digital goods are also prone to piracy, and it is not clear what impact piracy might have on the efficacy of bundling. Prior research on this issue is limited, and it suggests that the appeal of bundling remains intact in the face of piracy. Using a model that recasts the classic bundling problem in the backdrop of piracy, we question this insight and show that piracy can severely diminish the appeal of bundling. In fact, bundling exacerbates the piracy problem and pushes more consumers to substitute the legal products with illegal ones, which more than offsets the usual benefits of bundling to a monopolist seller. Overall, the manufacturers of digital goods need to take piracy into consideration in their bundling decision and, perhaps, refrain from bundling when they anticipate the threat of piracy to be severe

New noise-tolerant neural algorithms for future dynamic nonlinear optimization with estimation on hessian matrix inversion

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems

Novel joint-drift-free scheme at acceleration level for robotic redundancy resolution with tracking error theoretically eliminated

In this article, three acceleration-level joint-drift-free (ALJDF) schemes for kinematic control of redundant manipulators are proposed and analyzed from perspectives of dynamics and kinematics with the corresponding tracking error analyses. First, the existing ALJDF schemes for kinematic control of redundant manipulators are systematized into a generalized acceleration-level joint-drift-free scheme with a paradox pointing out the theoretical existence of the velocity error related to joint drift. Second, to remedy the deficiency of the existing solutions, a novel acceleration-level joint-drift-free (NALJDF) scheme is proposed to decouple Cartesian space error from joint space with the tracking error theoretically eliminated. Third, in consideration of the uncertainty at the dynamics level, a multi-index optimization acceleration-level joint-drift-free scheme is presented to reveal the influence of dynamics factors on the redundant manipulator control. Afterwards, theoretical analyses are provided to prove the stability and feasibility of the corresponding dynamic neural network with the tracking error deduced. Then, computer simulations, performance comparisons, and physical experiments on different redundant manipulators synthesized by the proposed schemes are conducted to demonstrate the high performance and superiority of the NALJDF scheme and the influence of dynamics parameters on robot control. This work is of great significance to enhance the product quality and production efficiency in industrial production

Distributed cooperative kinematic control of multiple robotic manipulators with improved communication efficiency

An efficiency-oriented solution is theoretically a preferred choice to support the efficient operation of a system. Although some studies on the multi-manipulator system share the load of the control center by transforming the network topology, the whole system often suffers an increased communication burden. In this article, a multi-manipulator cooperative control scheme with improved communication efficiency is proposed to allocate limited communication resources reasonably. The entire control process is formulated from the perspective of game theory and finally evolved into a problem of finding a Nash equilibrium with time-varying parameters. Then, a neural network solver is designed to update the strategies of manipulators. Theoretical analysis supports the convergence and robustness of the solver. In addition, Zeno behavior does not occur under the domination of the control strategy. Finally, simulative results reveal that the proposed control strategy has advantages over traditional periodic control in communication

A collaboration scheme for controlling multimanipulator system: A game-theoretic perspective

In some task-oriented multimanipulator applications, the system not only needs to complete the main assigned tasks, but also should optimize some subobjectives. In order to tap the redundancy potential of individual manipulators and improve the performance of the system, a hybrid multiobjective optimization solution with robustness is proposed in accordance with the realistic execution requirements of the tasks. The entire control scheme is designed from the perspective of the Nash game and further refined into a problem to determine the Nash equilibrium point. Furthermore, a neural-network-assisted model is established to seek the best response of each manipulator to others. Theoretical analysis provides support for proving the convergence and robustness of the model. Finally, the feasibility of the control design is illustrated by simulation studies of the multimanipulator system

Learning an Autonomous Dynamic System to Encode Periodic Human Motion Skills.

Learning an autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for human motion skills transfer. However, most existing approaches focus on goal-directed motion skills transfer, and the study on periodic motion skills transfer is rare. One popular approach for periodic motion skills transfer is learning periodic dynamic movement primitive (DMP); however, periodic DMP is sensitive to spatial disturbances due to the introduction of the phase parameters. To solve this issue, this brief presents a novel approach to learn an ADS with a stable limit cycle without introducing phase parameters. First, a data-driven Lyapunov function (energy function) is learned, such that one of its level surfaces is consistent with periodic human demonstration trajectories. Then, an ADS is learned by sequentially solving energy function-related constrained optimization problems. With a proper design of constraint functions, we can ensure that the trajectory generated by the ADS will converge to an energy function-level surface, of which the shape is similar to periodic human demonstration trajectories. Experiments are conducted to show the effectiveness of the proposed approach (PA)

A fast and robust deep convolutional neural networks for complex human activity recognition using smartphone

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. As a significant role in healthcare and sports applications, human activity recognition (HAR) techniques are capable of monitoring humans’ daily behavior. It has spurred the demand for intelligent sensors and has been giving rise to the explosive growth of wearable and mobile devices. They provide the most availability of human activity data (big data). Powerful algorithms are required to analyze these heterogeneous and high-dimension streaming data efficiently. This paper proposes a novel fast and robust deep convolutional neural network structure (FR-DCNN) for human activity recognition (HAR) using a smartphone. It enhances the effectiveness and extends the information of the collected raw data from the inertial measurement unit (IMU) sensors by integrating a series of signal processing algorithms and a signal selection module. It enables a fast computational method for building the DCNN classifier by adding a data compression module. Experimental results on the sampled 12 complex activities dataset show that the proposed FR-DCNN model is the best method for fast computation and high accuracy recognition. The FR-DCNN model only needs 0.0029 s to predict activity in an online way with 95.27% accuracy. Meanwhile, it only takes 88 s (average) to establish the DCNN classifier on the compressed dataset with less precision loss 94.18%

Whole exome sequencing identifies frequent somatic mutations in cell-cell adhesion genes in chinese patients with lung squamous cell carcinoma

Lung squamous cell carcinoma (SQCC) accounts for about 30% of all lung cancer cases. Understanding of mutational landscape for this subtype of lung cancer in Chinese patients is currently limited. We performed whole exome sequencing in samples from 100 patients with lung SQCCs to search for somatic mutations and the subsequent target capture sequencing in another 98 samples for validation. We identified 20 significantly mutated genes, including TP53, CDH10, NFE2L2 and PTEN. Pathways with frequently mutated genes included those of cell-cell adhesion/Wnt/Hippo in 76%, oxidative stress response in 21%, and phosphatidylinositol-3-OH kinase in 36% of the tested tumor samples. Mutations of Chromatin regulatory factor genes were identified at a lower frequency. In functional assays, we observed that knockdown of CDH10 promoted cell proliferation, soft-agar colony formation, cell migration and cell invasion, and overexpression of CDH10 inhibited cell proliferation. This mutational landscape of lung SQCC in Chinese patients improves our current understanding of lung carcinogenesis, early diagnosis and personalized therapy