Machine learning has evolved into an enabling technology for a wide range of highly successful applications. The potential for this success to continue and accelerate has placed machine learning (ML) at the top of research, economic and political agendas. Such unprecedented interest is fuelled by a vision of ML applicability extending to healthcare, transportation, defence and other domains of great societal importance. Achieving this vision requires the use of ML in safety-critical applications that demand levels of assurance beyond those needed for current ML applications. Our paper provides a comprehensive survey of the state-of-the-art in the assurance of ML, i.e. in the generation of evidence that ML is sufficiently safe for its intended use. The survey covers the methods capable of providing such evidence at different stages of the machine learning lifecycle, i.e. of the complex, iterative process that starts with the collection of the data used to train an ML component for a system, and ends with the deployment of that component within the system. The paper begins with a systematic presentation of the ML lifecycle and its stages. We then define assurance desiderata for each stage, review existing methods that contribute to achieving these desiderata, and identify open challenges that require further research.

Assuring the Machine Learning Lifecycle: Desiderata, Methods, and Challenges.

Machine learning has evolved into an enabling technology for a wide range of highly successful applications. The potential for this success to continue and accelerate has placed machine learning (ML) at the top of research, economic, and political agendas. Such unprecedented interest is fuelled by a vision of ML applicability extending to healthcare, transportation, defence, and other domains of great societal importance. Achieving this vision requires the use of ML in safety-critical applications that demand levels of assurance beyond those needed for current ML applications. Our article provides a comprehensive survey of the state of the art in the assurance of ML, i.e., in the generation of evidence that ML is sufficiently safe for its intended use. The survey covers the methods capable of providing such evidence at different stages of the machine learning lifecycle, i.e., of the complex, iterative process that starts with the collection of the data used to train an ML component for a system, and ends with the deployment of that component within the system. The article begins with a systematic presentation of the ML lifecycle and its stages. We then define assurance desiderata for each stage, review existing methods that contribute to achieving these desiderata, and identify open challenges that require further research.

https://dl.acm.org/doi/pdf/10.1145/3453444

Assuring the Machine Learning Lifecycle: Desiderata, Methods, and Challenges

Recently, the approach based on recurrent neural network (RNN) has been considered a powerful alternative to mathematical problem solving. In this study, a new discrete-time RNN (DTRNN) is proposed and investigated to determine an exact solution of dynamic nonlinear equations. Specifically, the resultant DTRNN model is established for solving dynamic nonlinear equations by utilizing a Taylor-type difference rule. This DTRNN model is then theoretically proven to have an $O(\tau ^4)$ error pattern, where $\tau$ denotes the sampling gap. Comparative numerical results are illustrated to further substantiate the efficacy and superiority of the proposed DTRNN model in comparison with the existing approach. Finally, the proposed DTRNN model is applied to redundant robot manipulators by solving the system of dynamic nonlinear kinematic equations, indicating the application prospect of the proposed model.

Design, Verification, and Application of New Discrete-Time Recurrent Neural Network for Dynamic Nonlinear Equations Solving

Nonlinear phenomena are often encountered in various practical systems, and most of the nonlinear problems in science and engineering can be simply described by nonlinear equation, effectively solving nonlinear equation (NE) has aroused great interests of the academic and industrial communities. In this paper, a robust zeroing neural network (RZNN) activated by a new power versatile activation function (PVAF) is proposed and analyzed for finding the solutions of dynamic nonlinear equations (DNE) within fixed time in noise polluted environment. As compared with the previous ZNN model activated by other commonly used activation functions (AF), the main improvement of the presented RZNN model is the fixed-time convergence even in the presence of noises. In addition, the convergence time of the proposed RZNN model is irrelevant to its initial states, and it can be computed directly. Both the rigorous mathematical analysis and numerical simulation results are provided for the verification of the effectiveness and robustness of the proposed RZNN model. Moreover, a successful robotic manipulator path tracking example in noise polluted environment further demonstrates the practical application prospects of the proposed RZNN models.

/pdf/a-robust-zeroing-neural-network-for-solving-dynamic-zec20yhbtk.pdf

A robust zeroing neural network for solving dynamic nonlinear equations and its application to kinematic control of mobile manipulator

To locate a locally-unique solution of a nonlinear equation, the local convergence analysis of a derivative-free fifth order method is studied in Banach space. This approach provides radius of convergence and error bounds under the hypotheses based on the first Frechet-derivative only. Such estimates are not introduced in the earlier procedures employing Taylor’s expansion of higher derivatives that may not exist or may be expensive to compute. The convergence domain of the method is also shown by a visual approach, namely basins of attraction. Theoretical results are endorsed via numerical experiments that show the cases where earlier results cannot be applicable.

https://www.mdpi.com/2227-7390/7/10/919/pdf

Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method

A fast and efficient composite Newton–Chebyshev method for systems of nonlinear equations

This paper presents the development and mechanical characterization of hybrid composite consisting of glass fiber and aluminum oxide (Al2O3) particles reinforced with epoxy matrix The hybrid Glass Fiber Reinforced Polymer (GFRP) composite has been fabricated using different weight fractions (20%, 30%, and 40%) and different particles size (20 µm, 40 µm and 60 µm) of Al2O3 along with chopped E-glass fiber reinforced with epoxy resin matrix, following the hand lay-up method Further, the mechanical characterization has been carried out through tensile test, impact test, and bending test The effect of process parameters on mechanical properties of the composite has been studied using response surface methodology (RSM) and analysis of variance (ANOVA) It has been found that an increase in weight percentage of Al2O3 particles improves the mechanical properties However, the increase in size of Al2O3 particles shows an adverse effect on mechanical properties The results have been optimized using the desirability function approach, and validated through a confirmation test

Fabrication and mechanical characterization of glass fiber/Al2O3 hybrid-epoxy composite

We study the local convergence of a fifth-order Newton–Gauss method in order to approximate a locally-unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the fifth derivative or even higher, although only the first derivatives are used in the method. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies can not apply.

Ball convergence of the Newton–Gauss method in Banach space

Supervised transfer learning algorithms utilize labeled data from auxiliary domains for learning in another domain where labeled data is scarce or absent. Given sufficient cross-domain corresponding instances, one can learn a robust transformation that maps the features across the domains by using any multi-output regression task. However, this cross-domain corresponding data is not available for real-world transfer tasks across heterogeneous feature spaces such as, cross-domain activity recognition and cross-lingual text/sentiment classification. In this paper, we present a shared label space driven algorithm that transfers labeled knowledge between heterogeneous feature spaces. The proposed algorithm treats the similar label distributions across the domains as pivots to generate cross-domain corresponding data. The shared label distributions and the corresponding data is obtained from the random forest models of the source and target domain. The experimental results on synthetic and real-world benchmark datasets having dissimilar modalities validate the performance of the proposed algorithm against state-of-the-art heterogeneous transfer learning approaches.

Deepak Kumar

Papers

A fast and efficient composite Newton–Chebyshev method for systems of nonlinear equations

Fabrication and mechanical characterization of glass fiber/Al2O3 hybrid-epoxy composite

Ball convergence of the Newton–Gauss method in Banach space

Supervised heterogeneous transfer learning using random forests

On a general class of optimal order multipoint methods for solving nonlinear equations