Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient dimension reduction methods often lack the scalability necessary for dealing with large-scale data. We propose a new type of stochastic neural network under a rigorous probabilistic framework and show that it can be used for sufficient dimension reduction for large-scale data. The proposed stochastic neural network is trained using an adaptive stochastic gradient Markov chain Monte Carlo algorithm, whose convergence is rigorously studied in the paper as well. Through extensive experiments on real-world classification and regression problems, we show that the proposed method compares favorably with the existing state-of-the-art sufficient dimension reduction methods and is computationally more efficient for large-scale data.

Recent years have witnessed the superiority of non-convex s parse learning formulations over their convex counterparts in both theory and pr actice. However, due to the non-convexity and non-smoothness of the regularizer, how to efficiently solve the non-convex optimization problem for large-scale data is still quite challenging. In this paper, we propose an efficient H ybrid O ptimization algorithm for NO n-convex R egularized problems (HONOR). Specifically, we develop a hybrid scheme which effectively integrates a Quasi-Newton (Q N) step and a Gradient Descent (GD) step. Our contributions are as follows: ( 1) HONOR incorporates the second-order information to greatly speed up th e convergence, while it avoids solving a regularized quadratic programming and o nly involves matrix-vector multiplications without explicitly forming the inv erse Hessian matrix.

Selecting relevant features is an important and necessary step for intelligent machines to maximize their chances of success. However, intelligent machines generally have no enough computing resources when faced with huge volume of data. This paper develops a new method based on sampling techniques and rough set theory to address the challenge of feature selection for massive data. To this end, this paper proposes using the ratio of discernible object pairs to all object pairs that should be distinguished to measure the discriminatory ability of a feature set. Based on this measure, a new feature selection method is proposed. This method constructs positive region preserved samples from massive data to find a feature subset with high discriminatory ability. Compared with other methods, the proposed method has two advantages. First, it is able to select a feature subset that can preserve the discriminatory ability of all the features of the target massive data set within an acceptable time on a personal computer. Second, the lower boundary of the probability of the object pairs that can be discerned using the feature subset selected in all object pairs that should be distinguished can be estimated before finding reducts. Furthermore, 11 data sets of different sizes were used to validate the proposed method. The results show that approximate reducts can be found in a very short period of time, and the discriminatory ability of the final reduct is larger than the estimated lower boundary. Experiments on four large-scale data sets also showed that an approximate reduct with high discriminatory ability can be obtained in reasonable time on a personal computer.

Weaknesses: Unfortunately, I strongly believe that this paper will have a very limited attraction from the research community since derivations are done for binary classification and the nearest neighbor classification is no longer popular as before as there are numerous good alternatives. To validate my claim, I looked at the recent Neurips 2019 paper cited as [45] which is quite similar to this paper. In one year, it is cited only once. This is quite natural in my opinion since deep neural networks dominated classification and there are good alternatives to the nearest neighbor classification for large-scale data as hashing, approximate nearest neighbor classification methods, etc. Especially, unsupervised and supervised hashing methods are quite popular for large-scale data with high-dimensional feature spaces. Therefore, I strongly believe that the impact of the paper is very limited and it will attract a very few attention from research community.

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient dimension reduction methods often lack the scalability necessary for dealing with large-scale data. We propose a new type of stochastic neural network under a rigorous probabilistic framework and show that it can be used for sufficient dimension reduction for large-scale data. The proposed stochastic neural network is trained using an adaptive stochastic gradient Markov chain Monte Carlo algorithm, whose convergence is rigorously studied in the paper as well. Through extensive experiments on real-world classification and regression problems, we show that the proposed method compares favorably with the existing state-of-the-art sufficient dimension reduction methods and is computationally more efficient for large-scale data.

Recent years have witnessed the superiority of non-convex sparse learning formulations over their convex counterparts in both theory and practice. However, due to the non-convexity and non-smoothness of the regularizer, how to efficiently solve the non-convex optimization problem for large-scale data is still quite challenging. Specifically, we develop a hybrid scheme which effectively integrates a Quasi-Newton (QN) step and a Gradient Descent (GD) step. Our contributions are as follows: (1) HONOR incorporates the second-order information to greatly speed up the convergence, while it avoids solving a regularized quadratic programming and only involves matrix-vector multiplications without explicitly forming the inverse Hessian matrix.

This paper addresses the problem of temperature and airflow regulation for a large-scale data center and considers how a data-driven, model-based approach using Reinforcement Learning (RL) might improve operational efficiency relative to the existing approach of hand-crafted PID controllers. Existing controllers in large-scale data centers tend to be simple, conservative and hand-tuned to physical equipment layouts and configurations. Safety constraints and a low tolerance for performance degradation and equipment damage impose additional constraints. The authors use model-predictive control (MPC) to learn a linear model of the data center dynamics (a LQ controller) using safe, random exploration, starting with little or no prior knowledge. They then determine the control actions at each time step by optimizing the cost of the model-predicted trajectories, ensuring to re-optimize at each time step.

Type-1 and Interval Type-2 (IT2) Fuzzy Logic Systems (FLS) excel in handling uncertainty alongside their parsimonious rule-based structure. Yet, in learning large-scale data challenges arise, such as the curse of dimensionality and training complexity of FLSs. The complexity is due mainly to the constraints to be satisfied as the learnable parameters define FSs and the complexity of the center of the sets calculation method, especially of IT2-FLSs. This paper explicitly focuses on the learning problem of FLSs and presents a computationally efficient learning method embedded within the realm of Deep Learning (DL). The proposed method tackles the learning challenges of FLSs by presenting computationally efficient implementations of FLSs, thereby minimizing training time while leveraging mini-batched DL optimizers and automatic differentiation provided within the DL frameworks. We illustrate the efficiency of the DL framework for FLSs on benchmark datasets.

Multiscale phenomena manifest across various scientific domains, presenting a ubiquitous challenge in accurately and effectively predicting multiscale dynamics in complex systems. In this paper, a novel decoupling solving mode is proposed through modelling large-scale dynamics independently and treating small-scale dynamics as a slaved system. A Spectral Physics-informed Neural Network (PINN) is developed to characterize the small-scale system in an efficient and accurate way. The effectiveness of the method is demonstrated through extensive numerical experiments, including one-dimensional Kuramot-Sivashinsky equation, two- and three-dimensional Navier-Stokes equations, showcasing its versatility in addressing problems of fluid dynamics. Furthermore, we also delve into the application of the proposed approach to more complex problems, including non-uniform meshes, complex geometries, large-scale data with noise, and high-dimensional small-scale dynamics. The discussions about these scenarios contribute to a comprehensive understanding of the method's capabilities and limitations. This paper presents a valuable and promising approach to enhance the computational simulations of multiscale spatiotemporal systems, which enables the acquisition of large-scale data with minimal computational demands, followed by Spectral PINN to capture small-scale dynamics with improved efficiency and accuracy.

Exploratory data analysis (EDA) is a vital procedure for data science projects. In this work, we introduce a stable equilibrium point (SEP) - based framework for improving the efficiency and solution quality of EDA. By exploiting the SEPs to be the representative points, our approach aims to generate high-quality clustering and data visualization for large-scale data sets. A very unique property of the proposed method is that the SEPs will directly encode the clustering properties of data sets. Compared with prior state-of-the-art clustering and data visualization methods, the proposed methods allow substantially improving computing efficiency and solution quality for large-scale data analysis tasks.