Contour regression: A general approach to dimension reduction

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response, leading to simple and general contour regression (SCR and GCR) methodology. In comparison with existing sufficient dimension reduction techniques, this contour-based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions, while maintaining \sqrtn-consistency and computational ease. Moreover, it proves robust to departures from ellipticity. We establish population properties for both SCR and GCR, and asymptotic properties for SCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal Hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses. We demonstrate the use of contour-based methods on a data set concerning soil evaporation.Comment: Published at http://dx.doi.org/10.1214/009053605000000192 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discretize Relaxed Solution of Spectral Clustering via a Non-Heuristic Algorithm

Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization techniques are mainly heuristic methods, e.g., k-means, spectral rotation. Unfortunately, the goal of the existing methods is not to find a discrete solution that minimizes the original objective. In other words, the primary drawback is the neglect of the original objective when computing the discrete solution. Inspired by the first-order optimization algorithms, we propose to develop a first-order term to bridge the original problem and discretization algorithm, which is the first non-heuristic to the best of our knowledge. Since the non-heuristic method is aware of the original graph cut problem, the final discrete solution is more reliable and achieves the preferable loss value. We also theoretically show that the continuous optimum is beneficial to discretization algorithms though simply finding its closest discrete solution is an existing heuristic algorithm which is also unreliable. Sufficient experiments significantly show the superiority of our method

Self-Paced Multi-Task Learning

In this paper, we propose a novel multi-task learning (MTL) framework, called Self-Paced Multi-Task Learning (SPMTL). Different from previous works treating all tasks and instances equally when training, SPMTL attempts to jointly learn the tasks by taking into consideration the complexities of both tasks and instances. This is inspired by the cognitive process of human brain that often learns from the easy to the hard. We construct a compact SPMTL formulation by proposing a new task-oriented regularizer that can jointly prioritize the tasks and the instances. Thus it can be interpreted as a self-paced learner for MTL. A simple yet effective algorithm is designed for optimizing the proposed objective function. An error bound for a simplified formulation is also analyzed theoretically. Experimental results on toy and real-world datasets demonstrate the effectiveness of the proposed approach, compared to the state-of-the-art methods

Critical natural frequency: an improved empirical effectiveness criterion in vibration stress relief of rectangle welded plates

Decreasing of natural frequency of the treated structure is the most frequently used empirical effectiveness criteria in vibration stress relief (VSR). However, dependability and reliability of this criteria is still far from sufficient. In this study, a covert negative treatment phenomenon was investigated, i.e. natural frequency of welded structures decreased after VSR but residual stress in one direction increased. Relationship between natural frequency and residual stresses was studied by mathematical deduction and finite element method. “Natural Frequency Function” and “Natural Frequency Surface (NFS)” was proposed to describe that relationship. “Critical Natural Frequency” (CNF) was proposed to depict possible situations after VSR. A quantitative natural frequency criterion for VSR effectiveness estimation was proposed

Hessian-Free High-Resolution Nesterov Acceleration for Sampling

We propose an accelerated-gradient-based MCMC method. It relies on a modification of the Nesterov's accelerated gradient method for strongly convex functions (NAG-SC): We first reformulate NAG-SC as a Hessian-Free High-Resolution ODE, then release the high-resolution coefficient as a free hyperparameter, and finally inject appropriate noise and discretize the diffusion process. Accelerated sampling enabled by this new hyperparameter is not only experimentally demonstrated on several learning tasks, but also theoretically quantified, both at the continuous level and after discretization. For (not-necessarily-strongly-) convex and $L$-smooth potentials, exponential convergence in $\chi^2$ divergence is proved, with a rate analogous to state-of-the-art results of underdamped Langevin dynamics, plus an additional acceleration. At the same time, the method also works for nonconvex potentials, for which we also establish exponential convergence as long as the potential satisfies a Poincar\'e inequality

Analysis of Thermal Environment in a Hospital Operating Room

AbstractThis paper presents a computational fluid dynamics (CFD) study for thermal comfort in a hospital operating room. The research aims to analyze indoor thermal comfort using the predicted mean vote (PMV) model which has been presented by ISO7730. The room model includes a patient lying on an operating table with a surgical staff of six members standing around under surgical lights. The airflow is supplied to the room from the ceiling diffuser and exhausted through low-level side walls on both sides. Solutions of distribution of airflow velocity, temperature, relative humidity and so on are presented and discussed. The PMV and PPD are calculated for assessing thermal comfort based on TCM model. The simulation results show that the values of PMV and PPD in some parts of human body are not within the standard acceptable range defined by ISO, but its comfortableness satisfies China national standard GB/T18049 request. It is found that TCM model is a more comprehensive model for thermal comfort analysis

Variational Positive-incentive Noise: How Noise Benefits Models

A large number of works aim to alleviate the impact of noise due to an underlying conventional assumption of the negative role of noise. However, some existing works show that the assumption does not always hold. In this paper, we investigate how to benefit the classical models by random noise under the framework of Positive-incentive Noise (Pi-Noise). Since the ideal objective of Pi-Noise is intractable, we propose to optimize its variational bound instead, namely variational Pi-Noise (VPN). With the variational inference, a VPN generator implemented by neural networks is designed for enhancing base models and simplifying the inference of base models, without changing the architecture of base models. Benefiting from the independent design of base models and VPN generators, the VPN generator can work with most existing models. From the experiments, it is shown that the proposed VPN generator can improve the base models. It is appealing that the trained variational VPN generator prefers to blur the irrelevant ingredients in complicated images, which meets our expectations