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Towards Understanding Variation-Constrained Deep Neural Networks

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 631-640页

作者： Li, Gen Ding, Jie Univ Penn Wharton Sch Dept Stat & Data Sci Philadelphia PA 19104 USA Univ Minnesota Twin Cities Sch Stat Minneapolis MN 55455 USA

Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. A fundamental problem is understanding the generalizability of a neural network model through its statistical risk, or the expected test error. In particular, it is important to understand the phenomenon that overparameterized deep neural networks may not suffer from overfitting when the number of neurons and learning parameters rapidly grow with n or even surpass n. In this paper, we show that a class of variation-constrained regression neural networks, with arbitrary width, can achieve a near-parametric rate n(-1/2+d) for an arbitrarily small positive constant d. It is equivalent to n(-1+2d) under the mean squared error. This rate is also observed from numerical experiments. The result provides an insight into the benign overparameterization phenomenon. It indicates that the number of trainable parameters may not be a suitable complexity measure as often perceived for classical regression models. We also discuss the convergence rate regarding other network parameters, including the input dimension, network layer, and coefficient norm.

关键词： Biological neural networks complexity theory Deep learning Neurons Feedforward neural networks Data models Convergence model complexity neural network statistical risk

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Calibrated initials for an EM applied to recursive models of categorical variables

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2002年第1期40卷 97-110页

作者： Kim, SH Korea Adv Inst Sci & Technol Div Appl Math Taejon 305701 South Korea

The estimates from an EM, when it is applied to a large causal model of 10 or more categorical variables, are often subject to the initial values for the estimates. This phenomenon becomes more serious as the model structure becomes more complicated involving more variables. As a measure of compensation for this, it has been recommended in literature that EMs are implemented several times with different sets of initial values to obtain more appropriate estimates. We propose an improved approach for initial values. The main idea is that we use initials that are calibrated to data. A simulation result strongly indicates that the calibrated initials give rise to the estimates that are far closer to the true values than the initials that are not calibrated. (C) 2002 Published by Elsevier Science B.V.

关键词： calibrated initial values directed acyclic graph euclidean distance model complexity model structure randomly selected initial values root nodes and terminal nodes subjective probability well-calibrated

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Sequence-to-Sequence Load Disaggregation Using Multiscale Residual Neural Network

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2021年 70卷 1-10页

作者： Zhou, Gan Li, Zhi Fu, Meng Feng, Yanjun Wang, Xingyao Huang, Chengwei Southeast Univ Sch Elect Engn Nanjing 210096 Peoples R China Southeast Univ Sch Instrument Sci & Engn Nanjing 210096 Peoples R China Jiangsu Intever Energy Technol Co Ltd Nanjing 211100 Peoples R China

With the increased demand on economy and efficiency of measurement technology, nonintrusive load monitoring (NILM) has received more and more attention as a cost-effective way to monitor electricity and provide feedback to users. Deep neural networks have been showing a great potential in the field of load disaggregation. In this article, first, a new convolutional model based on residual blocks is proposed to avoid the degradation problem whose traditional networks more or less suffer from when network layers are increased in order to learn more complex features. Second, we propose dilated convolution to curtail the excessive quantity of model parameters and obtain bigger receptive field and multiscale structure to learn mixed data features in a more targeted way. Third, we give details about generating training and test set under certain rules. Finally, the algorithm is tested on real-house public data set, UK Domestic Application Level Electric (UK-DALE), with three existing neural networks. The results are compared and analyzed, and the proposed model shows improvements on F1 score, MAE, as well as model complexity across different appliances.

关键词： Load disaggregation model complexity multiscale nonintrusive load monitoring (NILM) residual neural network

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Integer quadratic programming model for dynamic VAR compensation considering short-term voltage stability

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第5期13卷 652-661页

作者： Wu, Liang Guan, Lin South China Univ Technol Sch Elect Power Guangzhou Guangdong Peoples R China

Dynamic VAR compensation (DVC) planning is important in power system planning to enhance short-term voltage stability. However, since its optimisations models include differential algebraic equations (DAEs), existing methods cannot directly solve the problem as that in the optimal power flow problem. In this study, the authors design an integer quadratic programming (IQP) model for the DVC planning problem which can simultaneously optimise the sites and size of DVCs. On the basis of the defined dynamic correlation indices, a quadratic programming objective function is defined to minimise the total investment of DVCs as well as to avoid redundant installation of DVCs on adjacent buses. Subsequently, sensitivity coefficients about the control effect of DVCs are introduced to form the linear inequations as the substitute for DAEs in constraints. Then, an iterative process is applied to solve the IQP. The proposed method is applied on a modified NE 39-bus system and a real power grid. Comparisons to the existing methods are carried out to show its superiority in model complexity and solving efficiency.

关键词： differential algebraic equations integer programming iterative methods load flow power system stability quadratic programming optimisation power grids DAEs optimal power flow problem integer quadratic programming model DVC planning problem defined dynamic correlation indices quadratic programming objective function modified NE 39-bus system power grid model complexity solving efficiency IQP model short-term voltage stability dynamic VAR compensation planning power system planning optimisations models differential algebraic equations

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Comparative evaluation of MILP flowshop models

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2005年第1期56卷 88-101页

作者： Stafford, EF Tseng, FT Gupta, JND Univ Alabama Dept Econ & Finance Huntsville AL 35899 USA Univ Alabama Dept Accounting & Management Informat Syst Huntsville AL USA

This paper investigates the performance of two families of mixed-integer linear programing (MILP) models for solving the regular permutation flowshop problem to minimize makespan. The three models of the Wagner family incorporate the assignment problem while the five members of the Manne family use pairs of dichotomous constraints, or their mathematical equivalents, to assign jobs to sequence positions. For both families, the problem size complexity and computational time required to optimally solve a common set of problems are investigated. In so doing, this paper extends the application of MILP approaches to larger problem sizes than those found in the existing literature. The Wagner models require more than twice the binary variables and more real variables than do the Manne models, while Manne models require more constraints for the same sized problems. All Wagner models require much less computational time than any of the Manne models for solving the common set of problems, and these differences increase dramatically with increasing number of jobs and machines. Wagner models can solve problems containing larger numbers of machines and jobs than the Manne models, and hence are preferable for finding optimal solutions to the permutation. owshop problem with makespan objective.

关键词： flowshop scheduling integer programming model complexity empirical evaluation Wagner models Manne models

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Mass and heat balances for biological nitrogen removal in an activated sludge process: to couple or not to couple?

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ENVIRONMENTAL TECHNOLOGY 2021年第26期42卷 4047-4056页

作者： Corbala-Robles, L. Volcke, E. I. P. Univ Ghent Dept Green Chem & Technol Biosyst Control BioCo Res Unit Coupure Links 653 B-9000 Ghent Belgium

models adapt constantly, usually increasing the degree of detail describing physical phenomena. In water resource recovery facilities, models based on mass and/or heat balances have been used to describe and improve operation. While both mass and heat balances have proven their worth individually, the question arises to which extent their coupling, which entails increased model complexity, warrants the supposedly more precise simulation results. In order to answer this question, the need for and effects of coupling mass and heat balances in modelling studies were evaluated in this work for a biological nitrogen removal process treating highly concentrated wastewater. This evaluation consisted on assessing the effect of the coupling of mass and heat balances on the prediction of: (1) nitrogen removal efficiency;(2) temperature;(3) heat recovery. In general, mass balances are sufficient for evaluating nitrogen removal efficiency and effluent nitrogen concentrations. If one desires to evaluate the effect of temperature changes (e.g. daily, weekly, seasonally) on nitrogen removal efficiency, the use of temperature profiles as an input variable to a mass balance-based model is recommended over the coupling of mass and heat balances. In terms of temperature prediction, considering a constant biological heat generation term in the heat balance model provides sufficient information - i.e. without the coupling of mass and heat balances. Also, for evaluating the heat recovery potential of the system, constant biological heat generation values provide valuable information, at least under normal operating conditions, i.e. when the solids retention time is large enough to maintain nitrification.

关键词： modelling model complexity wastewater treatment nitrification heat recovery

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The optimal size of dynamic phosphorus models for Baltic coastal areas

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ECOLOGICAL modelLING 2008年第3-4期216卷 303-315页

作者： Malmaeus, J. M. Eklund, J. M. Karlsson, O. M. Lindgren, D. IVL Svenska Miljoinst AB S-10031 Stockholm Sweden Dept Earth Sci S-75236 Uppsala Sweden

6 models for phosphorus and chlorophyll of different complexity were applied in 11 Swedish coastal areas. The number of state variables varied between I in the simplest model to 7 in the most complex. The results were compared for total phosphor-us and chlorophyll in surface water compartments. The results imply that for the studied water bodies, models containing separate state variables for phosphorus in surface water and deep water are superior to models treating the water column as a completely mixed entity. The results do not justify separation of phosphorus into dissolved and particulate fractions. modeling chlorophyll as a separate state variable did not improve the results for individual values compared to a simple regression against total phosphorus in surface water. Unless detailed descriptions or predictions of chlorophyll dynamics are required, modeling eutrophication in coastal areas may thus be considered as a matter of total phosphorus in two water compartments plus sediments. (C) 2008 Elsevier B.V. All rights reserved.

关键词： phosphorus ecosystem model coastal model model complexity water management

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Robust sequential high-resolution range profile recognition based on the infinite conditional restricted Boltzmann machine

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IET RADAR SONAR AND NAVIGATION 2020年第1期14卷 71-80页

作者： Gao, Xunzhang Peng, Xuan Natl Univ Def Technol Coll Elect Sci Changsha Peoples R China Natl Univ Def Technol Coll Meteorol & Oceanog Nanjing 211101 Peoples R China

Feature extraction for radar high-resolution range profiles (HRRPs) is an essential procedure for robust target recognition based on radar HRRPs. It is almost always better to utilise multiple HRRPs from the target than a single HRRP. The commonly used recognition techniques are not robust enough to extract features from HRRP sequences, especially when there is not enough training data. In this study, the authors present a compact model named the infinite conditional restricted Boltzmann machine (iCRBM) for jointly feature learning and recognition of radar HRRPs. The model is developed from the conditional restricted Boltzmann machine, which is a powerful model for representing high-dimensional and multi-modal conditional distributions. Unlike ordinary RBMs, iCRBM can automatically select the model complexity according to the data, which especially suits for the case of large data dimensionality and small training dataset. A multi-scale structure is also proposed for learning multiple scales of temporal/spatial dependencies. Two types of radar HRRP recognition experiments were conducted to validate the efficiency and robustness of iCRBM: the multi-view HRRP recognition and the small aperture HRRP recognition. The results indicate that, the proposed model can be more adaptive at learning the feature of HRRPs than other common methods. The multi-scale structure is helpful for better recovering missing HRRP samples from non-consecutive sequences.

关键词： learning (artificial intelligence) feature extraction radar resolution radar target recognition radar computing Boltzmann machines radar theory robust sequential high-resolution range profile recognition infinite conditional restricted Boltzmann machine feature extraction radar high-resolution range profiles robust target recognition single HRRP HRRP sequences iCRBM jointly feature learning multimodal conditional distributions model complexity data dimensionality multiscale structure radar HRRP recognition experiments robustness aperture HRRP recognition recovering missing HRRP samples multiple HRRP radar HRRP

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Reduced support vector machines: A statistical theory

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2007年第1期18卷 1-13页

作者： Lee, Yuh-Jye Huang, Su-Yun Natl Taiwan Univ Sci & Technol Dept Comp Sci & Informat Engn Taipei 106 Taiwan Acad Sinica Inst Stat Sci Taipei 115 Taiwan

In dealing with large data sets, the reduced support vector machine (RSVM) was proposed for the practical objective to overcome some computational difficulties as well as to reduce the model complexity. In this paper, we study the RSVM from the viewpoint of sampling design, its robustness, and the spectral analysis of the reduced kernel. We consider the nonlinear separating surface as a mixture of kernels. Instead of a full model, the RSVM uses a reduced mixture with kernels sampled from certain candidate set. Our main results center on two major themes. One is the robustness of the random subset mixture model. The other is the spectral analysis of the reduced kernel. The robustness is judged by a few criteria as follows: 1) model variation measure;2) model bias (deviation) between the reduced model and the full model;and 3) test power in distinguishing the reduced model from the full one. For the spectral analysis, we compare the eigenstructures of the full kernel matrix and the approximation kernel matrix. The approximation kernels are generated by uniform random subsets. The small discrepancies between them indicate that the approximation kernels can retain most of the relevant information for learning tasks in the full kernel. We focus on some statistical theory of the reduced set method mainly in the context of the RSVM. The use of a uniform random subset is not limited to the RSVM. This approach can act as a supplemental algorithm on top of a basic optimization algorithm, wherein the actual optimization takes place on the subset-approximated data. The statistical properties discussed in this paper are still valid.

关键词： canonical angles kernel methods maximinity minimaxity model complexity Monte Carlo sampling Nystrom approximation reduced set spectral analysis support vector machines (SVMs) uniform design uniform random subset

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Parameter and predictive outcomes of model simplification

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WATER RESOURCES RESEARCH 2013年第7期49卷 3952-3977页

作者： Watson, Ty A. Doherty, John E. Christensen, Steen Flinders Univ S Australia Natl Ctr Groundwater Res & Training Adelaide SA 5001 Australia Flinders Univ S Australia Sch Environm Adelaide SA 5001 Australia Watermark Numer Comp Corinda Qld Australia Aarhus Univ Dept Geosci Aarhus Denmark

Simplification is an unavoidable aspect of model usage. Even complex, physically based models are simplifications of reality. More profound simplification is required to construct the lumped parameter models of semiphysical basis that are often employed for simulation of large-scale processes operative over one or many watersheds. Simplification can lead to model predictive error beyond that which would be expected on the basis of study-area information deficits alone. Building on a recently developed mathematical description of the model simplification process, this work employs linear subspace methods to analyze in detail the nature and ramifications of that process when applied to a 1-D, Richards equation-based unsaturated zone model used to predict recharge to a groundwater system. Two simplified versions of this model are examined. The first achieves simplification through assuming vertical parameter uniformity. The second achieves simplification through use of a lumped parameter model in place of the Richards equation-based model. Relationships between parameters employed by the complex model and those used by each of the simplified models are analyzed. The nature of predictive errors incurred through simplification is explored. Also explored is the ability of the calibration process to decrease the propensity for model error in making some predictions, while increasing the propensity for model error in the making of others (an outcome that may be considered counterintuitive from a Bayesian perspective, but which is a natural consequence of suboptimal simplification).

关键词： parameter estimation uncertainty analysis calibration model simplification model complexity paired model analysis

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