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CNN originates from image processing and is not commonly known as a forecasting technique in time-series analysis which depends on the quality of input data. One of the methods to improve the quality is by smoothing the data. This study introduces a novel hybrid exponential smoothing using CNN called Smoothed-CNN (S-CNN). The method of combining tactics outperforms the majority of individual solutions in forecasting. The S-CNN was compared with the original CNN method and other forecasting methods such as Multilayer Perceptron (MLP) and Long Short-Term Memory (LSTM). The dataset is a year time-series of daily website visitors. Since there are no special rules for using the number of hidden layers, the Lucas number was used. The results show that S-CNN is better than MLP and LSTM, with the best MSE of 0.012147693 using 76 hidden layers at 80%:20% data composition.

In numerical simulations such as computational fluid dynamics simulations or finite element analyses, mesh quality affects simulation accuracy directly and significantly. Smoothing is one of the most widely adopted methods to improve unstructured mesh quality in mesh generation practices. Compared with the optimization-based smoothing method, heuristic smoothing methods are efficient but yield lower mesh quality. The balance between smoothing efficiency and mesh quality has been pursued in previous studies. In this paper, we propose a new smoothing method that combines the advantages of the heuristic Laplacian method and the optimization-based method based on the deep reinforcement learning method under the Deep Deterministic Policy Gradient framework. Within the framework, the actor artificial neural network predicts the optimal position of each interior free node with its surrounding ring nodes. At the same time, a critic-network is established and takes the mesh quality as input and outputs the reward of the action taken by the actor-network. Training of the networks will maximize the cumulative long-term reward, which ends up maximizing the mesh quality. Training and validation of the proposed method are presented both on 2-dimensional triangular meshes and 3-dimensional surface meshes, which demonstrates the efficiency and mesh quality of the proposed method. Finally, numerical simulations on perturbed meshes and smoothed meshes are carried out and compared which prove the influence of mesh quality on the simulation accuracy.

Recent work by Reiss and Ogden provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross-validation (GCV) for smoothing parameter selection in semiparametric regression. However, existing REML or marginal likelihood (ML) based methods for semiparametric generalized linear models (GLMs) use iterative REML or ML estimation of the smoothing parameters of working linear approximations to the GLM. Such indirect schemes need not converge and fail to do so in a non-negligible proportion of practical analyses. By contrast, very reliable prediction error criteria smoothing parameter selection methods are available, based on direct optimization of GCV, or related criteria, for the GLM itself. Since such methods directly optimize properly defined functions of the smoothing parameters, they have much more reliable convergence properties. The paper develops the first such method for REML or ML estimation of smoothing parameters. A Laplace approximation is used to obtain an approximate REML or ML for any GLM, which is suitable for efficient direct optimization. This REML or ML criterion requires that Newton-Raphson iteration, rather than Fisher scoring, be used for GLM fitting, and a computationally stable approach to this is proposed. The REML or ML criterion itself is optimized by a Newton method, with the derivatives required obtained by a mixture of implicit differentiation and direct methods. The method will cope with numerical rank deficiency in the fitted model and in fact provides a slight improvement in numerical robustness on the earlier method of Wood for prediction error criteria based smoothness selection. Simulation results suggest that the new REML and ML methods offer some improvement in mean-square error performance relative to GCV or Akaike's information criterion in most cases, without the small number of severe undersmoothing failures to which Akaike's information criterion and GCV are prone. This is achieved at the same computational cost as GCV or Akaike's information criterion. The new approach also eliminates the convergence failures of previous REML- or ML-based approaches for penalized GLMs and usually has lower computational cost than these alternatives. Example applications are presented in adaptive smoothing, scalar on function regression and generalized additive model selection.

Background Fatal opioid-involved overdose rates increased precipitously from 5.0 per 100,000 population to 33.5 in Massachusetts between 1999 and 2022. Methods We used spatial rate smoothing techniques to identify persistent opioid overdose-involved fatality clusters at the ZIP Code Tabulation Area (ZCTA) level. Rate smoothing techniques were employed to identify locations of high fatal opioid overdose rates where population counts were low. In Massachusetts, this included areas with both sparse data and low population density. We used Local Indicators of Spatial Association (LISA) cluster analyses with the raw incidence rates, and the Empirical Bayes smoothed rates to identify clusters from 2011 to 2021. We also estimated Empirical Bayes LISA cluster estimates to identify clusters during the same period. We constructed measures of the socio-built environment and potentially inappropriate prescribing using principal components analysis. The resulting measures were used as covariates in Conditional Autoregressive Bayesian models that acknowledge spatial autocorrelation to predict both, if a ZCTA was part of an opioid-involved cluster for fatal overdose rates, as well as the number of times that it was part of a cluster of high incidence rates. Results LISA clusters for smoothed data were able to identify whether a ZCTA was part of a opioid involved fatality incidence cluster earlier in the study period, when compared to LISA clusters based on raw rates. PCA helped in identifying unique socio-environmental factors, such as minoritized populations and poverty, potentially inappropriate prescribing, access to amenities, and rurality by combining socioeconomic, built environment and prescription variables that were highly correlated with each other. In all models except for those that used raw rates to estimate whether a ZCTA was part of a high fatality cluster, opioid overdose fatality clusters in Massachusetts had high percentages of Black and Hispanic residents, and households experiencing poverty. The models that were fitted on Empirical Bayes LISA identified this phenomenon earlier in the study period than the raw rate LISA. However, all the models identified minoritized populations and poverty as significant factors in predicting the persistence of a ZCTA being part of a high opioid overdose cluster during this time period. Conclusion Conducting spatially robust analyses may help inform policies to identify community-level risks for opioid-involved overdose deaths sooner than depending on raw incidence rates alone. The results can help inform policy makers and planners about locations of persistent risk.

Continuous treatments (e.g. doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection. The methods are illustrated via simulation and in a study of the effect of nurse staffing on hospital readmissions penalties.

This article discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be present. By construction the method is numerically stable and convergent, and enables smoothing parameter uncertainty to be quantified. The latter enables us to fix a well known problem with AIC for such models, thereby improving the range of model selection tools available. The smooth functions are represented by reduced rank spline like smoothers, with associated quadratic penalties measuring function smoothness. Model estimation is by penalized likelihood maximization, where the smoothing parameters controlling the extent of penalization are estimated by Laplace approximate marginal likelihood. The methods cover, for example, generalized additive models for nonexponential family responses (e.g., beta, ordered categorical, scaled t distribution, negative binomial and Tweedie distributions), generalized additive models for location scale and shape (e.g., two stage zero inflation models, and Gaussian location-scale models), Cox proportional hazards models and multivariate additive models. The framework reduces the implementation of new model classes to the coding of some standard derivatives of the log-likelihood. Supplementary materials for this article are available online.

Image smoothing is a long-studied research area with tremendous approaches proposed. However, how to perform high-quality image smoothing with less computational cost still remains a challenging problem. In this paper, we try to solve this problem with a newly proposed global optimization based method named quasi weighted least squares. In our method, the 2D image is first re-ordered into a 1D vector via a newly proposed 2D-to-1D transformation. We then properly remove some original 2D neighborhood connections. The remaining neighboring pixels can simply form 1D neighborhood connections in the transformed 1D vector while they still contain the 2D neighborhood information in the original 2D image space. These together result in a quite compact linear system that can be easily and efficiently solved, which makes our method a fast global image smoothing approach. Our method is on par with the fastest approaches in terms of processing speed, however, it is able to yield comparable performance with the state-of-the-art ones in terms of smoothing quality. Our method can also work as a solver to approximate the weighted least squares problem in complex systems, and it can achieve similar results but runs much faster. The efficiency and effectiveness of our method are validated through comprehensive experiments in several tasks. Our code is publicly available at: https://github.com/wliusjtu/Q-WLS.

Conventional smoothing methods sometimes perform badly when used to smooth data over complex domains, by smoothing inappropriately across boundary features, such as peninsulas. Solutions to this smoothing problem tend to be computationally complex, and not to provide model smooth functions which are appropriate for incorporating as components of other models, such as generalized additive models or mixed additive models. We propose a class of smoothers that are appropriate for smoothing over difficult regions of [graphic removed] ² which can be represented in terms of a low rank basis and one or two quadratic penalties. The key features of these smoothers are that they do not 'smooth across' boundary features, that their representation in terms of a basis and penalties allows straightforward incorporation as components of generalized additive models, mixed models and other non-standard models, that smoothness selection for these model components is straightforward to accomplish in a computationally efficient manner via generalized cross-validation, Akaike's information criterion or restricted maximum likelihood, for example, and that their low rank means that their use is computationally efficient.

Since Deep Convolutional Generative Adversarial Networks (DCGAN) was proposed, it has been perceived as a model with difficulty in training due to several factors. To solve this problem, dozens of optimization strategies were presented, but none of them was compared with the others. In this paper, the author chose three representative methods, namely one-label smoothing, the two Time-Scale Update Rule (TTUR), and the Earth-Mover Distance (EMD) or Wasserstein-1 to make a comparison of the optimization effect on the DCGAN model. To be specific, these three approaches were adopted respectively while using MNIST and Fashion-MNIST as datasets. One-side label smoothing was designed to prevent overconfidence in the model by adding a penalty term in the discriminator. TTUR was a simpler update strategy that could help the model find the stationary local Nash equilibrium under mild assumptions. EMD was an alternative loss function that enabled the model to distinguish the difference while the real distribution and generated distribution were not overlapped. Contrast experiments were conducted both vertically and horizontally. The author applied these three methods with the same dataset and the same method with different datasets in order to compare the time of the model collapse, the trend of loss in line graphs, and the impact of different datasets on results. Experimental results indicated that both one-label smoothing and TTUR postponed the model collapse while EMD completely get rid of it. Furthermore, generated images may lose texture information when using more complicated datasets.