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Journal articles on the topic 'Regularized quantiles'

Author: Grafiati

Published: 7 December 2024

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1

Santos, Patricia Mendes dos, Ana Carolina Campana Nascimento, Moysés Nascimento, Fabyano Fonseca e. Silva, Camila Ferreira Azevedo, Rodrigo Reis Mota, Simone Eliza Facioni Guimarães, and Paulo Sávio Lopes. "Use of regularized quantile regression to predict the genetic merit of pigs for asymmetric carcass traits." Pesquisa Agropecuária Brasileira 53, no. 9 (September 2018): 1011–17. http://dx.doi.org/10.1590/s0100-204x2018000900004.

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Abstract: The objective of this work was to evaluate the use of regularized quantile regression (RQR) to predict the genetic merit of pigs for asymmetric carcass traits, compared with the Bayesian lasso (Blasso) method. The genetic data of the traits carcass yield, bacon thickness, and backfat thickness from a F2 population composed of 345 individuals, generated by crossing animals from the Piau breed with those of a commercial breed, were used. RQR was evaluated considering different quantiles (τ = 0.05 to 0.95). The RQR model used to estimate the genetic merit showed accuracies higher than or equal to those obtained by Blasso, for all studies traits. There was an increase of 6.7 and 20.0% in accuracy when the quantiles 0.15 and 0.45 were considered in the evaluation of carcass yield and bacon thickness, respectively. The obtained results are indicative that the regularized quantile regression presents higher accuracy than the Bayesian lasso method for the prediction of the genetic merit of pigs for asymmetric carcass variables.

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Bang, Sungwan, and Myoungshic Jhun. "Adaptive sup-norm regularized simultaneous multiple quantiles regression." Statistics 48, no. 1 (August 30, 2012): 17–33. http://dx.doi.org/10.1080/02331888.2012.719512.

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3

Zou, Hui, and Ming Yuan. "Regularized simultaneous model selection in multiple quantiles regression." Computational Statistics & Data Analysis 52, no. 12 (August 2008): 5296–304. http://dx.doi.org/10.1016/j.csda.2008.05.013.

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4

Nascimento, Ana Carolina Campana, Camila Ferreira Azevedo, Cynthia Aparecida Valiati Barreto, Gabriela França Oliveira, and Moysés Nascimento. "Quantile regression for genomic selection of growth curves." Acta Scientiarum. Agronomy 46, no. 1 (December 12, 2023): e65081. http://dx.doi.org/10.4025/actasciagron.v46i1.65081.

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This study evaluated the efficiency of genome-wide selection (GWS) based on regularized quantile regression (RQR) to obtain genomic growth curves based on genomic estimated breeding values (GEBV) of individuals with different probability distributions. The data were simulated and composed of 2,025 individuals from two generations and 435 markers randomly distributed across five chromosomes. The simulated phenotypes presented symmetrical, skewed, positive, and negative distributions. Data were analyzed using RQR considering nine quantiles (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9) and traditional methods of genomic selection (specifically, RR-BLUP, BLASSO, BayesA, and BayesB). In general, RQR-based estimation of the GEBV was efficient—at least for a quantile model, the results obtained were more accurate than those obtained by the other evaluated methodologies. Specifically, in the symmetrical-distribution scenario, the highest accuracy values were obtained for the parameters with the models RQR0.4, RQR0.3, and RQR0.4. For positive skewness, the models RQR0.2, RQR0.3, and RQR0.1 presented higher accuracy values, whereas for negative skewness, the best model was RQR0.9. Finally, the GEBV vectors obtained by RQR facilitated the construction of genomic growth curves at different levels of interest (quantiles), illustrating the weight–age relationship.

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Li, Jia, Viktor Todorov, and George Tauchen. "ESTIMATING THE VOLATILITY OCCUPATION TIME VIA REGULARIZED LAPLACE INVERSION." Econometric Theory 32, no. 5 (May 25, 2015): 1253–88. http://dx.doi.org/10.1017/s0266466615000171.

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We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in the second step, we conduct a regularized Laplace inversion. Monte Carlo evidence suggests that the proposed estimator has good small-sample performance and in particular it is far better at estimating lower volatility quantiles and the volatility median than a direct estimator formed from the empirical cumulative distribution function of local spot volatility estimates. An empirical application shows the use of the developed techniques for nonparametric analysis of variation of volatility.

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Oliveira, Gabriela França, Ana Carolina Campana Nascimento, Moysés Nascimento, Isabela de Castro Sant'Anna, Juan Vicente Romero, Camila Ferreira Azevedo, Leonardo Lopes Bhering, and Eveline Teixeira Caixeta Moura. "Quantile regression in genomic selection for oligogenic traits in autogamous plants: A simulation study." PLOS ONE 16, no. 1 (January 5, 2021): e0243666. http://dx.doi.org/10.1371/journal.pone.0243666.

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This study assessed the efficiency of Genomic selection (GS) or genome‐wide selection (GWS), based on Regularized Quantile Regression (RQR), in the selection of genotypes to breed autogamous plant populations with oligogenic traits. To this end, simulated data of an F2 population were used, with traits with different heritability levels (0.10, 0.20 and 0.40), controlled by four genes. The generations were advanced (up to F6) at two selection intensities (10% and 20%). The genomic genetic value was computed by RQR for different quantiles (0.10, 0.50 and 0.90), and by the traditional GWS methods, specifically RR-BLUP and BLASSO. A second objective was to find the statistical methodology that allows the fastest fixation of favorable alleles. In general, the results of the RQR model were better than or equal to those of traditional GWS methodologies, achieving the fixation of favorable alleles in most of the evaluated scenarios. At a heritability level of 0.40 and a selection intensity of 10%, RQR (0.50) was the only methodology that fixed the alleles quickly, i.e., in the fourth generation. Thus, it was concluded that the application of RQR in plant breeding, to simulated autogamous plant populations with oligogenic traits, could reduce time and consequently costs, due to the reduction of selfing generations to fix alleles in the evaluated scenarios.

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Sun, Pengju, Meng Li, and Hongwei Sun. "Quantile Regression Learning with Coefficient Dependent lq-Regularizer." MATEC Web of Conferences 173 (2018): 03033. http://dx.doi.org/10.1051/matecconf/201817303033.

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In this paper, We focus on conditional quantile regression learning algorithms based on the pinball loss and lq-regularizer with 1≤q≤2. Our main goal is to study the consistency of this kind of regularized quantile regression learning. With concentration inequality and operator decomposition techniques, we obtained satisfied error bounds and convergence rates.

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Papp, Gábor, Imre Kondor, and Fabio Caccioli. "Optimizing Expected Shortfall under an ℓ1 Constraint—An Analytic Approach." Entropy 23, no. 5 (April 24, 2021): 523. http://dx.doi.org/10.3390/e23050523.

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Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical ratio r=N/T, where N is the number of different assets in the portfolio, and T is the length of the available time series. The critical ratio depends on the confidence level α, which means we have a line of critical points on the α−r plane. The large fluctuations in the estimation of ES can be attenuated by the application of regularizers. In this paper, we calculate ES analytically under an ℓ1 regularizer by the method of replicas borrowed from the statistical physics of random systems. The ban on short selling, i.e., a constraint rendering all the portfolio weights non-negative, is a special case of an asymmetric ℓ1 regularizer. Results are presented for the out-of-sample and the in-sample estimator of the regularized ES, the estimation error, the distribution of the optimal portfolio weights, and the density of the assets eliminated from the portfolio by the regularizer. It is shown that the no-short constraint acts as a high volatility cutoff, in the sense that it sets the weights of the high volatility elements to zero with higher probability than those of the low volatility items. This cutoff renormalizes the aspect ratio r=N/T, thereby extending the range of the feasibility of optimization. We find that there is a nontrivial mapping between the regularized and unregularized problems, corresponding to a renormalization of the order parameters.

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9

Wu, Hanwei, and Markus Flierl. "Vector Quantization-Based Regularization for Autoencoders." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6380–87. http://dx.doi.org/10.1609/aaai.v34i04.6108.

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Autoencoders and their variations provide unsupervised models for learning low-dimensional representations for downstream tasks. Without proper regularization, autoencoder models are susceptible to the overfitting problem and the so-called posterior collapse phenomenon. In this paper, we introduce a quantization-based regularizer in the bottleneck stage of autoencoder models to learn meaningful latent representations. We combine both perspectives of Vector Quantized-Variational AutoEncoders (VQ-VAE) and classical denoising regularization methods of neural networks. We interpret quantizers as regularizers that constrain latent representations while fostering a similarity-preserving mapping at the encoder. Before quantization, we impose noise on the latent codes and use a Bayesian estimator to optimize the quantizer-based representation. The introduced bottleneck Bayesian estimator outputs the posterior mean of the centroids to the decoder, and thus, is performing soft quantization of the noisy latent codes. We show that our proposed regularization method results in improved latent representations for both supervised learning and clustering downstream tasks when compared to autoencoders using other bottleneck structures.

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Li, Meng, and Hong-Wei Sun. "Asymptotic analysis of quantile regression learning based on coefficient dependent regularization." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 04 (July 2015): 1550018. http://dx.doi.org/10.1142/s0219691315500186.

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In this paper, we consider conditional quantile regression learning algorithms based on the pinball loss with data dependent hypothesis space and ℓ2-regularizer. Functions in this hypothesis space are linear combination of basis functions generated by a kernel function and sample data. The only conditions imposed on the kernel function are the continuity and boundedness which are pretty weak. Our main goal is to study the consistency of this regularized quantile regression learning. By concentration inequality with ℓ2-empirical covering numbers and operator decomposition techniques, satisfied error bounds and convergence rates are explicitly derived.

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11

Adlouni, Salaheddine El, Garba Salaou, and André St-Hilaire. "Regularized Bayesian quantile regression." Communications in Statistics - Simulation and Computation 47, no. 1 (June 2, 2017): 277–93. http://dx.doi.org/10.1080/03610918.2017.1280830.

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12

Li, Qing, Ruibin Xi, and Nan Lin. "Bayesian regularized quantile regression." Bayesian Analysis 5, no. 3 (September 2010): 533–56. http://dx.doi.org/10.1214/10-ba521.

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13

Yao, Fang, Shivon Sue-Chee, and Fan Wang. "Regularized partially functional quantile regression." Journal of Multivariate Analysis 156 (April 2017): 39–56. http://dx.doi.org/10.1016/j.jmva.2017.02.001.

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14

Choi, Ho-Sik, and Yong-Dai Kim. "The Doubly Regularized Quantile Regression." Communications for Statistical Applications and Methods 15, no. 5 (September 30, 2008): 753–64. http://dx.doi.org/10.5351/ckss.2008.15.5.753.

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15

Feng, Xiang-Nan, Yifan Wang, Bin Lu, and Xin-Yuan Song. "Bayesian regularized quantile structural equation models." Journal of Multivariate Analysis 154 (February 2017): 234–48. http://dx.doi.org/10.1016/j.jmva.2016.11.002.

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16

Pan, Xiao, Gokhan Yildirim, Ataur Rahman, Khaled Haddad, and Taha B. M. J. Ouarda. "Peaks-Over-Threshold-Based Regional Flood Frequency Analysis Using Regularised Linear Models." Water 15, no. 21 (October 31, 2023): 3808. http://dx.doi.org/10.3390/w15213808.

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Regional flood frequency analysis (RFFA) is widely used to estimate design floods in ungauged catchments. Most of the RFFA techniques are based on the annual maximum (AM) flood model; however, research has shown that the peaks-over-threshold (POT) model has greater flexibility than the AM model. There is a lack of studies on POT-based RFFA techniques. This paper presents the development of POT-based RFFA techniques, using regularised linear models (least absolute shrinkage and selection operator, ridge regression and elastic net regression). The results of these regularised linear models are compared with multiple linear regression. Data from 145 stream gauging stations of south-east Australia are used in this study. A leave-one-out cross-validation is adopted to compare these regression models. It has been found that the regularised linear models provide quite accurate flood quantile estimates, with a median relative error in the range of 37 to 47%, which outperform the AM-based RFFA techniques currently recommended in the Australian Rainfall and Runoff guideline. The developed RFFA technique can be used to estimate flood quantiles in ungauged catchments in the study region.

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Zhao, Wei-hua, Ri-quan Zhang, Ya-zhao Lü, and Ji-cai Liu. "Bayesian regularized regression based on composite quantile method." Acta Mathematicae Applicatae Sinica, English Series 32, no. 2 (April 29, 2016): 495–512. http://dx.doi.org/10.1007/s10255-016-0579-4.

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18

Horvat, D., and S. Ilijić. "Regular and singular solutions for charged dust distributions in the Einstein-Maxwell theory." Canadian Journal of Physics 85, no. 9 (September 1, 2007): 957–65. http://dx.doi.org/10.1139/p07-090.

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Solutions for the static spherically symmetric extremally charged dust in the Majumdar–Papapetrou system have been found. For a certain amount of the allocated mass and (or) charge, the solutions have singularities of a type that could render them physically unacceptable, since the corresponding physically relevant quantities are singular as well. These solutions, with a number of zero-nodes in the metric tensor, are regularized through the δ-shell formalism, thus redefining the mass and (or) charge distributions. The bifurcating behaviour of regular solutions found before is no longer present in these singular solutions, but quantized-like behaviour in the total mass is observed. The spectrum of regularized solutions restores the equality of the Tolman–Whittaker and Arnowitt–Deser–Misner (ADM) mass, as well the equality of the net charge and ADM mass, which is the distinctive feature of Majumdar–Papapetrou systems.PACS No.:04.40.Nr

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19

Paycha, Sylvie. "(Second) Quantised resolvents and regularised traces." Journal of Geometry and Physics 57, no. 5 (April 2007): 1345–69. http://dx.doi.org/10.1016/j.geomphys.2006.10.010.

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Yousif, Ali Hameed, and Wafaa Jaafer Housain. "Atan Regularized in Quantile Regression for High Dimensional Data." Journal of Physics: Conference Series 1818, no. 1 (March 1, 2021): 012098. http://dx.doi.org/10.1088/1742-6596/1818/1/012098.

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Uniejewski, Bartosz, and Rafał Weron. "Regularized quantile regression averaging for probabilistic electricity price forecasting." Energy Economics 95 (March 2021): 105121. http://dx.doi.org/10.1016/j.eneco.2021.105121.

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22

Alhamzawi, Rahim, Ahmed Alhamzawi, and Haithem Taha Mohammad Ali. "New Gibbs sampling methods for bayesian regularized quantile regression." Computers in Biology and Medicine 110 (July 2019): 52–65. http://dx.doi.org/10.1016/j.compbiomed.2019.05.011.

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23

Christmann, Andreas, and Ding-Xuan Zhou. "Learning rates for the risk of kernel-based quantile regression estimators in additive models." Analysis and Applications 14, no. 03 (April 13, 2016): 449–77. http://dx.doi.org/10.1142/s0219530515500050.

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Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel-based methods for additive models. These learning rates compare favorably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel-based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.

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Wei, Long, and Yang Wang. "The Lagrangian, Self-Adjointness, and Conserved Quantities for a Generalized Regularized Long-Wave Equation." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/173192.

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We consider the Lagrangian and the self-adjointness of a generalized regularized long-wave equation and its transformed equation. We show that the third-order equation has a nonlocal Lagrangian with an auxiliary function and is strictly self-adjoint; its transformed equation is nonlinearly self-adjoint and the minimal order of the differential substitution is equal to one. Then by Ibragimov’s theorem on conservation laws we obtain some conserved qualities of the generalized regularized long-wave equation.

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Alkenani, Ali, and Basim Shlaibah Msallam. "Group Identification and Variable Selection in Quantile Regression." Journal of Probability and Statistics 2019 (April 10, 2019): 1–7. http://dx.doi.org/10.1155/2019/8504174.

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Using the Pairwise Absolute Clustering and Sparsity (PACS) penalty, we proposed the regularized quantile regression QR method (QR-PACS). The PACS penalty achieves the elimination of insignificant predictors and the combination of predictors with indistinguishable coefficients (IC), which are the two issues raised in the searching for the true model. QR-PACS extends PACS from mean regression settings to QR settings. The paper shows that QR-PACS can yield promising predictive precision as well as identifying related groups in both simulation and real data.

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Tang, Qiaoqiao, Haomin Zhang, and Shifeng Gong. "Bayesian Regularized Quantile Regression Analysis Based on Asymmetric Laplace Distribution." Journal of Applied Mathematics and Physics 08, no. 01 (2020): 70–84. http://dx.doi.org/10.4236/jamp.2020.81006.

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Barroso, L. M., F. Morgante, T. F. Mackay, A. C. C. Nascimento, M. Nascimento, and N. V. Serão. "032 Genomic prediction accuracies using regularized quantile regression (RQR) methodology." Journal of Animal Science 95, suppl_2 (March 1, 2017): 14–15. http://dx.doi.org/10.2527/asasmw.2017.032.

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Zhang, Yongxia, Qi Wang, and Maozai Tian. "Smoothed Quantile Regression with Factor-Augmented Regularized Variable Selection for High Correlated Data." Mathematics 10, no. 16 (August 15, 2022): 2935. http://dx.doi.org/10.3390/math10162935.

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This paper studies variable selection for the data set, which has heavy-tailed distribution and high correlations within blocks of covariates. Motivated by econometric and financial studies, we consider using quantile regression to model the heavy-tailed distribution data. Considering the case where the covariates are high dimensional and there are high correlations within blocks, we use the latent factor model to reduce the correlations between the covariates and use the conquer to obtain the estimators of quantile regression coefficients, and we propose a consistency strategy named factor-augmented regularized variable selection for quantile regression (Farvsqr). By principal component analysis, we can obtain the latent factors and idiosyncratic components; then, we use both as predictors instead of the covariates with high correlations. Farvsqr transforms the problem from variable selection with highly correlated covariates to that with weakly correlated ones for quantile regression. Variable selection consistency is obtained under mild conditions. Simulation study and real data application demonstrate that our method is better than the common regularized M-estimation LASSO.

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Ding, Xianwen, Jiandong Chen, and Xueping Chen. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses." Metrika 83, no. 5 (September 7, 2019): 545–68. http://dx.doi.org/10.1007/s00184-019-00744-3.

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Bracale, Antonio, Guido Carpinelli, and Pasquale De Falco. "Developing and Comparing Different Strategies for Combining Probabilistic Photovoltaic Power Forecasts in an Ensemble Method." Energies 12, no. 6 (March 15, 2019): 1011. http://dx.doi.org/10.3390/en12061011.

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Accurate probabilistic forecasts of renewable generation are drivers for operational and management excellence in modern power systems and for the sustainable integration of green energy. The combination of forecasts provided by different individual models may allow increasing the accuracy of predictions; however, in contrast to point forecast combination, for which the simple weighted averaging is often a plausible solution, combining probabilistic forecasts is a much more challenging task. This paper aims at developing a new ensemble method for photovoltaic (PV) power forecasting, which combines the outcomes of three underlying probabilistic models (quantile k-nearest neighbors, quantile regression forests, and quantile regression) through a weighted quantile combination. Due to the challenges in combining probabilistic forecasts, the paper presents different combination strategies; the competing strategies are based on unconstrained, constrained, and regularized optimization problems for estimating the weights. The competing strategies are compared to individual forecasts and to several benchmarks, using the data published during the Global Energy Forecasting Competition 2014. Numerical experiments were run in MATLAB and R environments; the results suggest that unconstrained and Least Absolute Shrinkage and Selection Operator (LASSO)-regularized strategies exhibit the best performances for the datasets under study, outperforming the best competitors by 2.5 to 9% of the Pinball Score.

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He, Qianchuan, Linglong Kong, Yanhua Wang, Sijian Wang, Timothy A. Chan, and Eric Holland. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits." Computational Statistics & Data Analysis 95 (March 2016): 222–39. http://dx.doi.org/10.1016/j.csda.2015.10.007.

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Tian, Yuzhu, Silian Shen, Ge Lu, Manlai Tang, and Maozai Tian. "Bayesian LASSO-Regularized quantile regression for linear regression models with autoregressive errors." Communications in Statistics - Simulation and Computation 48, no. 3 (December 6, 2017): 777–96. http://dx.doi.org/10.1080/03610918.2017.1397166.

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Xiang, Dao-Hong, Ting Hu, and Ding-Xuan Zhou. "Approximation Analysis of Learning Algorithms for Support Vector Regression and Quantile Regression." Journal of Applied Mathematics 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/902139.

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We study learning algorithms generated by regularization schemes in reproducing kernel Hilbert spaces associated with anϵ-insensitive pinball loss. This loss function is motivated by theϵ-insensitive loss for support vector regression and the pinball loss for quantile regression. Approximation analysis is conducted for these algorithms by means of a variance-expectation bound when a noise condition is satisfied for the underlying probability measure. The rates are explicitly derived under a priori conditions on approximation and capacity of the reproducing kernel Hilbert space. As an application, we get approximation orders for the support vector regression and the quantile regularized regression.

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Hwang, Duckdong, Bruno Clerckx, and Gil Kim. "Regularized channel inversion with quantized feedback in down-link multiuser channels." IEEE Transactions on Wireless Communications 8, no. 12 (December 2009): 5785–89. http://dx.doi.org/10.1109/twc.2009.12.090117.

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Chan, Yuk-Hee, and Yik-Hing Fung. "A regularized constrained iterative restoration algorithm for restoring color-quantized images." Signal Processing 85, no. 7 (July 2005): 1375–87. http://dx.doi.org/10.1016/j.sigpro.2005.01.009.

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Koçhan, Necla, G. Yazgi Tutuncu, Gordon K. Smyth, Luke C. Gandolfo, and Göknur Giner. "qtQDA: quantile transformed quadratic discriminant analysis for high-dimensional RNA-seq data." PeerJ 7 (December 18, 2019): e8260. http://dx.doi.org/10.7717/peerj.8260.

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Classification on the basis of gene expression data derived from RNA-seq promises to become an important part of modern medicine. We propose a new classification method based on a model where the data is marginally negative binomial but dependent, thereby incorporating the dependence known to be present between measurements from different genes. The method, called qtQDA, works by first performing a quantile transformation (qt) then applying Gaussian quadratic discriminant analysis (QDA) using regularized covariance matrix estimates. We show that qtQDA has excellent performance when applied to real data sets and has advantages over some existing approaches. An R package implementing the method is also available on https://github.com/goknurginer/qtQDA.

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Li, Jessie. "The Proximal Bootstrap for Finite-Dimensional Regularized Estimators." AEA Papers and Proceedings 111 (May 1, 2021): 616–20. http://dx.doi.org/10.1257/pandp.20211036.

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We propose a proximal bootstrap that can consistently estimate the limiting distribution of sqrt(n)-consistent estimators with nonstandardasymptotic distributions in a computationally efficient manner by formulating the proximal bootstrap estimator as the solution to aconvex optimization problem, which can have a closed-form solution for certain designs. This paper considers the application to finite-dimensionalregularized estimators, such as the lasso, l1-norm regularized quantile regression, l1-norm support vector regression, and trace regression via nuclear norm regularization.

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Anand, Namit, and Paolo Zanardi. "BROTOCs and Quantum Information Scrambling at Finite Temperature." Quantum 6 (June 23, 2022): 744. http://dx.doi.org/10.22331/q-2022-06-23-744.

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Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

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Anand, Namit, and Paolo Zanardi. "BROTOCs and Quantum Information Scrambling at Finite Temperature." Quantum 6 (June 27, 2022): 746. http://dx.doi.org/10.22331/q-2022-06-27-746.

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Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

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Nashed, Gamal G. L. "Physical Quantities of Reissner-Nordström Spacetime with Arbitrary Function and Regularized Procedure." Advances in High Energy Physics 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/298616.

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We use the covariant teleparallel approach to compute the total energy ofa spherically symmetric frame with an arbitrary function, that is,ℑ(r). We show how the total energy is always effected by the inertia. When use is made of the pure gauge connection, teleparallel gravity always yields the physically relevant result. We also calculate the total conserved charge and show how inertia spoils the physics in the time coordinate direction. Therefore, a regularized expression is employed to get a plausible value of energy. Finally, we use the Euclidean continuation method, in the context of TEGR, to calculate the energy, Hawking temperature, entropy, and first law of thermodynamics.

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Pérez-Rodríguez, Paulino, Osval A. Montesinos-López, Abelardo Montesinos-López, and José Crossa. "Bayesian regularized quantile regression: A robust alternative for genome-based prediction of skewed data." Crop Journal 8, no. 5 (October 2020): 713–22. http://dx.doi.org/10.1016/j.cj.2020.04.009.

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42

Koné, N’Golo. "Regularized Maximum Diversification Investment Strategy." Econometrics 9, no. 1 (December 29, 2020): 1. http://dx.doi.org/10.3390/econometrics9010001.

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The maximum diversification has been shown in the literature to depend on the vector of asset volatilities and the inverse of the covariance matrix of the asset return covariance matrix. In practice, these two quantities need to be replaced by their sample statistics. The estimation error associated with the use of these sample statistics may be amplified due to (near) singularity of the covariance matrix, in financial markets with many assets. This, in turn, may lead to the selection of portfolios that are far from the optimal regarding standard portfolio performance measures of the financial market. To address this problem, we investigate three regularization techniques, including the ridge, the spectral cut-off, and the Landweber–Fridman approaches in order to stabilize the inverse of the covariance matrix. These regularization schemes involve a tuning parameter that needs to be chosen. In light of this fact, we propose a data-driven method for selecting the tuning parameter. We show that the selected portfolio by regularization is asymptotically efficient with respect to the diversification ratio. In empirical and Monte Carlo experiments, the resulting regularized rules are compared to several strategies, such as the most diversified portfolio, the target portfolio, the global minimum variance portfolio, and the naive 1/N strategy in terms of in-sample and out-of-sample Sharpe ratio performance, and it is shown that our method yields significant Sharpe ratio improvements.

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ICHINOSE, SHOICHI. "CASIMIR ENERGY OF 5D ELECTRO-MAGNETISM AND SPHERE LATTICE REGULARIZATION." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2245–48. http://dx.doi.org/10.1142/s0217751x08040949.

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Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called sphere lattice regularization, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do not take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence.

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Hable, R., and A. Christmann. "Estimation of scale functions to model heteroscedasticity by regularised kernel-based quantile methods." Journal of Nonparametric Statistics 26, no. 2 (February 12, 2014): 219–39. http://dx.doi.org/10.1080/10485252.2013.875547.

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Yu, Liju, and Jingjun Zhang. "Global solution to the complex short pulse equation." Electronic Research Archive 32, no. 8 (2024): 4809–27. http://dx.doi.org/10.3934/era.2024220.

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<p>This paper deals with global well-posedness of the solution to the complex short pulse equation. We first use regularized technology and the approximation argument to prove the local existence and uniqueness of this equation. Then, based on conserved quantities and energy analysis, we show that the solution can be extended globally in time for suitably small initial data.</p>

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Gunzburger, Max, Traian Iliescu, and Michael Schneier. "A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows." IMA Journal of Numerical Analysis 40, no. 2 (January 25, 2019): 886–913. http://dx.doi.org/10.1093/imanum/dry094.

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Abstract Partial differential equations (PDEs) are often dependent on input quantities that are uncertain. To quantify this uncertainty PDEs must be solved over a large ensemble of parameters. Even for a single realization this can be a computationally intensive process. In the case of flows governed by the Navier–Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble-proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introduction of POD spatial filtering for ensemble-POD methods. The POD spatial filter makes possible the construction of the Leray ensemble-POD model, which is a regularized-reduced order model for the numerical simulation of convection-dominated flows of moderate Reynolds number. The Leray ensemble-POD model employs the POD spatial filter to smooth (regularize) the convection term in the Navier–Stokes equations, and diminishes the numerical inaccuracies produced by the ensemble-POD method in the numerical simulation of convection-dominated flows. Specifically, for the numerical simulation of a convection-dominated two-dimensional flow between two offset cylinders, we show that the Leray ensemble-POD method better reflects the dynamics of the benchmark results than the ensemble-POD scheme. The second contribution of this work is a new numerical discretization of the variable viscosity ensemble algorithm in which the average viscosity is replaced with the maximum viscosity. It is shown that this new numerical discretization is significantly more stable than those in current use. Furthermore, error estimates for the novel Leray ensemble-POD algorithm with this new numerical discretization are also proven.

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Kumar, Arun, Rahul Kumar Walia, and Sushant G. Ghosh. "Bardeen Black Holes in the Regularized 4D Einstein–Gauss–Bonnet Gravity." Universe 8, no. 4 (April 10, 2022): 232. http://dx.doi.org/10.3390/universe8040232.

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We obtain exact Bardeen black holes to the regularized 4D Einstein–Gauss–Bonnet (EGB) gravity minimally coupled with the nonlinear electrodynamics (NED). In turn, we analyze the horizon structure to determine the effect of GB parameter α on the minimum cutoff values of mass, M0, and magnetic monopole charge, g0, for the existence of a black hole horizon. We obtain an exact expression for thermodynamic quantities, namely, Hawking temperature T+, entropy S+, Helmholtz free energy F+, and specific heat C+ associated with the black hole horizon, and they show significant deviations from the 4D EGB case owing to NED. Interestingly, there exists a critical value of horizon radius, r+c, corresponding to the local maximum of Hawking temperature, at which heat capacity diverges, confirming the second-order phase transition. A discussion on the black holes of alternate regularized 4D EGB gravity belonging to the scalar-tensor theory is appended.

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Momoniat, E. "A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation." Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/754543.

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Two nonstandard finite difference schemes are derived to solve the regularized long wave equation. The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. The two “best” nonstandard numerical schemes are shown to preserve conserved quantities when compared to an implicit scheme in which the nonlinear term is approximated in the usual way. Comparisons to the single solitary wave solution show significantly better results, measured in theL2andL∞norms, when compared to results obtained using a Petrov-Galerkin finite element method and a splitted quadratic B-spline collocation method. The growth in the error when simulating the single solitary wave solution using the two “best” nonstandard numerical schemes is shown to be linear implying the nonstandard finite difference schemes are conservative. The formation of an undular bore for both steep and shallow initial profiles is captured without the formation of numerical instabilities.

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Ajeel, Sherzad M., and Hussein A. Hashem. "Comparison Some Robust Regularization Methods in Linear Regression via Simulation Study." Academic Journal of Nawroz University 9, no. 2 (August 20, 2020): 244. http://dx.doi.org/10.25007/ajnu.v9n2a818.

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In this paper, we reviewed some variable selection methods in linear regression model. Conventional methodologies such as the Ordinary Least Squares (OLS) technique is one of the most commonly used method in estimating the parameters in linear regression. But the OLS estimates performs poorly when the dataset suffer from outliers or when the assumption of normality is violated such as in the case of heavy-tailed errors. To address this problem, robust regularized regression methods like Huber Lasso (Rosset and Zhu, 2007) and quantile regression (Koenker and Bassett ,1978] were proposed. This paper focuses on comparing the performance of the seven methods, the quantile regression estimates, the Huber Lasso estimates, the adaptive Huber Lasso estimates, the adaptive LAD Lasso, the Gamma-divergence estimates, the Maximum Tangent Likelihood Lasso (MTE) estimates and Semismooth Newton Coordinate Descent Algorithm (SNCD ) Huber loss estimates.

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Mohammed, F. A. "Soliton solutions for some nonlinear models in mathematical physics via conservation laws." AIMS Mathematics 7, no. 8 (2022): 15075–93. http://dx.doi.org/10.3934/math.2022826.

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<abstract><p>In this paper, we derive the soliton solutions from conserved quantities for the Benjamin-Bona-Mahoney equation with dual-power law nonlinearity (BBM), modified regularized long wave (MRLW) equation, modified nonlinearly dispersive KdV equations 2K(2, 2, 1) and 3K(3, 2, 2) equation, which are constructed by the multiplier approach (variational derivative method). Finally, we give the numerical simulations to illustrate this method.</p></abstract>

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