In the current study, a brand-new SINARS(1) model is proposed for stationary discrete time series defined on $\boldsymbol{Z}$, based on extended binomial distribution and the Pegram's operator. The model effectively characterizes the series of positive and negative integer values generated after differencing some non-stationary time series. The model's attributes are addressed. For the parameter estimation of the model, the conditional maximum likelihood method and Yule-Walker method are taken into consideration. And we prove the asymptotic normality of CML method. By using these two methods, we simulate our model comparing with some relevant ones proposed before. The model can deal with positive or negative autocorrelation data. The analysis of the number of differenced daily new cases in Barbados is done using the suggested model.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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To address the problem of NLP classifiers learning spurious correlations between training features and target labels, a common approach is to make the model's predictions invariant to these features. However, this can be counter-productive when the features have a non-zero causal effect on the target label and thus are important for prediction. Therefore, using methods from the causal inference literature, we propose an algorithm to regularize the learnt effect of the features on the model's prediction to the estimated effect of feature on label. This results in an automated augmentation method that leverages the estimated effect of a feature to appropriately change the labels for new augmented inputs. On toxicity and IMDB review datasets, the proposed algorithm minimises spurious correlations and improves the minority group (i.e., samples breaking spurious correlations) accuracy, while also improving the total accuracy compared to standard training.
The sensitivity of loss reserving techniques to outliers in the data or deviations from model assumptions is a well known challenge. It has been shown that the popular chain-ladder reserving approach is at significant risk to such aberrant observations in that reserve estimates can be significantly shifted in the presence of even one outlier. As a consequence the chain-ladder reserving technique is non-robust. In this paper we investigate the sensitivity of reserves and mean squared errors of prediction under Mack's Model (Mack, 1993). This is done through the derivation of impact functions which are calculated by taking the first derivative of the relevant statistic of interest with respect to an observation. We also provide and discuss the impact functions for quantiles when total reserves are assumed to be lognormally distributed. Additionally, comparisons are made between the impact functions for individual accident year reserves under Mack's Model and the Bornhuetter-Ferguson methodology. It is shown that the impact of incremental claims on these statistics of interest varies widely throughout a loss triangle and is heavily dependent on other cells in the triangle. Results are illustrated using data from a Belgian non-life insurer.
Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and has significant impacts in industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop an efficient local search solver, which is the first local search solver for general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. We design tailored operators adapted to different modes, thus improving the quality of the current solution according to different situations. For the Search and Restore modes, we propose an operator named tight move, which adaptively modifies variables' values, trying to make some constraint tight. For the Improve mode, an efficient operator lift move is proposed to improve the quality of the objective function while maintaining feasibility. Putting these together, we develop a local search solver for integer linear programming called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our solver in solving large-scale hard integer linear programming problems within a reasonably short time. Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our solver establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions and also maintain good connectivity of targeted solutions.
Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be considered to preserve the complete information of the original data and limit the dimensionality. Dimensionality reduction and feature selection are common preprocessing techniques addressing the challenge of efficiently dealing with high-dimensional data. Dimensionality reduction methods control the number of features in the dataset while preserving its structure and minimizing information loss. Feature selection aims to identify the most relevant features for a task, discarding the less informative ones. Previous works have proposed approaches that aggregate features depending on their correlation without discarding any of them and preserving their interpretability through aggregation with the mean. A limitation of methods based on correlation is the assumption of linearity in the relationship between features and target. In this paper, we relax such an assumption in two ways. First, we propose a bias-variance analysis for general models with additive Gaussian noise, leading to a dimensionality reduction algorithm (NonLinCFA) which aggregates non-linear transformations of features with a generic aggregation function. Then, we extend the approach assuming that a generalized linear model regulates the relationship between features and target. A deviance analysis leads to a second dimensionality reduction algorithm (GenLinCFA), applicable to a larger class of regression problems and classification settings. Finally, we test the algorithms on synthetic and real-world datasets, performing regression and classification tasks, showing competitive performances.
In this paper, we present a novel characterization of the smoothness of a model based on basic principles of Large Deviation Theory. In contrast to prior work, where the smoothness of a model is normally characterized by a real value (e.g., the weights' norm), we show that smoothness can be described by a simple real-valued function. Based on this concept of smoothness, we propose an unifying theoretical explanation of why some interpolators generalize remarkably well and why a wide range of modern learning techniques (i.e., stochastic gradient descent, $\ell_2$-norm regularization, data augmentation, invariant architectures, and overparameterization) are able to find them. The emergent conclusion is that all these methods provide complimentary procedures that bias the optimizer to smoother interpolators, which, according to this theoretical analysis, are the ones with better generalization error.
Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and memory expense -- these systems are often forced to rely on autoregressive time-stepping of the neural network to predict future temporal states. While this is effective in managing costs, it can lead to uncontrolled error growth over time and eventual instability. We analyze the sources of this autoregressive error growth using prototypical neural operator models for physical systems and explore ways to mitigate it. We introduce architectural and application-specific improvements that allow for careful control of instability-inducing operations within these models without inflating the compute/memory expense. We present results on several scientific systems that include Navier-Stokes fluid flow, rotating shallow water, and a high-resolution global weather forecasting system. We demonstrate that applying our design principles to prototypical neural networks leads to significantly lower errors in long-range forecasts with 800\% longer forecasts without qualitative signs of divergence compared to the original models for these systems. We open-source our \href{//anonymous.4open.science/r/stabilizing_neural_operators-5774/}{code} for reproducibility.
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data dependence structure. Before applying such methods, we need to decide whether the data are elliptically distributed. Currently existing tests either focus exclusively on spherical distributions, or rely on bootstrap to determine the null distribution, or require specific forms of the alternative distribution. In this paper, we introduce a general nonparametric test for elliptical distribution based on kernel embedding of the probability measure that embodies the two properties that characterize an elliptical distribution: namely, after centering and rescaling, (1) the direction and length of the random vector are independent, and (2) the directional vector is uniformly distributed on the unit sphere. We derive the null asymptotic distribution of the test statistic via von-Mises expansion, develop the sample-level procedure to determine the rejection region, and establish the consistency and validity of the proposed test. We apply our test to a SENIC dataset with and without a transformation aimed to achieve ellipticity.
In multivariate time series analysis, the coherence measures the linear dependency between two-time series at different frequencies. However, real data applications often exhibit nonlinear dependency in the frequency domain. Conventional coherence analysis fails to capture such dependency. The quantile coherence, on the other hand, characterizes nonlinear dependency by defining the coherence at a set of quantile levels based on trigonometric quantile regression. Although quantile coherence is a more powerful tool, its estimation remains challenging due to the high level of noise. This paper introduces a new estimation technique for quantile coherence. The proposed method is semi-parametric, which uses the parametric form of the spectrum of the vector autoregressive (VAR) model as an approximation to the quantile spectral matrix, along with nonparametric smoothing across quantiles. For each fixed quantile level, we obtain the VAR parameters from the quantile periodograms, then, using the Durbin-Levinson algorithm, we calculate the preliminary estimate of quantile coherence using the VAR parameters. Finally, we smooth the preliminary estimate of quantile coherence across quantiles using a nonparametric smoother. Numerical results show that the proposed estimation method outperforms nonparametric methods. We show that quantile coherence-based bivariate time series clustering has advantages over the ordinary VAR coherence. For applications, the identified clusters of financial stocks by quantile coherence with a market benchmark are shown to have an intriguing and more accurate structure of diversified investment portfolios that may be used by investors to make better decisions.
The Exponential-family Random Graph Model (ERGM) is a powerful model to fit networks with complex structures. However, for dynamic valued networks whose observations are matrices of counts that evolve over time, the development of the ERGM framework is still in its infancy. To facilitate the modeling of dyad value increment and decrement, a Partially Separable Temporal ERGM is proposed for dynamic valued networks. The parameter learning algorithms inherit state-of-the-art estimation techniques to approximate the maximum likelihood, by drawing Markov chain Monte Carlo (MCMC) samples conditioning on the valued network from the previous time step. The ability of the proposed model to interpret network dynamics and forecast temporal trends is demonstrated with real data.
In this article a new approach in solving time fractional partial differential equations is introduced, that is, the ARA-residual power series method. The main idea of this technique, depends on applying the ARA-transform and using Taylor's expansion to construct approximate series solutions. The procedure of getting the approximate solutions for nonlinear time fractional partial differential equations is a difficult mission, the ARA-residual power series method over comes this trouble throughout expressing the solution in a series form then obtain the series coefficients using the idea of the residual function and the concept of the limit at infinity. This method is efficient and applicable to solve a wide family of time fractional partial differential equations. Four attractive applications are considered to show the speed and the strength of the proposed method in constructing solitary series solutions of the target equations.
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