Penalty Criterion Research Articles

Hierarchical estimation methods based on the penalty term for controlled autoregressive systems with colored noises

AbstractThis article considers the parameter estimation problems for the controlled autoregressive systems interfered by moving average noises. A recursive extended gradient algorithm with penalty term is proposed by using the penalty criterion function. By introducing three fictitious output variables, the original system can be decomposed into three subsystems based on the hierarchical principle. The hierarchical recursive extended gradient algorithm with penalty term is then proposed to achieve the parameter estimation. Finally, the experimental results demonstrate the effectiveness of the proposed algorithms.

Enhancing wind turbine site selection through a novel wake penalty criterion

In this study, a novel approach that incorporates the wake effect as a penalty criterion within the Analytical Hierarchy Process (AHP) method is proposed. The research introduces the wake penalty criterion for the first time, considering both existing and newly located turbines. The results demonstrate the impact of the wake effect and identify areas with varying wake penalties. A comprehensive suitability analysis is conducted using AHP and Geographic Information System (GIS) techniques, resulting in a suitability map for wind turbine site selection. The analysis considers seven criteria, including the novel wake penalty criterion. The suitability map reveals a distribution of suitability ranges, with 73.8% of the total area excluded due to various constraints. Additionally, a comparative analysis is performed by excluding the wake penalty criterion, highlighting the contrasting effects of wake on turbine placement. Case studies in the Karaburun and Çeşme regions of İzmir further illustrate the influence of wake on turbine clusters and their alignment with prevailing wind directions. The findings indicate that the inclusion of wake effects provides a more precise and realistic depiction of viable wind turbine site selection. This is evident in the reduction of 55.5% and 18.6% in the most suitable region (80–100% suitability) and highly suitable region (60–80% suitability), respectively.

A subjective interpretation of Liu–Liu’s credibility measures and expectations

We consider credibility measures introduced by Liu and Liu and the corresponding credibility expectations, obtained through the Choquet integral. In analogy with de Finetti’s approach to probability, we show that also for credibility measures and expectations, a subjective interpretation can be given through suitable notions of coherence. In detail, coherence can be expressed equivalently in terms of consistency, through a fair betting scheme and through a penalty criterion. Such notions of coherence rest upon the concepts of partially resolving uncertainty due to Jaffray, the notion of consonance due to Shafer and the notion of pessimism-optimism indifference introduced in this paper.

The Potential of Using Vortex Tube to Ameliorate Aircraft Environmental Control System

This paper proposes a new air cycle system by replacing the turbine assembly with vortex tubes and a parameter-matching method independent of the architecture of the air cycle system. Only, in terms of refrigerating and dehumidification, the performance of the newly proposed vortex system is worse than that of a conventional air cycle system under the same bleed air parameters. However, for aircraft practical applications, the overall performance of air cycle systems requires additional considerations such as the heating capacity, weight of the system, and extra aviation fuel used to transport that weight. Therefore, this paper conducts an integrated performance comparison between the new system and a conventional system based on the overall fuel mass penalty criterion. The results show that whether the new system has a smaller total takeoff mass depends on the bleed air parameters, flight duration, and flight speed. For specific bleed air parameters, there is a specific R=1 curve where the new system and the turbine system have the same total takeoff mass. The performance of the new system is better than that of the turbine system only when the values of flight Mach number and flight duration are at the lower left of the R=1 curve.

The disorder problem for diffusion processes with the [formula omitted]-linear and expected total miss criteria

We study the disorder problem for a time-homogeneous diffusion process. The aim is to determine an efficient detection strategy of the disorder time θ, at which the process changes its drift. We focus on the ϵ-linear and the expected total miss criteria, where, unlike the well known linear penalty criterion, the expected penalty for an early/wrong detection of θ is expressed as the frequency of false alarms launched at least ϵ units of time before θ and as the expected advance in the detection of θ, respectively. We show that the original optimal stopping problems can be reduced to a unifying optimal stopping problem; then, we derive the associated free-boundary problem and we provide sufficient conditions for the existence and uniqueness of its solution.

Applying the Pre-Commitment Approach to bottom-up stress tests: A new old story

The Pre-Commitment Approach (PCA) to capital requirements was developed and promoted by the US Federal Reserve in the 1990s. The proposal was conceived as an alternative to the market-risk capital requirements based on internal models then under discussion, and eventually adopted, by the Basel Committee. Notwithstanding the Fed continued to support the PCA, the idea was abandoned, probably because it was considered too optimistic to allow banks determine the level of capital. In this paper, we study the possibility to adapt the PCA as to work as a complementary (and not alternative) tool applied to the banking book Prudential Regulation. In particular, we explore the application of this approach to a well-known issue in the context of the Stress tests: the top-down vs bottom-up debate. We focus on bottom-up stress tests and suggest creating a system of monetary penalties (charges) proportional to the difference between the expected and the realised losses of a portfolio. The charges would aim to induce model developers to reveal their best forecasts. We show that this approach can be seen as an adaptation of the pre-commitment approach (PCA) but also as an application of the penalty criterion proposed by the Italian mathematician de Finetti as the foundation of the subjectivist definition of probability. We explain how the PCA could be adapted to bottom-up stress testing and provide a practical example of the application of our proposal to the banking book. What emerges is that the PCA can indeed mitigate banks’ incentives to provide underestimated measures of risk under the adverse scenario and thus better align the incentives of banks and supervisors.

Vector Gaussian CEO Problem Under Logarithmic Loss and Applications

In this paper, we study the vector Gaussian Chief Executive Officer (CEO) problem under logarithmic loss distortion measure. Specifically, ${K} \geq 2$ agents observe independently corrupted Gaussian noisy versions of a remote vector Gaussian source, and communicate independently with a decoder or CEO over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source and wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. We find an explicit characterization of the rate-distortion region of this model. The result can be seen as the counterpart to the vector Gaussian setting of that by Courtade-Weissman which provides the rate-distortion region of the model in the discrete memoryless setting. For the proof of this result, we obtain an outer bound by means of a technique that relies on the de Bruijn identity and the properties of Fisher information. The approach is similar to Ekrem-Ulukus outer bounding technique for the vector Gaussian CEO problem under quadratic distortion measure, for which it was there found generally non-tight; but it is shown here to yield a complete characterization of the region for the case of logarithmic loss measure. Also, we show that Gaussian test channels with time-sharing exhaust the Berger-Tung inner bound, which is optimal. Furthermore, application of our results allows us to find the complete solutions of two related problems: a quadratic vector Gaussian CEO problem with determinant constraint and the vector Gaussian distributed Information Bottleneck problem. Finally, we develop Blahut-Arimoto type algorithms that allow to compute numerically the regions provided in this paper, for both discrete and Gaussian models. With the known relevance of the logarithmic loss fidelity measure in the context of learning and prediction, the proposed algorithms may find usefulness in a variety of applications where learning is performed distributively. We illustrate the efficiency of our algorithms through some numerical examples.

Applying the Precommitment Approach to Bottom-Up Stress Tests: A New Old Story

Stress tests have become a key tool for banks, supervisors and macro prudential authorities. An aspect of these exercises is the need for statistical models to obtain risk measurements under an adverse scenario and a fundamental question is who should develop such models. If models are developed by the authorities (top-down approach), homogeneity of treatment among banks and more control over results are achieved, but the authorities do not necessarily have all the information that individual banks have. Banks’ models (bottom-up approach) may be more accurate. However, banks may have incentives to underestimate the impact of a shock, thus reducing the supervisory reaction. In this paper, we focus on bottom-up stress tests and suggest creating a system of monetary penalties (charges) proportional to the difference between the expected and the realised losses of a portfolio. The charges would aim to induce model developers to reveal their best forecasts. We show that this approach can be seen as an adaptation of the pre-commitment approach (PCA) developed and promoted by the US Federal Reserve in the 1990s but also as an application of the penalty criterion proposed by the Italian mathematician de Finetti as the foundation of the subjectivist definition of probability. We explain how the PCA could be adapted to bottom-up stress testing and provide a practical example of the application of our proposal to the banking book. What emerges is that the PCA can indeed mitigate banks’ incentives to provide underestimated measures of risk under the adverse scenario and thus better align the incentives of banks and supervisors.

Neural network approach based on a bilevel optimization for the prediction of underground blast-induced ground vibration amplitudes

Due to its technical and economic advantages, the use of explosives in underground rock excavation is widely adopted. However, some safety and, especially, environmental issues arise when using this technique, mainly concerning ground vibrations induced by blasts. Thus, to minimize dynamic environmental impacts, prediction of blast-induced vibrations is imperative. In the last few years, artificial neural networks (ANNs) have been applied to model blast-induced ground vibrations. Nevertheless, ANN’s architecture, mainly the number of neurons in the hidden layer, has been selected manually concerning ANN’s performance parameters. To avoid over-fitting and reduce model’s complexity, this paper presents a bilevel optimization of ANN architecture, considering two transfer functions, based on the maximization of quality of the adjustment and model’s complexity, this last one as a penalty criterion. An ANN approach based on this bilevel optimization was successfully applied on a database of 1188 samples obtained from underground blast-induced ground vibration monitoring in a granitic rock mass. A residual analysis of the best-fitted model is performed to ensure the quality of the adjustment. It is demonstrated that the determined ANN model offers much higher generalization ability than the traditional prediction models usually used for blast-induced ground vibration amplitude predictions and other ANN architectures applied to ground vibration prediction.

The maximum penalty criterion for ridge regression: application to the calibration of the force constant in elastic network models.

Tikhonov regularization, or ridge regression, is a popular technique to deal with collinearity in multivariate regression. We unveil a formal analogy between ridge regression and statistical mechanics, where the objective function is comparable to a free energy, and the ridge parameter plays the role of temperature. This analogy suggests two novel criteria for selecting a suitable ridge parameter: specific-heat (Cv) and maximum penalty (MP). We apply these fits to evaluate the relative contributions of rigid-body and internal fluctuations, which are typically highly collinear, to crystallographic B-factors. This issue is particularly important for computational models of protein dynamics, such as the elastic network model (ENM), since the amplitude of the predicted internal motion is commonly calibrated using B-factor data. After validation on simulated datasets, our results indicate that rigid-body motions account on average for more than 80% of the amplitude of B-factors. Furthermore, we evaluate the ability of different fits to reproduce the amplitudes of internal fluctuations in X-ray ensembles from the B-factors in the corresponding single X-ray structures. The new ridge criteria are shown to be markedly superior to the commonly used two-parameter fit that neglects rigid-body rotations and to the full fits regularized under generalized cross-validation. In conclusion, the proposed fits ensure a more robust calibration of the ENM force constant and should prove valuable in other applications.

Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem

This paper addresses minimizing Tardy/Lost penalties with common due dates on a single machine. According to this penalty criterion, if tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. The problem is formulated as an integer programming model, and a heuristic algorithm is constructed. Then, using the proposed dominance rules and lower bounds, we develop two dynamic programming algorithms as well as a branch and bound. Experimental results show that the heuristic algorithm has an average optimality gap less than 2 % in all problem sizes. Instances up to 250 jobs with low variety of process times are optimally solved and for high process time varieties, the algorithms solved all instances up to 75 jobs.

Sustainability performance evaluation in industry by composite sustainability index

The growing importance of sustainable development as a policy objective has initiated a debate about those suitable frameworks and tools useful for policy makers when making a sustainable decision. Composite indicators (CIs) aggregate multidimensional issues into one index, thus providing comprehensive information. However, it is frequently argued that CIs are too subjective, as their results undesirably depend on the normalization method, a specific weighting scheme, and the aggregation method of sub-indicators. This article applies different combinations of normalization, weighting, and aggregation methods for the assessment of an industrial case study, with the aim of determining the best scheme for constructing CIs. The applied methodology gradually aggregates sustainable development indicators into sustainability sub-indices and, finally, to a composite sustainability index. The normalization methods included in this analysis are: minimum–maximum, distance to a reference, and the percentages of annual differences over consecutive years. Equal weightings, the ‘benefit of the doubt’ approach, and budget allocation process were used for determining the weights of individual indicators and sustainability sub-indices. The linear, geometric, and non-compensatory multi-criteria approaches (NCMCs) were used as aggregation methods. The NCMC is modified to fit the two-level aggregation, then to sub-indices, and finally to a composite sustainable index. Also, a penalty criterion is introduced into the evaluation process with the aim of motivating the company to move towards sustainable development. The results are analyzed by variance-based sensitivity analysis. According to the results the recommended scheme for CIs’ construction is: distance to a reference–benefit of the doubt–linear aggregation.

North Atlantic Power Dissipation Index (PDI) and Accumulated Cyclone Energy (ACE): Statistical Modeling and Sensitivity to Sea Surface Temperature Changes

Abstract This study focuses on the statistical modeling of the power dissipation index (PDI) and accumulated cyclone energy (ACE) for the North Atlantic basin over the period 1949–2008, which are metrics routinely used to assess tropical storm activity, and their sensitivity to sea surface temperature (SST) changes. To describe the variability exhibited by the data, four different statistical distributions are considered (gamma, Gumbel, lognormal, and Weibull), and tropical Atlantic and tropical mean SSTs are used as predictors. Model selection, both in terms of significant covariates and their functional relation to the parameters of the statistical distribution, is performed using two penalty criteria. Two different SST datasets are considered [the Met Office’s Global Sea Ice and Sea Surface Temperature dataset (HadISSTv1) and NOAA’s extended reconstructed SST dataset (ERSSTv3b)] to examine the sensitivity of the results to the input data. The statistical models presented in this study are able to well describe the variability in the observations according to several goodness-of-fit diagnostics. Both tropical Atlantic and tropical mean SSTs are significant predictors, independently of the SST input data, penalty criterion, and tropical storm activity metric. The application of these models to centennial reconstructions and seasonal forecasting is illustrated. The sensitivity of North Atlantic tropical cyclone frequency, duration, and intensity is examined for both uniform and nonuniform SST changes. Under uniform SST warming, these results indicate that there is a modest sensitivity of intensity, and a decrease in tropical storm and hurricane frequencies. On the other hand, increases in tropical Atlantic SST relative to the tropical mean SST suggest an increase in the intensity and frequency of North Atlantic tropical storms and hurricanes.

Nonparametric Fitting of Aerodynamic Data Using Smoothing Thin-Plate Splines

This paper introduces a nonparametric fitting method for the interpolation of aerodynamic observations over a large range of multiple angles of attack. The method is based on the employment of smoothing thin-plate spline class functions, a well-renewed mathematical tool for multivariate data mining based on the generalization of the univariate natural cubic splines, in which a roughness penalty criterion is used to produce very smooth predictive hypersurfaces. Compared with other methods, such as parametric or even conventional nonparametric methods, the use of a smoothing thin-plate spline is more effective, in that the predictive surface comes directly from the observed points, thus minimizing any intervention of the analyst aimed at introducing model parameters. This forms the basis for a very reliable fitting technique, in which model construction can be relatively easy to implement. An application of the method is carried out on a case study representative of some experimental data coming from a wind-tunnel campaign on a typical three-dimensional fuselage-shaped body, aimed at the acquisition of its aerodynamic coefficients over a rather extensive attitude range. Specifically, the application is focused on the body lift coefficient as a function of both angle of attack and sideslip angle. The data set is also interpolated using concurrent response-surface methods: namely, a linear model, a bivariate spline, a radial basis function network, a support vector regression technique, a regression kriging, and a moving-least-squares approach, alternatively known as local polynomial regression. Results of data fitting are assessed using a cross-validation approach and reveal a clear superiority of smoothing thin-plate spline over the other methods, leading to a more regular fitted surface and a more reliable prediction tool, even when some observations are omitted. This is important per se, but acquires even more significance when an aerodynamic test campaign is to be planned with the minimum number of experimental observations.

Missing Data Imputation in Time Series of Air Pollution

ISEE-0841 Background and Objective: Missing data is a frequent problem in epidemiological studies on the effects of air pollution on health. Air quality monitoring stations can present failures and stay off-line for several days. These gaps can distort the exposure assessment since the missing data mechanism is often ignored in the analysis. Analyses based only on the available observations can yield biased estimates of the association as well as overestimate the precision. We propose an imputation procedure for multivariate time series data, e.g. daily concentrations of atmospheric contaminants, based on the EM algorithm. The time component of the series can be modelled by using splines, regression models, or ARIMA models with multiple covariance regime. Methods: A simulation study was carried out in order to evaluate the validity of the proposed method and compare it with those available as default in most software packages for statistical analysis. The accuracy and agreement of the methods were also evaluated and a penalty criterion due to the lost information was proposed in order to account for the imputation uncertainty in the analysis. Results: (i) data analysis using only the complete units tended to underestimate the association between the air contaminants and the health events even when only a small amount of data is missing; (ii) mean and median imputation overestimated the association and estimates show high dispersion and low agreement between when compared to the original values; (iii) multivariate procedures presented better performance and accuracy than the univariate ones; (iv) multivariate methods with temporal adjustment presented higher accuracy and precision. This last approach also presented smaller prediction error and higher agreement between the imputed and the original values. Conclusion: The methods proposed in this work are implemented as an open source library called mtsdi for the statistical software R.

Smooth Location-Dependent Bandwidth Selection for Local Polynomial Regression

A bandwidth function for local polynomial models is commonly obtained by optimizing a pointwise penalty criterion, such as an estimated mean squared error (MSE), over a grid of predictor locations. A resultant regression estimate may suffer from irregularities, such as discontinuities, and contextual information over nearby predictor locations is not used. To mediate these difficulties, ad hoc postprocessing is sometimes carried out in the form of smoothing of the penalty criterion and/or the bandwidth estimates. In this work a technique is developed for choosing a smooth bandwidth function that uses a smoothing spline selected based on new “fit” and “roughness” penalties. The fit penalty pushes the bandwidth estimate to adhere to the chosen pointwise criterion, whereas the roughness penalty is imposed on the fitted regression estimate as opposed to the bandwidth estimate, which usually is not of direct interest. The technique can be used in conjunction with various adaptive bandwidth selection methods and provides a systematic way of incorporating contextual information into bandwidth estimation. To justify a spline bandwidth function, we show that under mild regularity conditions, there exists a smooth, asymptotically optimal bandwidth function. We also demonstrate empirically that the technique outperforms the empirical-bias bandwidth selector (EBBS) of Ruppert when using an EBBS MSE pointwise penalty estimate.

Amorphous swelling: A macromodel for mass and energy flow

A mathematical model is proposed to explain amorphous swelling. The model is based on nonequilibrium thermodynamics and optimization techniques. The swelling stress and strains in each amorphously swelling morphomk are calculated in terms of the absorbed water. Since each morphoma's swelling is controlled by the adjacent morphoma's activity, an optimization technique is proposed to calculate stress and strains between two (or more) neighboring swelling morphoma. By considering a penalty criterion for constraints violation, a condition is imposed in order that swelling in each morphoma is produced with a preferred mode. The premise of the model is general and may be applied to explain growth and remodeling of living tissues, foams, and growth of highly compressive cellular solids; the latter are widely used for energy absorbers.

On the convexity of games corresponding to sequencing situations with due dates

This paper considers sequencing situations with due date criteria. Three different types of criteria are considered: the weighted penalty criterion, the weighted tardiness criterion and the completion time criterion. The main focus is on convexity of the associated cooperative games.

Characteristics of polymeric optical passive single-mode waveguiding devices fabricated by an argon-ion laser

The fabrication of polymeric single-mode Gaussian profile optical waveguides is described. We used poly(methyl methacrylate) and a mixture of two intermiscible monomers for the cladding and the core, respectively, of the waveguides. The cores of the waveguides were fabricated by with an argon-ion laser beam. The waveguides had single-mode Gaussian refractive-index profiles. By using such waveguides, we fabricated directional couplers for power coupling to the adjacent waveguides and also parallel waveguide arrays for preventing power coupling to adjacent waveguides for use in interconnect chips. We analyzed the characteristics of these couplers by using the coupled-mode theory and compared the results with those obtained with the beam propagation method. Experimental results showed good correlation with the theoretical values. We designed optical bus arrays for interconnect chips, considering the variation of normalized frequency V, the power penalty, and the dimensions of the waveguides and the separation between them. The number of waveguides in the bus array increased with increasing V. For a known value of V, a waveguide's density increases with a decrease of its dimensions. The theoretical maximum number of waveguides is ~1490/cm and ~846/cm for 2 mum x 2 mum and 4 mum x 4 mum single-mode waveguides, respectively, to satisfy a 1-dB power penalty criterion at bit-error rate of 10(-9). We fabricated interconnect bus arrays with fifteen 4 mum x 4 mum waveguides for a 3-cm coupling length, and the experimental results were verified to be in good agreement with the theoretical values.

Analysis of crosstalk penalty in dense optical chip interconnects using single-mode waveguides

A crosstalk model to analyze the impact of crosstalk on the system parameters is developed. The following light source scenarios are investigated: (1) weakly coherent and uncorrelated, (2) weakly coherent and correlated, and (3) strongly coherent and correlated. Using a 1-dB power penalty criterion at a bit-error-rate of 10/sup -15/, it is shown that the crosstalk between neighboring waveguides must be smaller than -12 dB if the wavelength spacing or the linewidth of the sources is much larger than the receiver bandwidth. In the worst case, where the channels share the same monochromatic light source, the maximum crosstalk level declines to -25 dB. In a practical realization, where the sampling level is not optimized, the allowable crosstalk is reduced to -32 dB.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>