Minimum Risk Criterion Research Articles

Incremental Learning and Conditional Drift Adaptation for Nonstationary Industrial Process Fault Diagnosis

Incremental learning based fault diagnosis is effective to learn from continuous industrial data on an ongoing basis. However, in the case of non-stationary industrial processes, new data distribution often gradually shifts away from that of historical data, due to equipment aging and manufacturing strategies, etc. Thus, conventional incremental methods with the identical independent distribution (i.i.d) assumption may no longer promise satisfied diagnosis performance. This paper concerns the conditional drift phenomenon, a relaxation of the i.i.d assumption, in which the conditional distribution of industrial data changes within different time. From a mathematical point of view, we firstly give the problem formulation of conditional drift and introduce a target mapping strategy for drift adaptation, under the minimum risk criteria. Then, following this strategy, an incremental diagnosis model with adaptation ability is designed. Particularly, a transformation matrix keeps matching the distributions of historical and new data. Thus, our method can quickly adapt to the conditional drift and be more robust against the evolving environment. The proposed method is applied for diagnosing faults in two industrial processes to demonstrate its effectiveness.

Application of mathematical and statistical methods to the problem of resource management in agricultural production, taking into account uncertainty and risk

The agricultural sphere of production has always been accompanied by the influence of a wide range of factors, among which a large share is assigned to natural and climatic. The activities of agricultural organizations, especially in the field of crop production, are directly related to weather events, and in addition, a number of unstable processes of economic content (prices, demand, etc.), as well as problems caused by sanctions and the need to resolve import substitution issues, force management decisions to be made in conditions of uncertainty and risk. At the same time, the competent use of resource potential enables enterprises to reduce production costs and increase its efficiency in general. The purpose of the study was to develop a procedure for the formation of alternative solutions to the problem of land management for optimal placement of crops in fields using mathematical and statistical methods. The article presents an overview of a number of scientific studies related to the improvement of the activities of agricultural organizations, the results of which highlight and consider the main factors, methods and methods of increasing its effectiveness. According to official statistical sources, the analysis of the state of agricultural production in Russia, the Volga Federal District and the Orenburg Region in the context of the crop industry is given. The methods of game theory are chosen as tools that allow the formation of alternative options according to a number of criteria (Maximax criterion, Wald maximin criterion, Savage minimum risk criterion, Hurwitz pessimism-optimism criterion). The testing of the computational algorithm was carried out on the materials of one of the agricultural organizations of the Orenburg region. As a result of the study, several strategies for the use of land resources were formed when the enterprise was operating under conditions of uncertainty and risk, depending on the behavior of market conditions and natural and climatic factors. The analysis of the presented calculations showed an increase in the profit of the organization when planning the distribution of areas for agricultural crops using mathematical and statistical tools, and the possibility of automating the computational process (against the background of the digitalization of data flow processing that is relevant today) will significantly reduce the time when making managerial decisions. The results of the work can be recommended to agricultural organizations for use in the process of land management to achieve maximum efficiency and profitability of the business.

Predictive risks assessment of power supply interruption to oil production consumers, taking into account changes in significant factors

THE GOAL. To develop a decision-making procedure for the commissioning of equipment in the power supply system of oil production facilities in accordance with the minimum risk criterion. To substantiate the effectiveness of its practical application in the tasks of equipment repair management with the "technical condition" strategy based on a risk-oriented approach.METHODS. When solving the tasks, the following methods were used: the flowchart method for calculating the structural reliability indicators of the distribution electrical network with changes in its operational composition and technical condition of elements (equipment), the method for predicting the risks of power supply disruption in the circuit of each technological consumer, taking into account the possibility of reserving and imposing emergency recovery of the main element on the planned repair of the backup, scenario approach for determining scenarios for changing the risk of power supply failures when the operating state of the electrical network circuit changes.RESULTS. As a result of solving the problems, the values of the structural reliability indicators of the studied distribution electrical network are calculated under the most likely scenarios of changes in its operational composition and technical condition of equipment, the features of the integrated assessment of the technical condition of objects of voltage class 6 kV in their operating conditions are considered. The functions of forecasting the probabilities of power supply failures of oil production facilities are obtained depending on the integral assessment of their technical condition, which, along with the severity of the consequences of failures, make it possible to predict risks.CONCLUSION. A computational procedure has been developed that includes mathematical models and an algorithm for prioritizing equipment with a strategy "according to technical condition" when putting it into repair based on a forecast of the risks of power supply disruption to consumers. On a concrete example, the verification of calculation models and algorithm was carried out, the effectiveness of the developed computational procedure and its applicability in solving practical problems of managing repairs of electrical equipment of oil production facilities based on a risk-oriented approach was shown.

ВИКОРИСТАННЯ МЕТОДІВ ОЦІНКИ ЕКОНОМІЧНИХ РИЗИКІВ ДЛЯ ПРИЙНЯТТЯ РІШЕНЬ ЩОДО ІНВЕСТУВАННЯ

The article uses methods of quantitative evaluation of economic risks that allow in conditions of uncertainty to provide an industrial enterprise with information on a less risky investment project for the adoption of a managerial decision. Several methods for assessing the risk of investing are used: the size of the dispersion, the value of the coefficient variation, the size of the semivariation, the size of the coefficient of semivariation, the value of the coefficient of asymmetry. Dispersion is a statistical term that describes the value range values expected for a particular variable. Dispersion is used in studying the variability of profits from a specific trading strategy or investment portfolio. This is often interpreted as a degree of uncertainty and, therefore, the risk associated with a certain portfolio of securities or investments. Semiivariation is an indicator of data that can be used to assess potential investment risks. Semivarianity is calculated by measuring the dispersion of all observations that fall below the middle or target data set. Neoclassical theory goes out for understanding that risks are just unfavorable scenarios for an investor company. Therefore, it is necessary to take into account the unfavorable deviations. When the management subject is loyal to risk, then it is necessary to use the coefficient of semivariation, which can also be determined which of the projects. If the company wants to successfully investigate the project, it is important to identify situations where the probability and magnitude of a positive (or negative) result is much larger than the opposite result. Understanding asymmetric risk is crucial for making correct decisions. The ability to identify asymmetric risk helps to avoid potentially dangerous situations where there are not enough errors. It also allows you to use the opportunities for investments where there are several ways to win. The criterion of maximum asymmetry is the minimum risk criterion. The results of the quantitative assessment of economic risks enable to substantiate the economic efficiency of investment projects.

Local temporal-spatial multi-granularity learning for sequential three-way granular computing

Based on multiple levels of granularity, the notion of sequential three-way granular computing focuses on a multiple stages of thinking, problem-solving, and information processing in threes. This paper interprets, represents, and implements sequential three-way granular computing by a framework of temporal-spatial multi-granularity learning, which is described with the temporality of data and the spatiality of parameters. In real-world decision-making, such a sequential approach is useful to make faster decisions for some objects with the lower cost of decision process and the acceptable accuracy when information is insufficient or unavailable. However, the cost of time-consuming computation for hierarchical multilevel granularity is our concern. To address this issue, we utilize a local strategy to accelerate a sequence of neighborhood-based granulation induced by Gaussian kernel function. Subsequently, local three-way decision rules are investigated based on the Bayesian minimum risk criterion. Moreover, by the construction of a novel local trisection model, we propose a local sequential approach of three-way granular computing under a temporal-spatial multilevel granular structure. Finally, a series of comparative experiments between global and local perspectives is carried out to verify the effectiveness of our proposed models.

A compromise solution method for the multiobjective minimum risk problem

We develop an approach which enables the decision maker to search for a compromise solution to a multiobjective stochastic linear programming (MOSLP) problem where the objective functions depend on parameters which are continuous random variables with normal multivariate distributions. The minimum-risk criterion is used to transform the MOSLP problem into its corresponding deterministic equivalent which in turn is reduced to a Chebyshev problem. An algorithm based on the combined use of the bisection method and the probabilities of achieving goals is developed to obtain the optimal or epsilon optimal solution of this specific problem. An illustrated example is included in this paper to clarify the developed theory.

The generalized degrees of freedom of multilinear principal component analysis

Tensor data, such as image set, movie data, gene-environment interactions, or gene–gene interactions, have become a popular data format in many fields. Multilinear Principal Component Analysis (MPCA) has been recognized as an efficient dimension reduction method for tensor data analysis. However, a gratifying rank selection method for a general application of MPCA is not yet available. For example, both the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), arguably two of the most commonly used model selection methods, require more strict model assumptions when applying on the rank selection in MPCA. In this paper, we propose a rank selection rule for MPCA based on the minimum risk criterion and Stein’s unbiased risk estimate (SURE). We derive a neat formula while using the minimum model assumptions for MPCA. It is composed of a residual sum of squares for model fitting and a penalty on the model complexity referred as the generalized degrees of freedom (GDF). We allocate each term in the GDF to either the number of parameters used in the model or the complexity in separating the signal from the noise. Compared with AIC and BIC and their modification methods, this criterion reaches higher accuracies in a thorough simulation study. Importantly, it has potential for more general application because it makes fewer model assumptions.

Convolutional support vector machines for speech recognition

Convolutional neural networks (CNNs) have demonstrated the state-of-the-art performances on automatic speech recognition. Softmax activation function for prediction and minimizing the cross-entropy loss is employed by most of the CNNs. This paper proposes a new deep architecture in which two heterogeneous classification techniques named as CNN and support vector machines (SVMs) are combined together. In this proposed model, features are learned using convolution layer and classified by SVMs. The last layer of CNN i.e. softmax layer is replaced by SVMs to efficiently deal with high dimensional features. This model should be interpreted as a special form of structured SVM and named as convolutional support vector machine (CSVM). Instead of training each component separately, the parameters of CNN and SVMs are jointly trained using frame level max-margin, sequence level max-margin, and state-level minimum Bayes risk criterion. The performance of CSVM is checked on TIMIT and Wall Street Journal datasets for phone recognition. By incorporating the features of both CNN and SVMs, CSVM improves the result by 13.33% and 2.31% over baseline CNN and segmental recurrent neural networks respectively.

Multi-target joint detection, tracking and classification based on random finite set for aerospace applications

Multi-target detection, tracking and classification are important problems in aerospace applications, such as reconnaissance, airborne and spaceborne sensing. These problems are correlated but are difficult to be solved simultaneously, especially for systems with multiple sensors. This paper summarized the existing work for multi-target joint detection, tracking and classification based on labeled random finite set. Furthermore, a new algorithm is proposed for multi-sensor multi-target joint detection, tracking and classification problem. A conditional multi-sensor multi-target state estimator is derived, and the optimal solution is then obtained based on the minimum Bayes risk criterion. The numerical simulations are performed, and the results are shown to be more accurate than that of the approximate solutions based on the unlabeled random finite set. It is observed that the labeled random finite set theory provides a good foundation for a joint solution for multi-target detection, tracking and classification.

Leveraging High Order Cumulants for Spectrum Sensing and Power Recognition in Cognitive Radio Networks

Hybrid interweave-underlay spectrum access in cognitive radio networks can explore spectrum opportunities when primary users (PUs) are either active or inactive, which significantly improves spectrum utilization. The practical wireless systems, such as long-term evolution-advanced, usually operate at multiple transmission power levels, leading to a multiple primary transmission power scenario. In such a case, the two fundamental issues in hybrid interweave-underlay spectrum access are to detect the “ON/OFF” status of PUs and to recognize the operating power level of PUs, which are challenging due to non-Gaussian transmitted signals. In this paper, we exploit high-order cumulants (HOCs) to efficiently perform spectrum sensing and power recognition. Specifically, for a given order and time lag, we first propose a single HOC-based spectrum sensing and power recognition scheme with low computational complexity, by leveraging minimum Bayes risk criterion. Moreover, we propose a hybrid multiple HOCs-based spectrum sensing and power recognition scheme with multiple orders and time lags, to further improve the detection performance. Both the proposed schemes can eliminate the adverse impact of the noise power uncertainty. Finally, simulation results are provided to evaluate the proposed schemes.

Hedging strategies for European contingent claims with the minimum shortfall risk criterion

This paper studied the optimal self-financing hedging strategies under the minimum shortfall risk criterion. By virtue of the Monte Carlo simulation, thousands of the underlying asset’s price paths are generated and the expected shortfall is estimated with the averaged terminal shortfall on all simulated price paths. Then, the Particle swarm optimization method is adopted to approximate the hedging positions. Compared with present researches, our numerical computing method can overcome the shortcomings that no explicit expressions about hedging strategies exist under the minimum shortfall risk criterion, And the empirically researching results show that, the higher strategy-adjusting-frequency may more excellently resist the financial market’s fluctuating risk and there is a reverse relationship between European call option’s strike prices and the hedging positions.

A Robust Statistics Approach to Minimum Variance Portfolio Optimization

We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market data often contain outliers which, if not correctly handled, may further corrupt the covariance estimation. We address these shortcomings by studying the performance of a hybrid covariance matrix estimator based on Tyler's robust M-estimator and on Ledoit-Wolf's shrinkage estimator while assuming samples with heavy-tailed distribution. Employing recent results from random matrix theory, we develop a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity. Our portfolio optimization method is shown via simulations to outperform existing methods both for synthetic and real market data.

Hybrid multiplicative multi-watermarking in DWT domain

Multiwatermarking embeds multiple watermarks into the media content imperceptibly. It is regarded as the potential means to protect the media contents' copyright and/or trace illegal redistributors in multi-user environments, e.g., collaborative media content production or layered media content distribution. However, there are still some open issues in designing a good multiwatermarking scheme, including the combination between multiple embedding steps, the combination between multiple watermarks and the security of embedding schemes. In this paper, novel multiwatermarking schemes are proposed, which are based on hybrid multi-bit multiplicative rules controlled by secret keys. Two hybrid multiplicative multiwatermarking decoders, i.e., optimum and locally optimum, are proposed, which are based on the minimum Bayesian risk criterion and the DWT coefficients are modeled as the generalized Gaussian distribution. The BER (average bit error rate) as the evaluation index of the performance of optimum hybrid decoders is exactly analyzed. Finally, experimental results are shown to confirm the validity of the theoretical and empirical analysis.

Shrinkage ridge estimators in semiparametric regression models

In this paper, ridge and non-ridge type shrinkage estimators and their positive parts are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. The exact risk expressions in addition to biases are derived for the estimators under study and the region of optimality of each estimator is exactly determined. Also, necessary and sufficient conditions, for the superiority of the ridge type estimator over its counterpart, for selecting the ridge parameter k are obtained. Lastly, a simulation study and real data analysis are performed to illustrate the efficiency of proposed estimators based on the minimum risk criterion. In this regard, kernel smoothing and modified cross-validation methods for estimating the non-parametric function are used.

Hybrid additive multi-watermarking and decoding

Hybrid multi-watermarking uses different embedding rules to embed one or multiple watermarks into the same region of the cover imperceptibly and alternatively. It is considered as a potential way to implement the copyright protection of the cover and the trace of illegal distribution in multi-party content distribution. However, there are some open issues in creating a good hybrid multi-watermarking scheme, including the combination among multiple embedding rules and the combination among multiple watermarks. In this paper, we establish two novel hybrid multi-bit additive multi-watermarking models, and a novel hybrid multi-watermarking scheme based on the models, which embeds the multiple watermarks into DWT coefficients controlled by a secret key. Nextly, the hybrid multi-watermarking decoders, i.e., optimum and locally optimum, are deduced based on the minimum Bayesian risk criterion and the generalized Gaussian distribution. To evaluate the schemes' performance, the average bit error rate is used to exactly analyze the performance of the optimum hybrid multi-watermarking decoders. Furthermore, the security of the proposed hybrid scheme is compared with that of the existing schemes. Finally, the robustness of the proposed hybrid scheme and the validity of the theoretical analysis is proved by the experimental results.

Hybrid additive watermarking and its decoders

With the rapid development of Internet-based media consuming, the piracy issue becomes urgent, which makes copyright protection a hot research topic. There exist various watermarking methods that are regarded as potential solutions to copyright protection. However, most of watermarking methods have different properties, and the combinatorial method is expected to make use of different methods' advantages and to get a good tradeoff. In this paper, a novel hybrid watermark embedding rule is proposed to select the general additive embedding rule or the special additive embedding rule securely. The selection is controlled by a secret key, and the watermark is embedded into the Discrete Wavelet Transform (DWT) domain. With respect to the hybrid embedding rule, the novel optimum and locally optimum hybrid additive decoder is proposed, which is based on the minimum Bayesian risk criterion. And simultaneously, the performance of the optimum hybrid decoder is theoretically analyzed, with the DWT coefficients modelled as the generalized Gaussian distribution. Furthermore, the security of the proposed hybrid watermarking scheme is proved higher than that of existing schemes. Finally, empirical experimental results are given to prove the validity of theoretical analysis.

NONPARAMETRIC DECODING OF BLOCK CODES IN CHANNELS WITH NON-GAUSSIAN NOISE

The problem of synthesis of the decoder of (n, k) block codes that is optimal by the minimum mean risk criterion is formulated and solved. The decision rule for the case of independent Markovian message and error sources is presented. A new algorithm for decoding (n, k) block codes that is based on the minimum mean risk criterion is proposed.

Applying Minimum-Risk Criterion to Stochastic Hub Location Problems

This paper presents a new class of two-stage stochastic hub location (HL) programming problems with minimum-risk criterion, in which uncertain demands are characterized by random vector. Meanwhile we demonstrate that the twostage programming problem is equivalent to a single-stage stochastic P-model. Under mild assumptions, we develop a deterministic binary programming problem by using standardization, which is equivalent to a binary fractional programming problem. Moreover, we show that the relaxation problem of the binary fractional programming problem is a convex programming problem. Taking advantage of branch-and-bound method, we provide a number of experiments to illustrate the efficiency of the proposed modeling idea.

Minimum risk criterion for uncertain production planning problems

This paper considers a new class of multi-product source and multi-period fuzzy random production planning problems with minimum risk and service levels where both the demands and the production costs are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The proposed problems are formulated as a fuzzy random production planning (FRPP) model by maximizing the mean chance of the total costs less than a given allowable investment level. Because the exact value of the objective function for a given decision variable cannot be easily obtained, we adopt an approximation approach (AA) to evaluate the objective value and then discuss the convergence of the AA, including the convergence of the objective value, the convergence of the optimal solutions and the convergence of the optimal value. Since the approximating multi-product source multi-period FRPP model is neither linear nor convex, an approximation-based hybrid monkey algorithm (MA) which combines the AA, stochastic simulation (SS), neural network (NN) and MA is designed to solve the proposed model. Finally, numerical examples are provided to illustrate the effectiveness of the hybrid monkey algorithm.

Allocation of public funds to R&D: a portfolio choice-styled decision model and a biotechnology case study

A decision problem—allocating public research and development (R&D) funding—is faced by a planner who has ambiguous knowledge of welfare effects of the various research areas. We model this as a reverse portfolio choice problem faced by a Bayesian decision-maker. Two elements of the planner’s inferential system are developed: a conditional distribution of welfare ‘returns’ on an allocation, given stated preferences of citizens for the different areas, and a minimum risk criterion for re-allocating these funds, given the performance of a status quo level of funding. A case study of Canadian public research funds expended on various applications of agricultural biotechnology is provided. The decision-making methodology can accommodate a variety of collective expenditure and resource allocation problems.