The optimal solution of ESG portfolio selection models that are based on the average ESG score

Recently, various models have been proposed to engage portfolio selection or ESG investments. In this brief report, we solve the problem of optimal portfolio selection of arbitrary ESG utility functions where the ESG preference function is based on the average ESG score. The proposed optimal solution shows that the impact of the ESG score and the expected return vectors on the optimal weights are equal, up to a scalar, regardless of the utility function of the investors.     

A fuzzy random forest

When individual classifiers are combined appropriately, a statistically significant increase in classification accuracy is usually obtained. Multiple classifier systems are the result of combining several individual classifiers. Following Breiman’s methodology, in this paper a multiple classifier system based on a “forest” of fuzzy decision trees, i.e., a fuzzy random forest, is proposed. This approach combines the robustness of multiple classifier systems, the power of the randomness to increase the diversity of the trees, and the flexibility of fuzzy logic and fuzzy sets for imperfect data management. Various combination methods to obtain the final decision of the multiple classifier system are proposed and compared. Some of them are weighted combination methods which make a weighting of the decisions of the different elements of the multiple classifier system (leaves or trees). A comparative study with several datasets is made to show the efficiency of the proposed multiple classifier system and the various combination methods. The proposed multiple classifier system exhibits a good accuracy classification, comparable to that of the best classifiers when tested with conventional data sets. However, unlike other classifiers, the proposed classifier provides a similar accuracy when tested with imperfect datasets (with missing and fuzzy values) and with datasets with noise.     

Graph homomorphisms through random walks

In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff–Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge‐transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides a proof of the fact that the Coxeter graph is a core. Also, we obtain some information about the cores of vertex‐transitive graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 15–38, 2003     

Stochastic gradient algorithm with random truncations

Let f : R^d × R^d → R be a Borel-measurable function which satisfies ∫_R^d′|f(θ, x) < ∞, ∨θ ϵ R^d, where q₀(·) is a probability measure on (R^d′, B^d′). The problem of minimization of the function f₀(θ) = ∫_R^d′(θ, x)q₀(d), θ ϵ R^d, is considered for the case when the probability measure q₀(·) is unknown, but a realization of a non-stationary random process {X_n}_n⩾1 whose single probability measures in a certain sense tend to q₀(·), is available. The random process {X_n}_n⩾1 is defined on a common probability space, R^′-valued, correlated and satisfies certain uniform mix conditions. The function f(·, ·) is completely known. A stochastic gradient algorithm with random truncations is used for the minimization of f₀(·), and its almost sure convergence is proved.     

A bias-variance analysis of state-of-the-art random forest text classifiers

Advances in Data Analysis and Classification - Random forest (RF) classifiers do excel in a variety of automatic classification tasks, such as topic categorization and sentiment analysis. Despite...     

On the number of trees in a random forest

The analytic methods of Pólya, as reported in [1, 6] are used to determine the asymptotic behavior of the expected number of (unlabeled) trees in a random forest of order p. Our results can be expressed in terms of η = .338321856899208 …, the radius of convergence of t(x) which is the ordinary generating function for trees. We have found that the expected number of trees in a random forest approaches 1 + Σ_k=1^∞t(η^k) = 1.755510 … and the form of this result is the same     

Asymptotic packing and the random greedy algorithm

Let H be an r-uniform hypergraph satisfying deg(x) = D(1 + o(1)) for each vertex xϵ V(H) and deg(x, y) = o(D) for each pair of vertices x, y ϵ V(H), where D → infinity. Recently, J. Spencer [5] showed, using a branching process approach, that almost surely the random greedy algorithm finds a packing of size at least n/r(1 − o(1)) for this class of hypergraphs. In this paper, we show an alternative proof of this via “nibbles.” Further, let T_α be the number of edges that the random greedy algorithm has to consider before yielding a packing of size [n/r · (1 − α)]. We show that almost surely T_α ∼ (1/α)^r−1 · n/r(r − 1) as α → 0⁺ holds. © 1996 John Wiley & Sons, Inc.     

随机化均匀设计遗传算法

众所周知,遗传算法的运行机理及特点是具有定向制导的随机搜索技术,其定向制导的原则是:导向以高适应度模式为祖先的家族方向.以此结论为基础.利用随机化均匀设计的理论和方法,对遗传算法中的交叉操作进行了重新设计,给出了一个新的GA算法,称之为随机化均匀设计遗传算法.最后将随机化均匀设计遗传算法应用于求解函数优化问题,并与简单遗传算法和佳点集遗传算法进行比较.通过模拟比较,可以看出新的算法不但提高了算法的速度和精度,而且避免了其它方法常有的早期收敛现象,     

On the greedy algorithm with random costs

We consider hereditary systems (such as matroids) where the underlying elements have independent random costs, and investigate the cost of the base picked by the greedy algorithm.     

The prediction theory of stationary random fields (II): Nonsymmetrical half-plane prediction

In this paper, we consider the nonsymmetrical half-plane prediction. A prediction theoretic proof of the fundamental formula about one step prediction error is given. A Wold-type decomposition and its spectral representation theorem are proved. Spectral extraction problems of the half-plane innovations and its singular components are investigated.Research supported in part by the National Natural Science Fundation of China.     

Multi-step prediction of time series with random missing data

Multi-step prediction is still an open challenge in time series prediction. Moreover, practical observations are often incomplete because of sensor failure or outliers causing missing data. Therefore, it is very important to carry out research on multi-step prediction of time series with random missing data. Based on nonlinear filters and multilayer perceptron artificial neural networks (ANNs), one novel approach for multi-step prediction of time series with random missing data is proposed in the study. With the basis of original nonlinear filters which do not consider the missing data, first we obtain the generalized nonlinear filters by using a sequence of independent Bernoulli random variables to model random interruptions. Then the multi-step prediction model of time series with random missing data, which can be fit for the online training of generalized nonlinear filters, is established by using the ANN’s weights to present the state vector and the ANN’s outputs to present the observation equation. The performance between the original nonlinear filters based ANN model for multi-step prediction of time series with missing data and the generalized nonlinear filters based ANN model for multi-step prediction of time series with missing data is compared. Numerical results have demonstrated that the generalized nonlinear filters based ANN are proportionally superior to the original nonlinear filters based ANN for multi-step prediction of time series with missing data.     

Nonparametric prediction of a Hilbert space valued random variable

Let $\text{ξ}{}_{\mathrm{t}}\text{, t ?}\text{R}$, be a Markovian, measurable, strictly stationary process taking values in a measurable space (E, $\text{B}$), and g a mapping from E into a separable Hilbert space H. A statistical nonparametric predictor of g(ξ_T+h) is studied in the paper. That predictor, based on the observations of the process between the times O and T generalizes the ‘predictogram’; its asymptotic consistency is proved and some applications are given.     

Alternative sampling strategy for a random optimization algorithm

Alternative sampling procedures are compared to the pure random search method. It is shown that the efficiency of the algorithm can be improved with respect to the expected number of steps to reach an -neighborhood of the optimal point.This research was partially supported by CNPq-Brasil.     

General algorithm of random solutions for random nonlinear variational inequalities in banach Spaces *

In this paper, we study a class of random nonlinear variational inequalities in Banach spaces. By applying a random minimax inequahty obtained by Tarafdar and Yuan, some existence uniqueness theorems of random solutions for the random nonhnear variational inequalities are proved. Next, by applying the random auxiliary problem technique, we suggest an innovative iterative algorithm to compute the random approximate solutions of the random nonlinear variational inequahty. Finally, the convergence criteria is also discussed     

Dynamic Data-Driven Genetic Algorithm for forest fire spread prediction

This work represents the first step towards a Dynamic Data-Driven Application System (DDDAS) for wildland fire prediction. Our main efforts are focused on taking advantage of the computing power provided by High Performance Computing systems and to propose computational data-driven steering strategies to overcome input data uncertainty. In doing so, prediction quality can be enhanced significantly. On the other hand, these proposals reduce the execution time of the overall prediction process in order to be of use during real-time crisis. In particular, this work describes a Dynamic Data-Driven Genetic Algorithm (DDDGA) used as steering strategy to automatically adjust highly dynamic input data values of forest fire simulators taking into account the underlying propagation model and real fire behaviour.     

A global optimization algorithm using adaptive random search

A new random-search global optimization is described in which the variance of the step-size distribution is periodically optimized. By searching over a variance range of 8 to 10 decades, the algorithm finds the step-size distribution that yields the best local improvement in the criterion function. The variance search is then followed by a specified number of iterations of local random search where the step-size variance remains fixed. Periodic wide-range searches are introduced to ensure that the process does not stop at a local minimum. The sensitivity of the complete algorithm to various search parameters is investigated experimentally for a specific test problem. The ability of the method to locate global minima is illustrated by an example. The method also displays considerable problem independence, as demonstrated by two large and realistic example problems: (1) the identification of 25 parameters in a nonlinear model of a five-degrees-of-freedom mechanical dynamic system and (2) solution of a 24-parameter inverse problem required to identify a pulse train whose frequency spectrum matched a desired reference spectrum.     

Grey prediction evolution algorithm for global optimization

This article uses the grey prediction theory to structure a new metaheuristic: grey prediction evolution algorithm based on the even grey model. The proposed algorithm considers the population series of evolutionary algorithms as a time series, and uses the even grey model as a reproduction operator to forecast the next population (without employing any mutation and crossover operators). It is theoretically proven that the reproduction operator based on the even grey model is adaptive. Additionally, the algorithmic search mechanism and its differences with other evolutionary algorithms are analyzed. The performance of the proposed algorithm is validated on CEC2005 benchmark functions and a test suite composed of six engineering constrained design problems. The comparison experiments show the effectiveness and superiority of the proposed algorithm.The proposed algorithm can be regarded as the first case of structuring metaheuristics by using the prediction theory. The novel algorithm is anticipated to influence two future works. The first is to propose more metaheuristics inspired by prediction theories (including some statistical algorithms). Another is that the theoretical results of these prediction systems can be used for this novel type of metaheuristics.