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Federated Learning (FL), a burgeoning technology, has received increasing attention due to its privacy protection capability. However, the base algorithm FedAvg is vulnerable when it suffers from so-called backdoor attacks. Former researchers proposed several robust aggregation methods. Unfortunately, due to the hidden characteristic of backdoor attacks, many of these aggregation methods are unable to defend against backdoor attacks. What's more, the attackers recently have proposed some hiding methods that further improve backdoor attacks' stealthiness, making all the existing robust aggregation methods fail.To tackle the threat of backdoor attacks, we propose a new aggregation method, X-raying Models with A Matrix (XMAM), to reveal the malicious local model updates submitted by the backdoor attackers. Since we observe that the output of the Softmax layer exhibits distinguishable patterns between malicious and benign updates, unlike the existing aggregation algorithms, we focus on the Softmax layer's output in which the backdoor attackers are difficult to hide their malicious behavior. Specifically, like medical X-ray examinations, we investigate the collected local model updates by using a matrix as an input to get their Softmax layer's outputs. Then, we preclude updates whose outputs are abnormal by clustering. Without any training dataset in the server, the extensive evaluations show that our XMAM can effectively distinguish malicious local model updates from benign ones. For instance, when other methods fail to defend against the backdoor attacks at no more than 20% malicious clients, our method can tolerate 45% malicious clients in the black-box mode and about 30% in Projected Gradient Descent (PGD) mode. Besides, under adaptive attacks, the results demonstrate that XMAM can still complete the global model training task even when there are 40% malicious clients. Finally, we analyze our method's screening complexity and compare the real screening time with other methods. The results show that XMAM is about 10–10000 times faster than the existing methods.

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This study addresses the issue of semantic similarity in sentences using the BERT model through various aggregation techniques, such as max-pooling, mean-pooling, and an LSTM network applied to the output of the BERT model. Subsequently, the linguistic interpretability of the BERT-Base transformer model is analyzed through the unsupervised learning approach, specifically through dimensionality reduction using autoencoders and clustering algorithms, utilizing the representation of the classification token CLS.The results highlight that the CLS classification token achieves better abstractions than the proposed methods. In terms of interpretability, it is observed that sequence length is relevant in the early layers, with a gradual decrease across the layers. Additionally, attention to semantic similarity is concentrated in the intermediate and upper layers, especially in layers 6, 8, 9, and 10. All these findings were obtained by addressing the semantic similarity task using the STS-Benchmark dataset. [ABSTRACT FROM AUTHOR]

Agriculture is a basic activity of human survival and its sustainability is of the utmost importance. In this paper, we present a novel mathematical model for the assessment of agricultural sustainability, based on certain intuitive and fundamental postulates. The resulting mathematical framework generalizes most existing models. We then rank 148 countries according to their agricultural sustainability, using data from the period 1995 to 2022 and pinpoint those aspects with the highest potential of improving sustainability using sensitivity analysis. Our findings demonstrate that farming is mostly unsustainable worldwide. The most crucial factors are connected with bad water use, destruction of biodiversity, and the prevalence of conventional chemical farming. As expected, poor countries make the bottom of the sustainability list. Surprisingly, several advanced countries such as Belgium, Japan, the Netherlands and Norway also occupy the bottom of the list because of very high emissions and bad performance concerning land and biodiversity. Finally, the highest score worldwide is of the order of only 70% and the median 50%, which exhibit a rather unsatisfactory farming state of affairs. Such findings ought to guide immediate action to make agriculture more sustainable.

Aggregation of species with similar ecological properties is one of the effective methods to simplify food web researches. However, species aggregation will affect not only the complexity of modeling process but also the accuracy of models' outputs. Selection of aggregation methods and the number of trophospecies are the keys to study the simplification of food web. In this study, three aggregation methods, including taxonomic aggregation (TA), structural equivalence aggregation (SEA), and self-organizing maps (SOM), were analyzed and compared with the linear inverse model–Markov Chain Monte Carlo (LIM-MCMC) model. Impacts of aggregation methods and trophospecies number on food webs were evaluated based on the robustness and unitless of ecological network indices. Results showed that aggregation method of SEA performed better than the other two methods in estimating food web structure and function indices. The effects of aggregation methods were driven by the differences in species aggregation principles, which will alter food web structure and function through the redistribution of energy flow. According to the results of mean absolute percentage error (MAPE) which can be applied to evaluate the accuracy of the model, we found that MAPE in food web indices will increase with the reducing trophospecies number, and MAPE in food web function indices were smaller and more stable than those in food web structure indices. Therefore, trade-off between simplifying food webs and reflecting the status of ecosystem should be considered in food web studies. These findings highlight the importance of aggregation methods and trophospecies number in the analysis of food web simplification. This study provided a framework to explore the extent to which food web models are affected by different species aggregation, and will provide scientific basis for the construction of food webs. [ABSTRACT FROM AUTHOR]

The reference point method (RPM) is based on the so-called augmented max-min aggregation where the worst individual achievement maximization process is additionally regularized with the average achievement. In order to avoid inconsistencies caused by the regularization, we replace it with the ordered weighted average (OWA) which combines all the individual achievements allocating the largest weight to the worst achievement, the second largest weight to the second worst achievement, and so on. Further following the concept of the weighted OWA (WOWA) we incorporate the importance weighting of several achievements into the RPM. Such a WOWA RPM approach uses importance weights to affect achievement importance by rescaling accordingly its measure within the distribution of achievements rather than by straightforward rescaling of achievement values. The recent progress in optimization methods for ordered averages allows us to implement the WOWA RPM quite effectively as extension of the original constraints and criteria with simple linear inequalities.

The problem of evaluation outcomes under several scenarios to form overall objective functions is of considerable importance in decision support under uncertainty. The fuzzy operator defined as the so-called weighted OWA (WOWA) aggregation offers a well-suited approach to this problem. The WOWA aggregation, similar to the classical ordered weighted averaging (OWA), uses the preferential weights assigned to the ordered values (i.e., to the worst value, the second worst and so on) rather than to the specific criteria. This allows one to model various preferences with respect to the risk. Simultaneously, importance weighting of scenarios can be introduced. In this paper we analyze solution procedures for optimization problems with the WOWA objective functions related to decisions under risk. Linear programming formulations are introduced for optimization of theWOWA objective representing risk averse preferences. Their computational efficiency is demonstrated.

In this work we present a large-scale comparison of 21 learning and aggregation methods proposed in the ensemble learning, social choice theory (SCT), information fusion and uncertainty management (IF-UM) and collective intelligence (CI) fields, based on a large collection of 40 benchmark datasets. The results of this comparison show that Bagging-based approaches reported performances comparable with XGBoost, and significantly outperformed other Boosting methods. In particular, ExtraTree-based approaches were as accurate as both XGBoost and Decision Tree-based ones while also being more computationally efficient. We also show how standard Bagging-based and IF-UM-inspired approaches outperformed the approaches based on CI and SCT. IF-UM-inspired approaches, in particular, reported the best performance (together with standard ExtraTrees), as well as the strongest resistance to label noise (together with XGBoost). Based on our results, we provide useful indications on the practical effectiveness of different state-of-the-art ensemble and aggregation methods in general settings. • Large-scale comparison of fusion and aggregation methods in ensemble learning. • Uncertainty management methods had the best performance and noise robustness. • Extra-Trees were the most efficient and had excellent baseline performance. • XGBoost had excellent accuracy and robustness but was significantly less efficient. [ABSTRACT FROM AUTHOR]

Sustainable consumption and production strive for the rational management of natural resources, which implies a transition to the production of fewer goods with the greatest consumer value. Consequently, the consumer value assessment is a key task in the product and service design. However, a large number of applied practices for assessing consumer value is a challenge for researchers. Multiple heterogeneous solutions without a common classification and structure do not allow comparing methods with each other. Thus, there is a demand for some universal algorithm for assessing consumer value, which would be a model for the development of individual industry practices. Therefore, the present research aims to develop a universal algorithm for assessing consumer value, which is a unified sample. The work analyzes the current expertise in assessing consumer value. The paper provides a comparison of mathematical tools for aggregate indicators in order to develop a general formula for assessing consumer value. As a result, an algorithm for assessing consumer value has been developed, which includes the following stages: market segmentation by consumer groups, taking into account their personal characteristics and needs; product hierarchical division into groups according to indicators valuable to the consumer; selection of a scale for evaluating indicators; hierarchical convolution, calculation of the consumer value of selected indicators and their aggregation into a final assessment in accordance with coefficients obtained as a result of the initial data analysis. As part of the algorithm verification, an example of the implementation of the algorithm steps based on expert assessment of the tourist product characteristics is proposed. At the next stage of the study, a register of mathematical tools will be specified to ensure the implementation of the algorithm steps, and practical testing on real data on several products from different industries. [ABSTRACT FROM AUTHOR]

Traditional machine learning projects have revolved around training the model with the help of previously observed data to be able to predict output for future unknown data. In the current scenario, when the data generated are huge, centralized training of the model becomes inefficient. Hence, distributed approach with client server model has to be used for training the models. This introduces data handling and critical data privacy issues. This paper concentrates on Federated learning (FL) which builds a model for the server by aggregating the parameters obtained from the local models of the client devices. The research work focuses on design and evaluation of three new FL algorithms against the average of the performances of the local models. The evolved approach considering weights of the local models proportional to accuracy of the local model is found to be the most accurate and better than the centralized approach. The evaluation is done using three different algorithms belonging to regression and classification on multiple datasets. It is observed that there is only one round of communication between the clients and server required in the federated learning setup to achieve the benchmarked accuracy set by the centralized setup. This is a considerable development and state-of-the-art approach to reduce communication and computation costs. [ABSTRACT FROM AUTHOR]

One of the problems in modern hydrology concerns the estimation of design events at sites with scarce or null data. This is a challenge for developing countries because they do not have monitoring networks as extensive and reliable as in developed nations. This situation has caused states in the Latin American and Caribbean region, in particular, to rely on hydrological regionalization techniques. These procedures implement clustering algorithms in combination with aggregation rules and metric distances to generate homogeneous groups from which hydrological information can be transferred. In addition, it has been proven that the analysis of spatial variables is sensitive to the magnitudes of extreme events; therefore, a mathematical formulation that adopts this fact into consideration must be included. For this purpose, the autocorrelation distance of the daily rainfall data series is proposed as an estimator of temporal variability. The fit parameters of the mixed Poisson-exponential probability distribution are operated as estimators of spatial variability. These spatio-temporal conditions are combined to obtain a mathematical relation of the autocorrelation as a measure of inertia for the classification of extreme events. This procedure is applied to Hydrologic Region 10 in northwestern Mexico from daily rainfall records. This zone has already been explored in terms of its regional homogeneity, which allows validating the results obtained. [ABSTRACT FROM AUTHOR]

Gaussian process regression is a flexible regression scheme but suffers from its high computational complexity regarding the inversion of a matrix with the same size as the training dataset. Aggregation method is one of the approximation techniques for reducing the complexity. In this paper, we propose a novel aggregation method, Nested Aggregation of Experts using Inducing Points (NAE-IP), which is an extension of a conventional method and enables dimensionality reduction by making use of the idea of linear sketching. There are some options for selecting inducing points in the proposed method. The options can introduce test points of interest as inducing points, albeit at the cost of slightly higher computational complexity. The other options exploiting less informative inducing points can yield a significant reduction of the computational complexity. The proposed NAE-IP is theoretically guaranteed to have consistency under certain conditions. Results of our computational experiments using synthetic and real data show that the proposed method achieves lower prediction error and even lower computing time than conventional methods. [ABSTRACT FROM AUTHOR]

One of the problems in modern hydrology concerns the estimation of design events at sites with scarce or null data. This is a challenge for developing countries because they do not have monitoring networks as extensive and reliable as in developed nations. This situation has caused states in the Latin American and Caribbean region, in particular, to rely on hydrological regionalization techniques. These procedures implement clustering algorithms in combination with aggregation rules and metric distances to generate homogeneous groups from which hydrological information can be transferred. In addition, it has been proven that the analysis of spatial variables is sensitive to the magnitudes of extreme events; therefore, a mathematical formulation that adopts this fact into consideration must be included. For this purpose, the autocorrelation distance of the daily rainfall data series is proposed as an estimator of temporal variability. The fit parameters of the mixed Poisson-exponential probability distribution are operated as estimators of spatial variability. These spatio-temporal conditions are combined to obtain a mathematical relation of the autocorrelation as a measure of inertia for the classification of extreme events. This procedure is applied to Hydrologic Region 10 in northwestern Mexico from daily rainfall records. This zone has already been explored in terms of its regional homogeneity, which allows validating the results obtained.