The Default Risk of Firms Examined with Smooth Support Vector Machines

In the era of Basel II a powerful tool for bankruptcy prognosis is vital for banks. The tool must be precise but also easily adaptable to the bank's objections regarding the relation of false acceptances (Type I error) and false rejections (Type II error). We explore the suitabil- ity of Smooth Support Vector Machines (SSVM), and investigate how important factors such as selection of appropriate accounting ratios (predictors), length of training period and structure of the training sample in°uence the precision of prediction. Furthermore we show that oversampling can be employed to gear the tradeo® between error types. Finally, we illustrate graphically how di®erent variants of SSVM can be used jointly to support the decision task of loan o±cers.Insolvency Prognosis, SVMs, Statistical Learning Theory, Non-parametric Classification models, local time-homogeneity

The Default Risk of Firms Examined with Smooth Support Vector Machines

In the era of Basel II a powerful tool for bankruptcy prognosis is vital for banks. The tool must be precise but also easily adaptable to the bank's objections regarding the relation of false acceptances (Type I error) and false rejections (Type II error). We explore the suitability of Smooth Support Vector Machines (SSVM), and investigate how important factors such as selection of appropriate accounting ratios (predictors), length of training period and structure of the training sample influence the precision of prediction. Furthermore we showthat oversampling can be employed to gear the tradeoff between error types. Finally, we illustrate graphically how different variants of SSVM can be used jointly to support the decision task of loan officers.Insolvency Prognosis, SVMs, Statistical Learning Theory, Non-parametric Classification

A Hierarchical Framework Using Approximated Local Outlier Factor for Efficient Anomaly Detection

AbstractAnomaly detection aims to identify rare events that deviate remarkably from existing data. To satisfy real-world appli- cations, various anomaly detection technologies have been proposed. Due to the resource constraints, such as limited energy, computation ability and memory storage, most of them cannot be directly used in wireless sensor networks (WSNs). In this work, we proposed a hierarchical anomaly detection framework to overcome the challenges of anomaly detection in WSNs. We aim to detect anomalies by the accurate model and the approximated model learned at the re- mote server and sink nodes, respectively. Besides the framework, we also proposed an approximated local outlier factor algorithm, which can be learned at the sink nodes. The proposed algorithm is more efficient in computation and storage by comparing with the standard one. Experimental results verify the feasibility of our proposed method in terms of both accuracy and efficiency

The Default Risk of Firms Examined with Smooth Support Vector Machines

In the era of Basel II a powerful tool for bankruptcy prognosis is vital for banks. The tool must be precise but also easily adaptable to the bank’s objections regarding the relation of false acceptances (Type I error) and false rejections (Type II error). We explore the suitability of Smooth Support Vector Machines (SSVM), and investigate how important factors such as selection of appropriate accounting ratios (predictors), length of training period and structure of the training sample influence the precision of prediction. Furthermore we show that oversampling can be employed to gear the tradeoff between error types. Finally, we illustrate graphically how different variants of SSVM can be used jointly to support the decision task of loan officers

Federated Learning for Sparse Principal Component Analysis

In the rapidly evolving realm of machine learning, algorithm effectiveness often faces limitations due to data quality and availability. Traditional approaches grapple with data sharing due to legal and privacy concerns. The federated learning framework addresses this challenge. Federated learning is a decentralized approach where model training occurs on client sides, preserving privacy by keeping data localized. Instead of sending raw data to a central server, only model updates are exchanged, enhancing data security. We apply this framework to Sparse Principal Component Analysis (SPCA) in this work. SPCA aims to attain sparse component loadings while maximizing data variance for improved interpretability. Beside the L1 norm regularization term in conventional SPCA, we add a smoothing function to facilitate gradient-based optimization methods. Moreover, in order to improve computational efficiency, we introduce a least squares approximation to original SPCA. This enables analytic solutions on the optimization processes, leading to substantial computational improvements. Within the federated framework, we formulate SPCA as a consensus optimization problem, which can be solved using the Alternating Direction Method of Multipliers (ADMM). Our extensive experiments involve both IID and non-IID random features across various data owners. Results on synthetic and public datasets affirm the efficacy of our federated SPCA approach.Comment: 11 pages, 7 figures, 1 table. Accepted by IEEE BigData 2023, Sorrento, Ital

RSVM: Reduced Support Vector Machines

An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset is used as a constraint in an optimization problem with very few variables corresponding to the 1% of the data kept. The remainder of the data can be thrown away after solving the optimization problem. This is achieved by making use of a rectangular m m kernel K(A;A 0) that greatly reduces the size of the quadratic program to be solved and simpli es the characterization of the nonlinear separating surface. Here, the m rows of A represent the original m data points while the m rows of A represent a greatly reduced m data points. Computational results indicate that test set correctness for the reduced support vector machine (RSVM), with a nonlinear separating surface that depends on a small randomly selected portion of the dataset, is better than that of a conventional support vector machine (SVM) with a nonlinear surface that explicitly depends on the entire dataset, and much better than a conventional SVM using a small random sample of the data. Computational times, as well as memory usage, are much smaller for RSVM than that of a conventional SVM using the entire dataset

SSVM: A Amooth Support Vector Machine for Classification

Smoothing methods, extensively used for solving important math- ematical programming problems and applications, are applied here to generate and solve an unconstrained smooth reformulation of the support vector machine for pattern classi cation using a completely arbitrary kernel. We term such reformulation a smooth support vec- tor machine (SSVM). A fast Newton-Armijo algorithm for solving the SSVM converges globally and quadratically. Numerical results and comparisons are given to demonstrate the e ectiveness and speed of the algorithm. On six publicly available datasets, tenfold cross vali- dation correctness of SSVM was the highest compared with four other methods as well as the fastest. On larger problems, SSVM was compa- rable or faster than SVMlight [17], SOR [23] and SMO [27]. SSVM can also generate a highly nonlinear separating surface such as a checker- board

RSVM: Reduced support vector machines

The reduced support vector machine (RSVM) has been proposed to avoid the computational difficulties in generating a nonlinear support vector machine classifier for a massive dataset. RSVM selects a small random subset from the entire dataset with a user pre-specified size ¯m to generate a reduced kernel (rectangular) matrix. This reduced kernel will replace the fully dense square kernel matrix used in the nonlinear support vector machine formulation to cut the problem size and computational time and will not scarify the prediction accuracy. In this paper, we propose a new algorithm, Incremental Reduced Support Vector Machine (IRSVM). In contrast to purely random selection scheme used in RSVM, IRSVM begins with an extremely small reduced set and incrementally expands the reduced set according to an information criterion. This information-criterion based incremental selection can be achieved by solving a series of small least squares problems. In our approach, the size of reduced set will be determined automatically and dynamically but not pre-specified. The experimental tests on four publicly available datasets from the University of California (UC) Irvine repository show that IRSVM used a smaller reduced set than RSVM without scarifying classification accuracy