Kernel Logistic Regression-linear for Leukemia Classification Using High Dimensional Data

Kernel Logistic Regression (KLR) is one of the statistical models that has been proposed for classification in the machine learning and data mining communities, and also one of the effective methodologies in the kernel–machine techniques. Basely, KLR is kernelized version of linear Logistic Regression (LR). Unlike LR, KLR has ability to classify data with non linear boundary and also can accommodate data with very high dimensional and very few instances. In this research, we proposed to study the use of Linear Kernel on KLR in order to increase the accuracy of Leukemia Classification. Leukemia is one of the cancer types that causes mortality in medical diagnosis problem. Improving the accuracy of Leukemia Classification is essential for more effective diagnosis and treatment of Leukemia disease. The Leukemia data sets consists of 7120 (very high dimensional) DNA micro arrays data of 72 (very few instances) patient samples on the state of Leukemia types. In Leukemia classification based upon gene expression, monitoring data using DNA micro array offer hope to achieve an objective and highly accurate classification. It can be demonstrated that the use of Linear Kernel on Kernel Logistic Regression (KLR–Linear) can improve the performance in classifying Leukemia patient samples and also can be shown that KLR–Linear has better accuracy than KLR–Polynomial and Penalized Logistic Regression

Gradient-enhanced deep neural network approximations

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated gradient information to yield enhanced approximation accuracy. In particular, the gradient information is included as a regularization term in the gradient-enhanced DNNs approach, for which we present similar posterior estimates (by the two-layer neural networks) as those in the path-norm regularized DNNs approximations. We also discuss the application of this approach to gradient-enhanced uncertainty quantification, and present several numerical experiments to show that the proposed approach can outperform the traditional DNNs approach in many cases of interests.Comment: 14 pages, 3 figure

SmOOD: Smoothness-based Out-of-Distribution Detection Approach for Surrogate Neural Networks in Aircraft Design

Aircraft industry is constantly striving for more efficient design optimization methods in terms of human efforts, computation time, and resource consumption. Hybrid surrogate optimization maintains high results quality while providing rapid design assessments when both the surrogate model and the switch mechanism for eventually transitioning to the HF model are calibrated properly. Feedforward neural networks (FNNs) can capture highly nonlinear input-output mappings, yielding efficient surrogates for aircraft performance factors. However, FNNs often fail to generalize over the out-of-distribution (OOD) samples, which hinders their adoption in critical aircraft design optimization. Through SmOOD, our smoothness-based out-of-distribution detection approach, we propose to codesign a model-dependent OOD indicator with the optimized FNN surrogate, to produce a trustworthy surrogate model with selective but credible predictions. Unlike conventional uncertainty-grounded methods, SmOOD exploits inherent smoothness properties of the HF simulations to effectively expose OODs through revealing their suspicious sensitivities, thereby avoiding over-confident uncertainty estimates on OOD samples. By using SmOOD, only high-risk OOD inputs are forwarded to the HF model for re-evaluation, leading to more accurate results at a low overhead cost. Three aircraft performance models are investigated. Results show that FNN-based surrogates outperform their Gaussian Process counterparts in terms of predictive performance. Moreover, SmOOD does cover averagely 85% of actual OODs on all the study cases. When SmOOD plus FNN surrogates are deployed in hybrid surrogate optimization settings, they result in a decrease error rate of 34.65% and a computational speed up rate of 58.36 times, respectively

Predicting Bankruptcy with Support Vector Machines

The purpose of this work is to introduce one of the most promising among recently developed statistical techniques – the support vector machine (SVM) – to corporate bankruptcy analysis. An SVM is implemented for analysing such predictors as financial ratios. A method of adapting it to default probability estimation is proposed. A survey of practically applied methods is given. This work shows that support vector machines are capable of extracting useful information from financial data, although extensive data sets are required in order to fully utilize their classification power.support vector machine, classification method, statistical learning theory, electric load prediction, optical character recognition, predicting bankruptcy, risk classification