Suppose h ( )=e x p ( ) . M -matrix (see [ 50 ]).

Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR.

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample theory provides asymptotic normality of the MLE under certain conditions, such classical results are expected to fail in high-dimensions as documented for the binary logistic case in the seminal work of Sur and Candès [2019]. We address this issue in classification problems with 3 or more classes, by developing asymptotic normality and asymptotic chi-square results for the multinomial logistic MLE (also known as cross-entropy minimizer) on null covariates. Our theory leads to a new methodology to test the significance of a given feature. Extensive simulation studies on synthetic data corroborate these asymptotic results and confirm the validity of proposed p-values for testing the significance of a given feature.

We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived excess risk bounds, we conduct experiments on synthetic datasets. Furthermore, we compare FIRAL with five other methods and found that our scheme outperforms them: it consistently produces the smallest classification error in the multiclass logistic regression setting, as demonstrated through experiments on MNIST, CIFAR-10, and 50-class ImageNet.

Neural Information Processing Systems http://nips.cc/

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample theory provides asymptotic normality of the MLE under certain conditions, such classical results are expected to fail in high-dimensions as documented for the binary logistic case in the seminal work of Sur and Candès [2019]. We address this issue in classification problems with 3 or more classes, by developing asymptotic normality and asymptotic chi-square results for the multinomial logistic MLE (also known as cross-entropy minimizer) on null covariates. Our theory leads to a new methodology to test the significance of a given feature. Extensive simulation studies on synthetic data corroborate these asymptotic results and confirm the validity of proposed p-values for testing the significance of a given feature.

We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived excess risk bounds, we conduct experiments on synthetic datasets. Furthermore, we compare FIRAL with five other methods and found that our scheme outperforms them: it consistently produces the smallest classification error in the multiclass logistic regression setting, as demonstrated through experiments on MNIST, CIFAR-10, and 50-class ImageNet.

In today's technology-driven era, the imperative for predictive maintenance and advanced diagnostics extends beyond aviation to encompass the identification of damages, failures, and operational defects in rotating and moving machines. Implementing such services not only curtails maintenance costs but also extends machine lifespan, ensuring heightened operational efficiency. Moreover, it serves as a preventive measure against potential accidents or catastrophic events. The advent of Artificial Intelligence (AI) has revolutionized maintenance across industries, enabling more accurate and efficient prediction and analysis of machine failures, thereby conserving time and resources. Our proposed study aims to delve into various machine learning classification techniques, including Support Vector Machine (SVM), Random Forest, Logistic Regression, and Convolutional Neural Network LSTM-Based, for predicting and analyzing machine performance. SVM classifies data into different categories based on their positions in a multidimensional space, while Random Forest employs ensemble learning to create multiple decision trees for classification. Logistic Regression predicts the probability of binary outcomes using input data. The primary objective of the study is to assess these algorithms' performance in predicting and analyzing machine performance, considering factors such as accuracy, precision, recall, and F1 score. The findings will aid maintenance experts in selecting the most suitable machine learning algorithm for effective prediction and analysis of machine performance.