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 largesample 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.

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.

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 Cand\`es [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.

Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Logistic regression is a supervised machine learning algorithm to create models used for binary classification problems conventionally.

Floods are one of nature's most catastrophic calamities which cause irreversible and immense damage to human life, agriculture, infrastructure and socio-economic system. Several studies on flood catastrophe management and flood forecasting systems have been conducted. The accurate prediction of the onset and progression of floods in real time is challenging. To estimate water levels and velocities across a large area, it is necessary to combine data with computationally demanding flood propagation models. This paper aims to reduce the extreme risks of this natural disaster and also contributes to policy suggestions by providing a prediction for floods using different machine learning models. This research will use Binary Logistic Regression, K-Nearest Neighbor (KNN), Support Vector Classifier (SVC) and Decision tree Classifier to provide an accurate prediction. With the outcome, a comparative analysis will be conducted to understand which model delivers a better accuracy.

In the supervised machine learning world, there are two types of algorithmic task often performed. One is called regression (predicting continuous values) and the other is called classification (predicting discrete values). In this blog, I have presented an example of a binary classification algorithm called "Binary Logistic Regression" which comes under the Binomial family with a logit link function. Binary logistic regression is used for predicting binary classes. For example, in cases where you want to predict yes/no, win/loss, negative/positive, True/False and so on.

However, if the argument to exp(wT x) is large enough to cause overflow, wouldn't that also be the case for standard binary logistic regression as well, since negative-log-likelihood in that case contains the sigmoid function, which also has exp(wT x)? However, I don't think log-sum-exp can be applied to binary logistic regression, right?