Nonlinear Monte Carlo Method for Imbalanced Data Learning

by   Xuli Shen, et al.

For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed (i.i.d.) and the mean value of loss function is used as the empirical risk by Law of Large Numbers (LLN). This is known as the Monte Carlo method. However, when LLN is not applicable, such as imbalanced data problems, empirical risk will cause overfitting and might decrease robustness and generalization ability. Inspired by the framework of nonlinear expectation theory, we substitute the mean value of loss function with the maximum value of subgroup mean loss. We call it nonlinear Monte Carlo method. In order to use numerical method of optimization, we linearize and smooth the functional of maximum empirical risk and get the descent direction via quadratic programming. With the proposed method, we achieve better performance than SOTA backbone models with less training steps, and more robustness for basic regression and imbalanced classification tasks.



There are no comments yet.


page 6


Wrapped Loss Function for Regularizing Nonconforming Residual Distributions

Multi-output is essential in machine learning that it might suffer from ...

Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo

Conditional value at risk (CVaR) is a popular measure for quantifying po...

Quasi-Newton Quasi-Monte Carlo for variational Bayes

Many machine learning problems optimize an objective that must be measur...

Strategic Monte Carlo Methods for State and Parameter Estimation in High Dimensional Nonlinear Problems

In statistical data assimilation one seeks the largest maximum of the co...

Adaptive Monte-Carlo Optimization

The celebrated Monte Carlo method estimates a quantity that is expensive...

Portfolio Selection under Multivariate Merton Model with Correlated Jump Risk

Portfolio selection in the periodic investment of securities modeled by ...

A flexible sequential Monte Carlo algorithm for parametric constrained regression

An algorithm is proposed that enables the imposition of shape constraint...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.