Extended Linear Regression: A Kalman Filter Approach for Minimizing Loss via Area Under the Curve

TL;DR

This paper introduces an innovative linear regression method that combines Kalman filtering and area-under-curve analysis to optimize model predictions and minimize loss, especially effective with partial datasets.

Contribution

It presents a novel approach integrating Kalman filters with area-under-curve analysis to enhance linear regression performance and robustness.

Findings

Achieves minimized loss through area under the curve optimization.

Works effectively with partial datasets, reducing computational needs.

Provides a new framework combining stochastic gradient descent and Kalman filtering.

Abstract

This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight updating. Our approach involves a stepwise process, starting with user-defined parameters. The linear regression model is trained using SGD, tracking weights and loss separately and zipping them finally. A Kalman filter is then trained based on weight and loss arrays to predict the next consolidated weights. Predictions result from multiplying input averages with weights, evaluated for loss to form a weight-versus-loss curve. The curve's equation is derived using the two-point formula, and area under the curve is calculated via integration. The linear regression equation with minimum area becomes the optimal curve for prediction. Benefits include avoiding constant weight updates via gradient descent and working with partial datasets, unlike methods needing the entire set. However, computational complexity should be considered. The Kalman filter's accuracy might diminish beyond a certain prediction range.