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