LWR in Machine Learning

LWR in Machine Learning Mathematical theorem and predicting credit card spending with Locally Weighted Regression (LWR) We’ll explore Locally Weighted Regression in this chapter. LWR Locally Weighted Regression (LWR) is a non-parametric regression technique that fits a linear regression model to a dataset by weighting neighboring data points more heavily. As LWR learns a local set of parameters for each prediction, LWR can capture non-linear relationships in the data. LWR approx. non-linear function. Image source: Research Gate Key Differences from Linear Regression: LWR has advantages in approximating non-linear function by using local neighborhood to the query point. Yet, it is not the best for addressing larger dataset due to its computational cost, or high-dimensional cost functions as the local neighborhood of given query points might not contain sufficient data points truly close to all dimensions. Comparison of Linear Regression vs LWR Mathematical Theorem LWR has same objectives as linear regression, finding parameters θ that can minimize loss function (1). Yet, its core idea is to assign weights to training points based on their proximity to a query point using weight (ω) based on Gaussian kernel controlled by a bandwidth parameter (τ): The weight: ω denotes (2): where * x(i): a random training example, * x: a given query point and, *

May 10, 2025 - 06:06

LWR in Machine Learning

Mathematical theorem and predicting credit card spending with Locally Weighted Regression (LWR)

We’ll explore Locally Weighted Regression in this chapter.

LWR

Locally Weighted Regression (LWR) is a non-parametric regression technique that fits a linear regression model to a dataset by weighting neighboring data points more heavily.

As LWR learns a local set of parameters for each prediction, LWR can capture non-linear relationships in the data.

LWR approx. non-linear function. Image source: Research Gate

Key Differences from Linear Regression:

LWR has advantages in approximating non-linear function by using local neighborhood to the query point.

Yet, it is not the best for addressing larger dataset due to its computational cost, or high-dimensional cost functions as the local neighborhood of given query points might not contain sufficient data points truly close to all dimensions.

Comparison of Linear Regression vs LWR

Mathematical Theorem

LWR has same objectives as linear regression, finding parameters θ that can minimize loss function (1).

Yet, its core idea is to assign weights to training points based on their proximity to a query point using weight (ω) based on Gaussian kernel controlled by a bandwidth parameter (τ):

The weight: ω denotes (2):

where

* x(i): a random training example,
* x: a given query point and,
*