[MXML-3-04] Linear Regression [4/7] - Total Least Squares (TLS)

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In this video, we will look at the Total Least Squares, TLS. We will create an objective function for TLS and implement it in code.

In this video, we will look at the Total Least Squares, TLS in Chapter 2. Let's briefly compare OLS and TLS, and create an objective function for TLS. And we will implement TLS in code using the scipy library. Finally, let's train the Boston house price dataset, and predict the prices.

Let’s briefly compare the differences between OLS and TLS.

OLS assumes that there are no errors in the independent variable x and that there are errors only in the dependent variable y. So we simply measure the errors as the magnitude of y minus y_hat parallel to the y axis.

TLS assumes that there are errors in both the independent variable x and the dependent variable y. So, we measure the errors as the perpendicular distances of the data points to the regression line. The ordinary TLS assumes that all independent and dependent variables have the same level of uncorrelated Gaussian noise. TLS is a generalized form of least squares regression.

TLS is about finding the function that best fits the data points by minimizing the square sum of the perpendicular distances between data points and the regression line.

#LinearRegression #Regularization #TotalLeastSquare #TLS