Interpolation in Machine Learning

Interpolation in Machine Learning

The practice of guessing unknown values based on available data points is known as interpolation in the context of machine learning. In tasks like regression and classification, where the objective is to predict outcomes based on input features, it is important. Machine learning algorithms are capable of producing well-informed predictions for unknown or intermediate values by interpolating between known data points....

Interpolation in Linear Form

A straightforward but efficient technique for guessing values between two known data points is linear interpolation....

Polynomial Interpolation

Polynomial interpolation is a method of estimating values between known data points by fitting a polynomial function to the data. The goal is to find a polynomial that passes through all the given points. This method is useful for approximating functions that may not have a simple analytical form. One common approach to polynomial interpolation is to use the Lagrange polynomial or Newton’s divided differences method to construct the interpolating polynomial....

Spline Interpolation

Spline interpolation is a method of interpolation where the interpolating function is a piecewise-defined polynomial called a spline. Unlike polynomial interpolation, which uses a single polynomial to fit all the data points, spline interpolation divides the data into smaller segments and fits a separate polynomial to each segment. This approach results in a smoother interpolating function that can better capture the local behavior of the data. The most common type of spline interpolation is cubic spline interpolation, which uses cubic polynomials for each segment and ensures continuity of the first and second derivatives at the endpoints of each segment. Spline interpolation is particularly useful for smoothing noisy data or interpolating functions with complex shapes....

Radial Basis Function Interpolation

Radial Basis Function (RBF) interpolation is a method of interpolation that uses radial basis functions to approximate the underlying data. Unlike polynomial interpolation, which fits a single polynomial to the entire dataset, RBF interpolation uses a combination of radial basis functions centered at each data point to construct the interpolating function....

Applications Of Interpolation in Machine Learning

Interpolation is a method used in various fields for estimating values between known data points. Some common applications of interpolation include:...