Isotônico regression is a non-parametric regression technique used to fit a non-decreasing function to a set of data points. Unlike traditional regression methods that may impose a linear or polynomial form on the data, isotonic regression allows for a more flexible approach that can capture the underlying trend without making strict assumptions about its forma.
The primary goal of isotonic regression is to estimate a function that is monotonically non-decreasing, meaning that as the variável de entrada increases, the variável de saída does not decrease. This is particularly useful in situations where the researcher knows that the relationship between the variables should logically follow this pattern, such as in dose-response relationships in pharmacology ou em vários modelos econômicos.
Matematicamente, a regressão isotônica pode ser formulada como uma problema de otimização where the objective is to minimize the sum of squared differences between the observed values and the fitted values, subject to the monotonicity constraint. This is typically solved using algorithms such as the pool-adjacent-violators algorithm (PAVA), which iteratively adjusts the fitted values to satisfy the non-decreasing condition.
A regressão isotônica é amplamente utilizada em várias áreas, incluindo aprendizado de máquina, statistics, and economics, due to its ability to provide a more accurate representation of data where monotonicity is expected. It is particularly valued for its simplicity and interpretability, making it a popular choice among practitioners who need to analyze and visualize relationships in data.