Parametric vs Nonparametric Methods: Estimating Functions and Making Predictions

📚 The goal is to find a function f-hat that can make predictions y hat from the data.

📈 We want to find the best fit line (F-hat) that minimizes the errors between predicted and actual labels.

💡 Two options to find the best fit line are parametric and non-parametric methods.

📏 Parametric methods involve making assumptions about the shape or form of the data.

🔍 Nonparametric methods do not make assumptions about the shape or form of the data.

📈 Estimating the function is simplified when assuming a linear form.

📊 Parametric methods simplify the estimation problem by using known parameters.

🔀 Nonparametric methods do not assume a specific form for the data distribution.

🔄 Parametric models may not accurately match the true form of the data.

Choosing a linear model for non-linear data results in poor predictions.

Using a parametric method involves expressing output based on a linear equation.

Estimating the beta values allows for predicting sales in the advertising dataset.

🔑 Parametric methods use predetermined parameters to make predictions based on specific assumptions.

🔑 Nonparametric methods do not make explicit assumptions about the shape or form of the data and seek to estimate it based on the data points.

🔑 Nonparametric methods have the advantage of being able to accurately fit a wider range of possible functions.

📊 Parametric methods assume a certain shape for the data, which can result in inaccurate predictions if the actual data shape is different.

🔄 Nonparametric methods do not make any assumptions about the shape of the data, resulting in better fitting models.

📉 However, nonparametric methods require a larger amount of data for accurate estimation.

📊 Parametric methods rely on predefined assumptions about the data, while nonparametric methods do not.

📉 Nonparametric methods may struggle to accurately estimate the response for observations not included in the training dataset.

🔍 Having a large, clean dataset with minimal outliers and noise is crucial for accurately estimating the best line in nonparametric methods.