# Partial Least Squares Regression

Examples & Code

Partial Least Squares Regression (PLSR) is a **dimensionality reduction** technique used in **supervised learning**. PLSR is a method for constructing predictive models when the factors are many and highly collinear. It is a regression-based approach that seeks to find the directions in the predictor space that explain the maximum covariance between the predictors and the response.

{% embed url="https://youtu.be/ApusVuE2zNY?si=ysytsTMpo3r6T306" %}

## Partial Least Squares Regression: Introduction

| Domains          | Learning Methods | Type                     |
| ---------------- | ---------------- | ------------------------ |
| Machine Learning | Supervised       | Dimensionality Reduction |

Partial Least Squares Regression (PLSR) is a popular algorithm in the field of machine learning and predictive analytics. It is a dimensionality reduction technique used to construct predictive models when dealing with highly collinear factors. In PLSR, the algorithm finds a linear combination of predictor variables that is most closely related to the response variable. This method is particularly useful when dealing with a large number of predictor variables, as it helps to reduce the dimensionality of the dataset without losing too much information.

PLSR falls under the category of supervised learning, which means that the algorithm requires labeled training data to build the model. It is commonly used in fields such as bioinformatics, chemometrics, and finance, where the number of variables is often much larger than the number of observations, and where traditional linear regression models may not be suitable.

By utilizing PLSR, engineers and data scientists can build more accurate predictive models and gain insights into complex systems with highly collinear variables.

In this guide, we will explore the inner workings of PLSR, its advantages and disadvantages, and provide examples of how it can be used in real-world applications.

## Partial Least Squares Regression: Use Cases & Examples

Partial Least Squares Regression (PLSR) is a method for constructing predictive models when the factors are many and highly collinear. It falls under the category of dimensionality reduction techniques, which are used to reduce the number of input variables in a model without losing too much information.

One of the most common use cases of PLSR is in the field of chemometrics, where it is used to analyze spectroscopic data. Spectroscopy is a technique used to measure the interaction between matter and electromagnetic radiation. The resulting spectra contain a large number of variables, which can be highly correlated. PLSR can be used to reduce the number of variables and build predictive models for various chemical properties.

Another application of PLSR is in the field of genetics, where it can be used to analyze gene expression data. Gene expression is the process by which genetic information is used to synthesize proteins. Microarray technology is often used to measure gene expression levels, resulting in a large number of variables that are highly correlated. PLSR can be used to identify the most important genes and build predictive models for various diseases.

PLSR has also been used in the field of finance, where it has been applied to build predictive models for stock prices. Stock prices are influenced by a large number of variables, such as company financials, economic indicators, and news events. PLSR can be used to identify the most important variables and build predictive models for future stock prices.

Lastly, PLSR has been used in the field of image analysis, where it can be used to analyze images containing a large number of pixels. PLSR can be used to identify the most important features in the images and build predictive models for various applications, such as facial recognition and object detection.

## Getting Started

Partial Least Squares Regression (PLSR) is a dimensionality reduction technique used for constructing predictive models when the factors are many and highly collinear. It is a supervised learning method that can be used for regression and classification tasks.

To get started with PLSR, you can use the scikit-learn library in Python. Here is an example code snippet:

```
import numpy as np
from sklearn.cross_decomposition import PLSRegression

# create sample data
X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
Y = np.array([1, 2, 3, 4])

# create PLSR object and fit the model
plsr = PLSRegression(n_components=2)
plsr.fit(X, Y)

# predict new values
new_X = np.array([[2, 3, 4], [5, 6, 7]])
predicted_Y = plsr.predict(new_X)

print(predicted_Y)

```

In this example, we first create sample data X and Y. X is a matrix with 4 rows and 3 columns, and Y is a vector with 4 elements. We then create a PLSRegression object with 2 components and fit the model using the fit() method. Finally, we use the predict() method to predict new values for a new X matrix.

## FAQs

### What is Partial Least Squares Regression (PLSR)?

Partial Least Squares Regression (PLSR) is a method for constructing predictive models when the factors are many and highly collinear. It is a technique that uses a linear regression model to analyze the relationship between the predictor variables and the response variable.

### What is the abbreviation for Partial Least Squares Regression?

The abbreviation for Partial Least Squares Regression is PLSR.

### What type of algorithm is Partial Least Squares Regression?

Partial Least Squares Regression is a dimensionality reduction algorithm. It is commonly used to extract important features from a large set of variables by projecting them onto a smaller dimensional space.

### What is the learning method used in Partial Least Squares Regression?

Partial Least Squares Regression is a supervised learning method. It requires a labeled dataset to train a model that can then be used to predict the response variable in new data.

### What are some applications of Partial Least Squares Regression?

PLSR is commonly used in chemometrics, where it is used to analyze data from spectroscopy, chromatography, and other analytical techniques. It is also used in other fields such as genetics, finance, and marketing to build predictive models and identify important features.

## Partial Least Squares Regression: ELI5

Imagine you're trying to bake a cake, but you have a bunch of ingredients that are all very similar, like different kinds of sugar. It's hard to know exactly how each sugar affects the final cake because they're all so similar and combined in different ways. This is similar to what happens when we have a lot of variables that are all related to each other. Partial Least Squares Regression (PLSR) helps us select only the most important variables and combine them in a way that predicts an outcome. It's like having a recipe that tells you exactly which sugars to use and how much of each one to add to make the perfect cake.

So, PLSR is a method for creating models to predict outcomes when we have lots of related variables. It helps us identify which variables are most important and how they should be combined to get accurate predictions.

PLRS is a type of dimensionality reduction where it combines similar variables and uses them to create predictors for the outcome variable.

PLRS only works as a supervised learning method, which means we need to have a set of data where we know the outcome variable in order to train the model to make accurate predictions.

In short, PLSR helps us pick out the most important variables from a large, related set of data and use them to predict an outcome, like baking a cake with only the best sugars.

\*\[MCTS]: Monte Carlo Tree Search [Partial Least Squares Regression](https://serp.ai/partial-least-squares-regression/)
