# ARGMAX LÀ GÌ

Argmax is a mathematical function that you may encounter in applied machine learning.Quý Khách sẽ xem: Argmax là gì

For example, you may see “argmax” or “arg max” used in a research paper used khổng lồ describe an algorithm. You may also be instructed khổng lồ use the argmax function in your algorithm implementation.

Bạn đang xem: Argmax là gì

This may be the first time that you encounter the argmax function and you may wonder what it is và how it works.

In this tutorial, you will discover the argmax function & how it is used in machine learning.

After completing this tutorial, you will know:

Argmax is an operation that finds the argument that gives the maximum value from a target function.Argmax is most commonly used in machine learning for finding the class with the largest predicted probability.Argmax can be implemented manually, although the argmax() NumPy function is preferred in practice.

Kick-start your project with my new book Linear Algebra for Machine Learning, including step-by-step tutorials và the Pythanh mảnh source code files for all examples.

Let’s get started. What Is argmax in Machine Learning?Photo by Bernard Spragg. NZ, some rights reserved.

## Tutorial Overview

This tutorial is divided inlớn three parts; they are:

What Is Argmax?How Is Argmax Used in Machine Learning?How to lớn Implement Argmax in Python

## What Is Argmax?

Argmax is a mathematical function.

It is typically applied lớn another function that takes an argument. For example, given a function g() that takes the argument x, the argmax operation of that function would be described as follows:

result = argmax(g(x))

The argmax function returns the argument or arguments (arg) for the target function that returns the maximum (max) value from the target function.

Consider the example where g(x) is calculated as the square of the x value & the domain or extent of input values (x) is limited khổng lồ integers from 1 lớn 5:

g(1) = 1^2 = 1g(2) = 2^2 = 4g(3) = 3^2 = 9g(4) = 4^2 = 16g(5) = 5^2 = 25

We can intuitively see that the argmax for the function g(x) is 5.

That is, the argument (x) to lớn the target function g() that results in the largest value from the target function (25) is 5. Argmax provides a shorth& for specifying this argument in an abstract way without knowing what the value might be in a specific case.

argmax(g(x)) = 5

chú ý that this is not the max() of the values returned from function. This would be 25.

It is also not the max() of the arguments, although in this case the argmax and max of the arguments is the same, e.g. 5. The argmax() is 5 because g returns the largest value (25) when 5 is provided, not because 5 is the largest argument.

Typically, “argmax” is written as two separate words, e.g. “arg max“. For example:

result = arg max(g(x))

It is also comtháng khổng lồ use the arg max function as an operation without brackets surrounding the target function. This is often how you will see the operation written và used in a retìm kiếm paper or textbook. For example:

result = arg max g(x)

You can also use a similar operation to lớn find the arguments to lớn the target function that result in the minimum value from the target function, called argmin or “arg min.”

## How Is Argmax Used in Machine Learning?

Nevertheless, there are specific situations where you will see argmax used in applied machine learning and may need khổng lồ implement it yourself.

The most comtháng situation for using argmax that you will encounter in applied machine learning is in finding the index of an array that results in the largest value.

ReGọi that an array is a menu or vector of numbers.

It is comtháng for multi-class classification models to predict a vector of probabilities (or probability-like values), with one probability for each class label. The probabilities represent the likelihood that a sample belongs to each of the class labels.

The predicted probabilities are ordered such that the predicted probability at index 0 belongs khổng lồ the first class, the predicted probability at index 1 belongs to lớn the second class, và so on.

Often, a single class label prediction is required from a mix of predicted probabilities for a multi-class classification problem.

This conversion from a vector of predicted probabilities to a class label is most often described using the argmax operation & most often implemented using the argmax function.

Let’s make this concrete with an example.

Consider a multi-class classification problem with three classes: “red“, “blue,” và “green.” The class labels are mapped to integer values for modeling, as follows:

red = 0blue = 1green = 2

Each class label integer values maps to lớn an index of a 3-element vector that may be predicted by a Mã Sản Phẩm specifying the likelihood that an example belongs to each class.

Consider a model has made one prediction for an input sample and predicted the following vector of probabilities:

yhat =

We can see that the example has a 40 percent probability of belonging to red, a 50 percent probability of belonging khổng lồ xanh, and a 10 percent probability of belonging to lớn green.

We can apply the argmax function to lớn the vector of probabilities. The vector is the function, the output of the function is the probabilities, và the đầu vào to lớn the function is a vector element index or an array index.

arg max yhat

We can intuitively see that in this case, the argmax of the vector of predicted probabilities (yhat) is 1, as the probability at array index 1 is the largest value.

Note that this is not the max() of the probabilities, which would be 0.5. Also note that this is not the max of the arguments, which would be 2. Instead it is the argument that results in the maximum value, e.g. 1 that results in 0.5.

arg max yhat = 1

We can then map this integer value baông xã to lớn a class label, which would be “blue.”

arg max yhat = “blue”

## How lớn Implement Argmax in Python

The argmax function can be implemented in Pyeo hẹp for a given vector of numbers.

### Argmax from Scratch

First, we can define a function called argmax() that enumerates a provided vector and returns the index with the largest value.