Argmax—Wolfram Language Documentation

Argmax is a mathematical function that you may encounter in applied machine learning.

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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 to lớn use the argmax function in your algorithm implementation.

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.

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What Is argmax in Machine Learning?Photo by Bernard Spragg. NZ, some rights reserved.

Tutorial Overview

This tutorial is divided into lớn 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 to 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 and the domain or extent of input đầu vào values (x) is limited to integers from 1 to 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) khổng lồ the target function g() that results in the largest value from the target function (25) is 5. Argmax provides a shorthvà for specifying this argument in an abstract way without knowing what the value might be in a specific case.

argmax(g(x)) = 5

Note 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 & 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 common 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 research paper or textbook. For example:

result = arg max g(x)

You can also use a similar operation to lớn find the arguments khổng lồ 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?

The argmax function is used throughout the field of mathematics và machine learning.

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

The most common 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.

Rehotline that an array is a danh mục or vector of numbers.

It is comtháng for multi-class classification models lớn predict a vector of probabilities (or probability-lượt thích 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, and so on.

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

This conversion from a vector of predicted probabilities to lớn a class label is most often described using the argmax operation và 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,” & “green.” The class labels are mapped lớn integer values for modeling, as follows:

red = 0xanh = 1green = 2

Each class label integer values maps lớn an index of a 3-element vector that may be predicted by a mã sản phẩm specifying the likelihood that an example belongs lớn each class.

Consider a Model has made one prediction for an input đầu vào sample và predicted the following vector of probabilities:

yhat = <0.4, 0.5, 0.1>

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

chú ý 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 maps this integer value baông chồng to a class label, which would be “blue.”

arg max yhat = “blue”

How khổng lồ Implement Argmax in Python

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

Argmax from Scratch

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