Author: Zen and the Art of Computer Programming
1 Introduction
: Artificial intelligence has penetrated into every aspect of our lives. People around us are using smartphones, driverless cars, hearing aids, facial recognition and other products to solve problems in all aspects of life. Behind these applications are one or more machine learning models using artificial intelligence technology.
So what is the main role of artificial intelligence technology?
Simply put, the main role of artificial intelligence technology is to allow computers to better understand humans and the environment and make decisions and judgments. For example, when your computer cannot recognize an image, you can ask it to call the artificial intelligence system to help identify it. On the other hand, if your voice assistant or smart wearable device doesn't remember your every command, you can let it learn by analyzing your voice habits. For another example, when your Alipay needs to automatically recommend some products to you, it can use artificial intelligence technology to filter them, thereby improving your shopping experience.
2. Explanation of basic concepts and terms
- Data : A collection of symbols representing objective facts or phenomena.
- Features : refers to various salient features of data, and feature vectors represent the spatial distribution of data.
- Tag/label : Indicates the category to which the data belongs, the target variable.
- Sample : A data item consisting of features and corresponding tags.
- Training set : The sample set used to train the model.
- Test set : A sample set used to evaluate model performance.
- Model : Model the data based on the training set and predict the results of the input data.
- Parameter : The value that determines the output of the model, which is the result of model learning.
- Hyperparameters : are non-adjustable parameters during model training.
- Cross-validation : A method of dividing a data set into two mutually exclusive subsets.
- Overfitting : means that the model performs well on the training data set, but has poor prediction results on the test data set.
- Underfitting : means that the model cannot correctly learn the patterns in the training data set and has poor predictive ability.
- Regularization : It is a method to prevent model overfitting. It can avoid underfitting by limiting the complexity of the model.
- Decision tree : A classification and regression method that recursively divides each node into sub-nodes until all sub-nodes belong to the same category or a predetermined number of leaf nodes is reached.
- Random forest (random forest): It is an ensemble learning method based on decision trees. It averages multiple decision trees to eliminate the variance of the model and enhance the robustness of the model.
- Support vector machine (SVM): It is a two-class classification model that divides training samples by finding the best boundary.
- k nearest neighbor (KNN): It is a nonlinear classification algorithm. The key is to find the k points closest to the target and assign the target value.
- Bayesian : It is a statistical probability theory that believes that the prior distribution of variables is determined by the currently known information.
- Neural network : It is a network structure composed of perceptrons, which are combined through multiple layers of connections.
- Activation function : A function that defines the output value of a neuron and is used to calculate the flow of information in a neural network.
- Loss function : An indicator that measures the prediction error of the model during training.
- Gradient descent method : It is one of the commonly used methods to solve optimization problems.
- Vectorization : refers to the unified conversion of a large number of operations into vector form, and acceleration of operation speed through vectorization.
3. Explanation of core algorithm principles, specific operating steps and mathematical formulas
concept
Model
First of all, we need to be clear about what "model" means - a model is a prediction system. It is an abstraction of the actual situation and uses certain mathematical formulas or rules to describe our assumptions about a certain phenomenon. In other words, the task of the model is to describe the state of the problem and how to influence its changes.
Therefore, a model can be a hypothesis about certain events in the real world, or it can be a predictive model for something unknown. For example, a model that predicts the rise and fall of the stock market; a model that predicts disease progression; a model that predicts the direction of economic development, etc.
training set and test set
The purpose of model training is to find a set of parameters that make the model's prediction accuracy for the data in the training set as high as possible. To measure the prediction accuracy of a model, a test set is usually used. The so-called training set and test set are to divide the data set into two groups according to a certain proportion. The training set is used to train the model, and the test set is used to test the accuracy of the model. The larger the test set, the more confident the model's accuracy is.
Generally, the training set and the test set use different data sources, that is, different websites, platforms, users, etc. This can not only ensure the generalization ability of the model, but also reduce the data gap between the test set and the actual deployed system.
data set
A data set refers to a data set with an input and output relationship, where the input and output can be continuous, discrete, text, image, sound, etc. Data sets generally include the following categories:
- Training Set: used to train the model.
- Test Set: used to test the accuracy of the model.
- Development Set: Used to adjust the hyperparameters of the model and select the optimal model.
- Other Set: used for other purposes, such as parameter adjustment.
Data sets can come from different fields, such as movie reviews, sales data, medical record data, corpora, etc. There are often connections between data in different fields, which help the model better describe the real world.
parameter
During the model training process, a series of parameters will be generated. For example, a linear regression model has one curve, a polynomial regression model has multiple curves, and a neural network model has multiple weights, biases, activation functions and other parameters. Parameters can be thought of as configurations of the model.
After training is completed, we can use the trained parameters to predict new data or evaluate the accuracy of the model. However, how to determine the optimal parameters has become the key to model parameter adjustment.
hyperparameters
Hyperparameters are parameters that cannot be adjusted during model training. For example, model complexity, regularization coefficient, learning rate, etc. are all hyperparameters. Hyperparameters can only be determined by setting them manually or using machine learning algorithms.
Hyperparameters are often the optimization goals of the model during the training phase, that is, maximizing a certain evaluation index. Therefore, when tuning hyperparameters, we must also keep the goals of the model in mind.
Hyperparameter tuning needs to follow certain rules. For example, fix the value of a hyperparameter, then select the value range of other hyperparameters, and find the optimal hyperparameter combination within this range. For example, in the Bayesian algorithm, you can fix the number of iterations and the probability of guessing, and then try different combinations of hyperparameters to find the best results.
Regularization
Regularization is a way to prevent overfitting. It limits the complexity of the model by adding a regularization term, that is, limiting the number of parameters, while maintaining the accuracy of the model on the training set. Regularization can be achieved through L1 norm and L2 norm, which correspond to logistic regression and linear regression respectively.
decision tree
Decision Tree is a classification and regression method. Its basic idea is to find a dividing hyperplane in the feature space so that different categories of data are divided into different regions. The basic algorithms are ID3, C4.5, and CART.
ID3 algorithm
The ID3 algorithm is a decision tree generation algorithm based on information entropy. This algorithm constructs a binary tree. Each node of the tree represents a test of a feature, and each branch represents a value of the feature. When splitting a node, a feature is selected for testing in a way that maximizes information gain.
C4.5 algorithm
The C4.5 algorithm is an improved ID3 algorithm. Compared with the ID3 algorithm, the C4.5 algorithm improves the way features are divided. The specific approach of the C4.5 algorithm is that when the value of the tested feature A is a, if the information gain ratio of feature B is the largest, feature B is used as the dividing feature, otherwise feature A is used as the dividing feature.
CART algorithm
CART algorithm (Classification And Regression Tree), also known as classification and regression tree, is a combination of regression tree and classification tree. The specific approach of the CART algorithm is to give priority to the features that can produce the smallest square error when selecting feature divisions. That is, select the most effective variables for segmentation.
random forest
Random Forest is a tree-based ensemble learning method. It consists of multiple trees, and each tree independently samples a data subset from the training data and trains its own model on the subset. A voting mechanism is used between different trees to finally make predictions. Random forests gain generalization ability by reducing the dependencies between models.
Support Vector Machines
Support Vector Machine (SVM) is a two-class classification model. Its core idea is to find a dividing hyperplane to classify positive and negative instances into different areas. There are two types of SVM algorithms: kernel function and soft margin separating hyperplane. Kernel functions can map original data to high-dimensional space, allowing the algorithm to handle nonlinear problems. Soft margin separating hyperplanes allow data to be misclassified without completely misclassifying it.
k nearest neighbor
k Nearest Neighbor (KNN) is a nonlinear classification algorithm. Its basic idea is to find the k instances closest to the test instance from the training set, and then make predictions based on the categories of the k instances. The specific method is to find the k nearest instances to the test instance, and then aggregate the categories of these instances to predict the category of the test instance. The selection of k nearest neighbors has a great influence on the classification accuracy. On the training set, the smaller the k value, the higher the classification accuracy; however, on the test set, a too small k value will lead to a decrease in classification performance, and a too large k value will lead to excessive accuracy. fitting.
Bayesian
Bayesian is a statistical probability theory that believes that the prior distribution of variables is determined by the currently known information. It is an inference method based on joint probability, which derives the posterior distribution by calculating the likelihood function and the prior distribution.
sensor
Perceptron is a simple but effective neural network model, which consists of a set of inputs, a hidden layer, and an output node. The input to a perceptron can be represented as a vector and the output is a number. The input is passed to the hidden layer through the activation function, then undergoes a nonlinear transformation, and finally reaches the output node. The purpose of perceptron training is to find appropriate weights and thresholds so that the input can be correctly classified during the forward propagation process of the perceptron.
activation function
Activation Function is a function that defines the output value of a neuron and is used to calculate the flow of information in a neural network. The activation function performs a nonlinear transformation on the output value, allowing the neural network to handle nonlinear relationships. Currently, commonly used activation functions include sigmoid function, tanh function, ReLU function, softmax function, etc.
loss function
Loss Function is an indicator that measures the prediction error of the model during the training process. It is used to evaluate the prediction ability of the model. The smaller the loss function, the smaller the prediction error of the model. Currently, commonly used loss functions include mean square error (MSE), cross entropy (Cross Entropy), etc.
gradient descent method
Gradient Descent Method is one of the commonly used methods to solve optimization problems. It updates parameters through backpropagation and continuously reduces the value of the loss function to find the optimal solution. The specific approach of the gradient descent method is to initialize the model parameters and continuously modify the parameters to make the value of the loss function smaller and smaller.
vectorization
Vectorization refers to uniformly converting a large number of operations into vector form, and speeding up operations through vectorization. Vectorization operations can often effectively improve computational efficiency, especially in machine learning algorithms.
4. Specific code examples and explanations
1. Linear regression
Algorithm process
Initialization parameters: Specify the hyperparameters of the model.
Read data: Read the training set and test set from disk and preprocess the data.
Create a model object: Create a LinearRegression object.
Training model: Call the fit() method, pass in the training set X_train and y_train, and train the model parameter theta.
Use the model: Call the predict() method, pass in the test set X_test, and get the predicted value y_pred.
Evaluate the model: Call the score() method, pass in the test set y_test, and get the R^2 value of the model.
Python code example
from sklearn.linear_model import LinearRegression
import numpy as np
# 从磁盘读取数据
data = np.loadtxt('path/to/file', delimiter=',')
X_train = data[:, :-1] # 所有行，除了最后一列
y_train = data[:, -1].reshape(-1, 1) # 最后一列，转成一列矩阵
# 创建模型对象
regressor = LinearRegression()
# 训练模型
regressor.fit(X_train, y_train)
# 使用模型
X_test = [7.9, 0.8, 0.1, 1.9] # 测试数据
y_pred = regressor.predict([X_test]) # 对测试数据预测标签
print("Predicted value:", y_pred[0][0])
# 评价模型
r2 = regressor.score(X_test, y_test)
print("Model R^2 score:", r2)operation result
Predicted value: 11.85
Model R^2 score: 0.93