Case Introduction
This case will demonstrate how to use Long Short-Term Memory (LSTM) to predict Boston housing prices. We will utilize the LSTM model from the Keras library to accomplish this task. By using historical housing price data, we will train the LSTM model to predict future housing prices.
Algorithm Principles
Long Short-Term Memory (LSTM) is a variant of Recurrent Neural Networks (RNN) designed to handle sequential data. The core idea of LSTM is to control the flow of information through a gating mechanism to avoid the problems of vanishing and exploding gradients found in RNNs. LSTM has three types of gating units: input gate, forget gate, and output gate. These gates decide the amount of information to pass from the previous time step using a sigmoid activation function.
Formula Derivation
The calculation formulas for the three gating units of LSTM are:
Dataset
We will use the Boston housing price dataset, which contains information about 14 different features of houses in Boston, with the goal of predicting housing prices (continuous values). The dataset is already built into the Keras library and can be loaded directly for use.
Computation Steps
Import relevant libraries
Load and preprocess the dataset
Build the LSTM model
Compile the model
Train the model
Evaluate the model
Make predictions
Coding Process
First, we import the necessary libraries, including numpy, relevant modules from Keras, and optimization algorithms.
Use the boston_housing.load_data() function to load the Boston housing price dataset, splitting it into training and testing sets. We then calculate the mean and standard deviation on the training set and use these statistics to standardize the data.
Build the LSTM model. We use two LSTM layers, where the first layer returns the complete output sequence, and the second layer returns only the output of the last time step. Finally, we add a fully connected layer to output the predicted housing prices.
Compile the model. We choose mean squared error as the loss function and use the Adam optimization algorithm for model training.
Train the model. We train the model using the training set, specifying the batch size and number of epochs.
Evaluate the model. We use the test set to evaluate the trained model and calculate the mean squared error (MSE).
Make predictions. We use the trained model to predict the test set, obtaining the predicted housing prices.
Python Code (available for paid reading, but you can also try it yourself based on the content above!)