Deep Learning PyTorch Course, Start with Kaggle

With the advancement of deep learning, AI technology is rapidly evolving in various fields. In particular, its application in the field of data science is prominent, and many people are studying through various online platforms to learn machine learning and deep learning. Among them, Kaggle is an all-in-one platform for data scientists and machine learning engineers that provides a variety of datasets and problems. In this article, we will explore how to gain practical experience on Kaggle using PyTorch.

1. What is PyTorch?

PyTorch is an open-source machine learning framework developed by Facebook AI Research (FAIR), and it is very useful for building and training deep learning models. In particular, it supports dynamic computation graphs, which provide flexibility and readability in code, making it easy to implement complex models.

1.1. Key Features of PyTorch

  • Dynamic Computation Graph: The computation graph is created during execution, allowing for flexible modification of the model’s structure.
  • Pythonic Design: It is very similar to the basic syntax of Python, enabling natural and intuitive code writing.
  • Strong GPU Support: Through CUDA, it supports powerful parallel processing, allowing for efficient handling of large datasets.

2. Introduction to Kaggle

Kaggle is a platform for data science competitions where participants analyze datasets and train models to solve various problems, ultimately submitting their prediction results. Kaggle serves as a competitive arena for everyone, from beginners to experts, providing various resources and tutorials to help build skills.

2.1. Creating a Kaggle Account

To get started with Kaggle, you first need to create an account. Visit the Kaggle website to sign up. After registering, you can set up your profile and participate in various competitions.

3. Basic Example Using PyTorch

Now let’s create a deep learning model through a simple PyTorch example. In this example, we will build a model to recognize handwritten digits using the MNIST digit data.

3.1. Installing Required Libraries

!pip install torch torchvision
    

3.2. Downloading the MNIST Dataset

The MNIST dataset consists of handwritten digit images. We will use the dataset provided by torchvision to download it.

import torch
from torchvision import datasets, transforms

# Data preprocessing
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])

# Download MNIST dataset
trainset = datasets.MNIST(root='./data', train=True, download=True, transform=transform)
trainloader = torch.utils.data.DataLoader(trainset, batch_size=64, shuffle=True)
    

3.3. Building the Model

We will build a neural network with an MLP (Multi-layer Perceptron) structure. The model can be defined using the code below.

import torch.nn as nn
import torch.nn.functional as F

class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(784, 128)  # 28*28 = 784
        self.fc2 = nn.Linear(128, 10)    # 10 classes for digits 0-9

    def forward(self, x):
        x = x.view(x.size(0), -1)  # flatten input
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return x

model = SimpleNN()
    

3.4. Model Training

To train the model, we will define a loss function and an optimization technique, followed by training over several epochs.

import torch.optim as optim

# Define loss function and optimizer
criterion = nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=0.01)

# Train the model
for epoch in range(5):  # 5 epochs
    running_loss = 0.0
    for images, labels in trainloader:
        optimizer.zero_grad()   # initialize gradients to zero
        outputs = model(images) # Forward pass
        loss = criterion(outputs, labels)  # Calculate loss
        loss.backward()  # Backward pass
        optimizer.step() # Update parameters
        running_loss += loss.item()
    print(f'Epoch {epoch+1}, Loss: {running_loss/len(trainloader)}')

    

3.5. Model Evaluation

To evaluate whether the model has been well trained, we will calculate the accuracy on the test data.

# Model evaluation
testset = datasets.MNIST(root='./data', train=False, download=True, transform=transform)
testloader = torch.utils.data.DataLoader(testset, batch_size=64, shuffle=False)

correct = 0
total = 0

with torch.no_grad():
    for images, labels in testloader:
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()

print(f'Accuracy: {100 * correct / total}%')
    

4. Participating in a Kaggle Competition

Having learned the basic usage of PyTorch through the MNIST example, let’s participate in a Kaggle competition. There are various competitions on Kaggle, and you can join one in a field that interests you. Each competition page provides dataset downloads and example code for you to review.

4.1. Understanding Competition Tasks

Before joining a competition, you need to fully understand the problem description and the structure of the dataset. For instance, in the Titanic Survival Prediction competition, you will create a model to predict survivors using passenger characteristics and survival information.

4.2. Data Preprocessing

To improve model performance, data preprocessing is essential. This includes handling missing values, adding needed features, and normalizing the data.

4.3. Model Selection

You need to choose a suitable model based on the characteristics of the problem. CNNs (Convolutional Neural Networks) are generally used for image data, while RNNs (Recurrent Neural Networks) are utilized for time series data.

4.4. Submission Process

After training the model, save the prediction results as a CSV file for submission. The format of the file may vary depending on the competition, so be sure to check the submission guidelines.

5. Communicating with the Community

One of the greatest advantages of Kaggle is the ability to receive help from the community. You can refer to other participants’ notebooks and learn a lot through questions and answers. Additionally, networking with experienced data scientists can greatly aid in your growth.

5.1. Utilizing Notebooks

Kaggle offers a notebook (NB) feature where you can share your code and processes. It is a great place to organize your know-how or learn from the insights of other participants.

5.2. Scripts and Kaggle API

Using the Kaggle API, you can easily download datasets and submit to competitions. This simplifies repetitive tasks through automation.

!kaggle competitions download -c titanic
!kaggle kernels push
    

6. Conclusion

For many starting in deep learning, PyTorch and Kaggle are excellent starting points. They provide opportunities to gain practical project experience, learn modeling techniques, and understand how to communicate within the community. If you have learned the basic usage of PyTorch and how to participate in Kaggle competitions through this tutorial, you can now start incorporating various theories and techniques to create your own projects. The future of AI lies in your hands!

Appendix

References

Deep Learning PyTorch Course, Supervised Learning

Deep learning is a field of artificial intelligence (AI) that uses multilayer neural networks to learn patterns from data.
Today, we will conduct an in-depth lecture on one of the two most commonly used learning methods in deep learning, known as supervised learning.

1. What is Supervised Learning?

Supervised learning is a method for learning predictive models based on given data.
Here, ‘supervised’ refers to labeled training data.
In supervised learning, relationships between input data and output labels are learned to create a model capable of making predictions on new data.

1.1 Types of Supervised Learning

Supervised learning can be broadly divided into two types: classification and regression.

  • Classification: Predicts whether a given input data belongs to a specific class.
    For example, classifying whether an email is spam or not falls into this category.
  • Regression: Predicts continuous numeric values based on input data.
    For instance, predicting house prices based on the area of the house is an example of regression.

2. Introduction to PyTorch

PyTorch is an open-source machine learning library developed by Facebook that provides a variety of useful features for deep learning researchers and developers.
In particular, it supports dynamic computation graphs,
which makes it easier to debug and modify models.

2.1 Installing PyTorch

To install PyTorch, you can use the following command.
The command below shows how to install PyTorch using pip:

pip install torch torchvision torchaudio

3. Creating a Deep Learning Model

Now, let’s create a simple deep learning model using PyTorch.
This example will address a classification problem, using the famous MNIST dataset to build a model that classifies handwritten digits.
The MNIST dataset consists of images of digits from 0 to 9.

3.1 Loading the Dataset

First, we will load the MNIST dataset and split it into training and testing data.

import torch
from torchvision import datasets, transforms

# Data transformation (normalization)
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))  # Normalized to mean 0.5, standard deviation 0.5
])

# Download and load the MNIST dataset
train_dataset = datasets.MNIST(root='./data', train=True, download=True, transform=transform)
test_dataset = datasets.MNIST(root='./data', train=False, download=True, transform=transform)

train_loader = torch.utils.data.DataLoader(dataset=train_dataset, batch_size=64, shuffle=True)
test_loader = torch.utils.data.DataLoader(dataset=test_dataset, batch_size=64, shuffle=False)

3.2 Defining the Model

Deep learning models are defined by inheriting from nn.Module. Here, we will define a simple neural network model.

import torch.nn as nn
import torch.nn.functional as F

class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(28 * 28, 128)  # First layer
        self.fc2 = nn.Linear(128, 64)       # Second layer
        self.fc3 = nn.Linear(64, 10)        # Output layer

    def forward(self, x):
        x = x.view(-1, 28 * 28)  # Convert 2D image to 1D vector
        x = F.relu(self.fc1(x))  # Apply ReLU activation function
        x = F.relu(self.fc2(x))
        x = self.fc3(x)
        return x

# Create an instance of the model
model = SimpleNN()

3.3 Defining the Loss Function and Optimizer

Now we will define the loss function and optimizer. We will use the cross-entropy loss function and the Adam optimizer.

import torch.optim as optim

# Loss function
criterion = nn.CrossEntropyLoss()
# Optimizer
optimizer = optim.Adam(model.parameters(), lr=0.001)

3.4 Training the Model

Now it’s time to train the model. For each epoch, we will pass the data through the model iteratively,
compute the loss, and update the weights.

num_epochs = 5

for epoch in range(num_epochs):
    for images, labels in train_loader:
        # Zero the gradients
        optimizer.zero_grad()
        # Pass images through the model
        outputs = model(images)
        # Calculate loss
        loss = criterion(outputs, labels)
        # Backpropagation
        loss.backward()
        # Update weights
        optimizer.step()
    
    print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')

3.5 Evaluating the Model

Once training is complete, let’s evaluate the model using the test data.

correct = 0
total = 0

with torch.no_grad():  # Disable gradient calculation
    for images, labels in test_loader:
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)  # Extract the index of the maximum value
        total += labels.size(0)
        correct += (predicted == labels).sum().item()

print(f'Accuracy of the model on the test images: {100 * correct / total:.2f}%')

4. Conclusion

In this lecture, we learned how to build a basic deep learning model using PyTorch and
solve a classification problem using the MNIST dataset.
This approach utilizing supervised learning can be applied in various fields and can be expanded into more complex models.

4.1 Additional Learning Resources

If you want to learn more about deep learning, check out the following resources:

Deep learning is a vast field of research that requires continuous learning.
We hope this will help you on your deep learning journey!

Deep Learning PyTorch Course, Principal Component Analysis (PCA)

Principal Component Analysis (PCA) is a representative technique for reducing the dimensionality of data,
mainly used for purposes such as high-dimensional data analysis, data visualization, noise reduction, and feature extraction.
PCA plays a very important role in the data preprocessing and analysis stages in the fields of deep learning and machine learning.

1. Overview of PCA

PCA is a useful tool when processing large datasets, with the following objectives:

  • Dimensionality Reduction: Reduces high-dimensional data to lower dimensions while preserving important information of the data.
  • Visualization: Provides insights through visualization of the data.
  • Noise Reduction: Removes noise from high-dimensional data and emphasizes the signal.
  • Feature Extraction: Extracts key features from the data to enhance the performance of machine learning models.

2. Mathematical Principles of PCA

PCA is conducted through the following steps:

  1. Data Normalization: Normalizes the data so that the mean of each variable is 0 and the variance is 1.
  2. Covariance Matrix Calculation: Calculates the covariance matrix of the normalized data. The covariance matrix indicates the correlation between data variables.
  3. Eigenvalue Decomposition: Decomposes the covariance matrix to find the eigenvectors (principal components). The eigenvectors indicate the directions of the data, and the eigenvalues represent the importance of those directions.
  4. Principal Component Selection: Selects principal components in descending order based on eigenvalue size and chooses them according to the desired number of dimensions.
  5. Data Transformation: Transforms the original data into a new lower-dimensional space using the selected principal components.

3. Example of PCA: Implementation Using PyTorch

Now we will implement PCA using PyTorch. The code below manually implements the PCA algorithm and shows how to transform data using it.

3.1. Data Generation

import numpy as np
import matplotlib.pyplot as plt

# Generate random data
np.random.seed(0)
mean = [0, 0]
cov = [[1, 0.8], [0.8, 1]]  # Covariance matrix
data = np.random.multivariate_normal(mean, cov, 100)

# Visualize the data
plt.scatter(data[:, 0], data[:, 1])
plt.title('Original Data')
plt.xlabel('X1')
plt.ylabel('X2')
plt.axis('equal')
plt.grid()
plt.show()

3.2. PCA Implementation

import torch

def pca_manual(data, num_components=1):
    # 1. Data Normalization
    data_mean = data.mean(dim=0)
    normalized_data = data - data_mean

    # 2. Covariance Matrix Calculation
    covariance_matrix = torch.mm(normalized_data.t(), normalized_data) / (normalized_data.size(0) - 1)

    # 3. Eigenvalue Decomposition
    eigenvalues, eigenvectors = torch.eig(covariance_matrix, eigenvectors=True)

    # 4. Sort by Eigenvalue
    sorted_indices = torch.argsort(eigenvalues[:, 0], descending=True)
    selected_indices = sorted_indices[:num_components]

    # 5. Principal Component Selection
    principal_components = eigenvectors[:, selected_indices]

    # 6. Data Transformation
    transformed_data = torch.mm(normalized_data, principal_components)
    
    return transformed_data

# Convert data to tensor
data_tensor = torch.tensor(data, dtype=torch.float32)

# Apply PCA
transformed_data = pca_manual(data_tensor, num_components=1)

# Visualize transformed data
plt.scatter(transformed_data.numpy(), np.zeros_like(transformed_data.numpy()), alpha=0.5)
plt.title('PCA Transformed Data')
plt.xlabel('Principal Component 1')
plt.axis('equal')
plt.grid()
plt.show()

4. Use Cases of PCA

PCA is utilized in various fields.

  • Image Compression: PCA is used to reduce pixel data of high-resolution images, minimizing quality loss while saving space.
  • Gene Data Analysis: Reduces the dimensionality of biological data to facilitate data analysis and visualization.
  • Natural Language Processing: Reduces the dimensionality of word embeddings to help computers understand similarities between words.

5. Deep Learning Preprocessing Using PCA

In deep learning, PCA is often used in the data preprocessing stage. By reducing the dimensionality of the data,
it increases the efficiency of model learning and helps prevent overfitting. For example,
when processing image data, PCA can be used to reduce the dimension of input images,
providing only the main features to the model. This can reduce computational costs and improve the training speed of the model.

6. Limitations of PCA

While PCA is a powerful technique, it has some limitations:

  • Assumption of Linearity: PCA is most effective when data is linearly distributed. It may not be sufficiently effective for nonlinear data.
  • Interpretation of the Space: Interpreting the dimensions reduced by PCA can be difficult, and principal components may not be relevant to the actual problem.

7. Alternative Techniques

Nonlinear dimensionality reduction techniques that serve as alternatives to PCA include:

  • Kernel PCA: A version of PCA that uses kernel methods to handle nonlinear data.
  • t-SNE: Useful for data visualization, placing similar data points close together.
  • UMAP: A faster and more efficient data visualization technique than t-SNE.

8. Conclusion

Principal Component Analysis (PCA) is one of the key techniques in deep learning and machine learning,
used for various purposes, including dimensionality reduction, visualization, and feature extraction.
I hope you learned the principles of PCA and how to implement it using PyTorch through this course.
I look forward to you achieving better results by utilizing PCA in future data analysis and modeling processes.
In the next course, we will cover deeper topics in deep learning.

Deep Learning PyTorch Course, Performance Optimization Using Early Stopping

Overfitting is one of the common problems that occur during the training of deep learning models. Overfitting refers to the phenomenon where a model is too closely fitted to the training data, leading to a decreased ability to generalize to new data. Therefore, many researchers and engineers strive to prevent overfitting through various methods. One of these methods is ‘Early Stopping.’

What is Early Stopping?

Early stopping is a technique that monitors the training process of a model and stops the training when the performance on validation data does not improve. This method prevents overfitting by stopping the training when the model performs poorly on validation data, even if it has learned successfully from the training data.

How Early Stopping Works

Early stopping fundamentally observes the validation loss or validation accuracy during model training and stops the training if there is no performance improvement for a certain number of epochs. At this point, the optimal model parameters are saved, allowing the use of this model after training is completed.

Implementing Early Stopping

Here, we will implement early stopping through a simple example of training an image classification model using PyTorch. In this example, we will use the MNIST dataset to train a model that recognizes handwritten digits.

Installing Required Libraries

pip install torch torchvision matplotlib numpy

Code Example

Below is a PyTorch code example with early stopping applied.

import torch
import torch.nn as nn
import torch.optim as optim
import torchvision
import torchvision.transforms as transforms
from torch.utils.data import DataLoader

# Hyperparameter settings
input_size = 28 * 28  # MNIST image size
num_classes = 10  # Number of classes to classify
num_epochs = 20  # Total number of training epochs
batch_size = 100  # Batch size
learning_rate = 0.001  # Learning rate

# Load MNIST dataset
transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.5,), (0.5,))
])

train_dataset = torchvision.datasets.MNIST(root='./data', train=True, transform=transform, download=True)
train_loader = DataLoader(dataset=train_dataset, batch_size=batch_size, shuffle=True)

test_dataset = torchvision.datasets.MNIST(root='./data', train=False, transform=transform, download=True)
test_loader = DataLoader(dataset=test_dataset, batch_size=batch_size, shuffle=False)

# Define a simple neural network model
class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(input_size, 128)
        self.fc2 = nn.Linear(128, num_classes)

    def forward(self, x):
        x = x.view(-1, input_size)  # Reshape image dimensions
        x = torch.relu(self.fc1(x))  # Activation function
        x = self.fc2(x)
        return x

# Initialize model, loss function, and optimizer
model = SimpleNN()
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=learning_rate)

# Initialize variables for early stopping
best_loss = float('inf')
patience, trials = 5, 0  # Stop training if no performance improvement for 5 trials
train_losses, val_losses = [], []

# Training loop
for epoch in range(num_epochs):
    model.train()  # Switch model to training mode
    running_loss = 0.0

    for images, labels in train_loader:
        optimizer.zero_grad()  # Reset gradients
        outputs = model(images)  # Model predictions
        loss = criterion(outputs, labels)  # Calculate loss
        loss.backward()  # Compute gradients
        optimizer.step()  # Update weights

        running_loss += loss.item()

    avg_train_loss = running_loss / len(train_loader)
    train_losses.append(avg_train_loss)

    # Validation step
    model.eval()  # Switch model to evaluation mode
    val_loss = 0.0

    with torch.no_grad():  # Disable gradient computation
        for images, labels in test_loader:
            outputs = model(images)
            loss = criterion(outputs, labels)
            val_loss += loss.item()

    avg_val_loss = val_loss / len(test_loader)
    val_losses.append(avg_val_loss)

    print(f'Epoch [{epoch+1}/{num_epochs}], Train Loss: {avg_train_loss:.4f}, Valid Loss: {avg_val_loss:.4f}')

    # Early stopping logic
    if avg_val_loss < best_loss:
        best_loss = avg_val_loss
        trials = 0  # Reset performance improvement record
        torch.save(model.state_dict(), 'best_model.pth')  # Save best model
    else:
        trials += 1
        if trials >= patience:  # Stop training if no improvement for patience
            print("Early stopping...")
            break

# Evaluate performance on test data
model.load_state_dict(torch.load('best_model.pth'))  # Load best model
model.eval()  # Switch model to evaluation mode
correct, total = 0, 0

with torch.no_grad():
    for images, labels in test_loader:
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)  # Select class with maximum probability
        total += labels.size(0)
        correct += (predicted == labels).sum().item()

print(f'Accuracy of the model on the test images: {100 * correct / total:.2f}%')

Code Explanation

The above code represents the process of training a simple neural network model using the MNIST dataset. First, we import the necessary libraries and load the MNIST dataset. Then, we define a simple neural network composed of two fully connected layers.

After that, at each epoch, we calculate the training loss and validation loss and stop the training if there is no improvement in the validation loss through the early stopping logic. Finally, we evaluate the model’s performance by calculating the accuracy on the test data.

Conclusion

Early stopping is a useful technique for optimizing the performance of deep learning models. It helps prevent overfitting and leads to the generation of an optimal model. In this tutorial, we demonstrated how to implement early stopping using PyTorch to solve the MNIST classification problem. We encourage you to apply early stopping techniques to various deep learning problems based on this.

References

Deep Learning PyTorch Course, Restricted Boltzmann Machine

The Restricted Boltzmann Machine (RBM) is a type of unsupervised learning algorithm, also known as a generative model. RBMs can effectively learn from large amounts of input data and are utilized in various fields. This document aims to provide a deep understanding of the fundamental principles of RBMs, how to implement them in Python, and examples using the PyTorch framework.

1. Understanding Restricted Boltzmann Machines (RBM)

RBM is a model that originated from statistical physics, based on the concept of ‘Boltzmann Machines’. An RBM consists of two types of nodes: visible nodes and hidden nodes. There are connections between these two nodes, but there are no connections between the hidden nodes, resulting in a restricted structure. This structure allows for more efficient learning in RBMs.

1.1 Structure of RBM

RBM consists of the following components:

  • Visible Units: Represents the characteristics of the input data.
  • Hidden Units: Learns the underlying characteristics of the data.
  • Weights: Represents the strength of the connections between visible and hidden nodes.
  • Bias: Represents the bias values for each node.

1.2 Energy Function

The learning of RBM occurs through the process of minimizing the Energy Function. The energy function is defined based on the states of the visible and hidden nodes as follows:

E(v, h) = -∑ vi * bi - ∑ hj * cj - ∑ vi * hj * wij

Here, \( v \) represents the visible node, \( h \) represents the hidden node, \( b \) is the bias of the visible node, \( c \) is the bias of the hidden node, and \( w \) is the weight.

2. Learning Process of Restricted Boltzmann Machines

The learning process of RBM proceeds as follows:

  • Initialize the visible nodes from the dataset.
  • Calculate the probabilities of the hidden nodes.
  • Sample the hidden nodes.
  • Calculate the probabilities of the new visible nodes through the reconstruction of visible nodes.
  • Calculate the probabilities of the new hidden nodes through the reconstruction of hidden nodes.
  • Update weights and biases.

2.1 Contrastive Divergence Algorithm

The learning of RBM occurs through the Contrastive Divergence (CD) algorithm. CD consists of two main phases:

  1. Positive Phase: Identify the activations of the hidden nodes from the input data and update the weights based on this value.
  2. Pseudo Negative Phase: Reconstruct visible nodes from the sampled hidden nodes and then sample hidden nodes again to update weights in a way that reduces similarity.

3. Implementing RBM with PyTorch

This section explains how to implement RBM using PyTorch. First, let’s install the required libraries and prepare the dataset.

3.1 Install Libraries and Prepare Dataset

!pip install torch torchvision

We will use the MNIST dataset to train the RBM. This dataset consists of handwritten digit images.

import torch
from torchvision import datasets, transforms

# Downloading and transforming MNIST dataset
transform = transforms.Compose([transforms.ToTensor(), transforms.Lambda(lambda x: x.view(-1))])
mnist = datasets.MNIST(root='./data', train=True, download=True, transform=transform)
train_loader = torch.utils.data.DataLoader(dataset=mnist, batch_size=64, shuffle=True)

3.2 Define RBM Class

Now let’s define the RBM class. The class should include methods for weight initialization, weight updates, and training.

class RBM:
    def __init__(self, visible_units, hidden_units, learning_rate=0.1):
        self.visible_units = visible_units
        self.hidden_units = hidden_units
        self.learning_rate = learning_rate
        self.weights = torch.randn(visible_units, hidden_units) * 0.1
        self.visible_bias = torch.zeros(visible_units)
        self.hidden_bias = torch.zeros(hidden_units)

    def sample_hidden(self, visible):
        activation = torch.mm(visible, self.weights) + self.hidden_bias
        probabilities = torch.sigmoid(activation)
        return probabilities, torch.bernoulli(probabilities)

    def sample_visible(self, hidden):
        activation = torch.mm(hidden, self.weights.t()) + self.visible_bias
        probabilities = torch.sigmoid(activation)
        return probabilities, torch.bernoulli(probabilities)

    def train(self, train_loader, num_epochs=10):
        for epoch in range(num_epochs):
            for data, _ in train_loader:
                # Sample visible nodes
                v0 = data
                h0, h0_sample = self.sample_hidden(v0)

                # Negative phase
                v1, v1_sample = self.sample_visible(h0_sample)
                h1, _ = self.sample_hidden(v1_sample)

                # Update weights
                self.weights += self.learning_rate * (torch.mm(v0.t(), h0) - torch.mm(v1.t(), h1)) / v0.size(0)
                self.visible_bias += self.learning_rate * (v0 - v1).mean(0)
                self.hidden_bias += self.learning_rate * (h0 - h1).mean(0)

                print('Epoch: {} - Loss: {:.4f}'.format(epoch, torch.mean((v0 - v1) ** 2).item()))

3.3 Perform RBM Training

Now let’s train the model using the defined RBM class.

visible_units = 784  # For MNIST, 28x28 pixels
hidden_units = 256    # Number of hidden nodes
rbm = RBM(visible_units, hidden_units)
rbm.train(train_loader, num_epochs=10)

4. Results and Interpretation

As training progresses, the loss value is printed for each epoch. The loss value indicates how similar the reconstruction of visible nodes is to the hidden state, so a decrease in the loss value signifies an improvement in model performance. Notably, the Boltzmann Machine forms the basis of many other algorithms and is combined with various deep learning models.

5. Conclusion

In this post, we addressed the concept of restricted Boltzmann machines, the learning process, and a practical implementation example using PyTorch. RBM is a highly effective tool for learning the underlying structure of data. Nevertheless, it is primarily used for pre-training or in combination with other architectures in current deep learning frameworks. Further research on various generative models is expected in the future.