What is a Restricted Boltzmann Machine?
A Restricted Boltzmann Machine (RBM) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs. RBMs were initially invented under the name Harmonium by Paul Smolensky in 1986, and they gained popularity for their effectiveness in dimensionality reduction, classification, regression, collaborative filtering, feature learning, and topic modeling.
RBMs are interesting in that they are unsupervised learning models with an ability to learn a probability distribution from the input. However, they can also be stacked to create more complex models such as Deep Belief Networks, which are used for supervised learning tasks.
Structure of a Restricted Boltzmann Machine
The structure of an RBM is relatively simple and consists of two layers: a visible layer and a hidden layer. The visible layer corresponds to the features of the data being modeled, while the hidden layer is used to capture the latent factors that explain correlations in the visible layer's features. Each node in the visible layer is connected to each node in the hidden layer, but there are no connections between nodes within a layer, hence the term "restricted." This restriction allows for more efficient training algorithms, most notably the contrastive divergence algorithm.
Energy-Based Model
RBMs are energy-based models, which means they associate a scalar energy to each configuration of the variables of interest. The network assigns a probability to every possible pair of a visible and hidden unit vector through this energy function, with lower-energy configurations being more probable.
Training an RBM
Training an RBM involves adjusting the weights and biases to minimize the energy of the system, which is equivalent to maximizing the likelihood of the data. This is typically done using a gradient descent algorithm, where the gradient is computed using a method called contrastive divergence.
Contrastive divergence is a learning algorithm that starts by initializing the visible units to a training vector and then uses this to infer the states of the hidden units. The states of the hidden units are then used to reconstruct the visible units. This process is repeated for a number of iterations, and the difference between the probabilities of the data-driven and model-driven samples is used to update the weights and biases.
Applications of RBMs
RBMs have been used in a variety of applications, including collaborative filtering for recommendation systems, dimensionality reduction, feature learning, and as building blocks for more complex models such as Deep Belief Networks (DBNs) and Deep Boltzmann Machines (DBMs).
In the context of recommendation systems, RBMs can learn to predict user preferences based on a history of user ratings. For dimensionality reduction, RBMs can learn to encode input data into a smaller set of latent variables, preserving the most significant structures of the data. Feature learning with RBMs involves learning representations that can be useful as inputs to other machine learning algorithms or for visualization purposes.
Advantages and Limitations
One of the advantages of RBMs is their ability to handle missing data, making them suitable for tasks like collaborative filtering where not all users have rated all items. They are also capable of learning complex, non-linear representations. However, RBMs can be difficult to train and may require careful tuning of parameters. They are also less popular in the current deep learning landscape due to the rise of other architectures like Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), which have shown better performance on tasks like image and speech recognition.
Conclusion
Despite the challenges in training and the emergence of more powerful neural network architectures, RBMs remain a significant part of the history of deep learning. Their ability to learn deep representations in an unsupervised manner and their application in various domains mark them as an important stepping stone in the development of more complex deep learning models.
References
Smolensky, P. (1986). Information processing in dynamical systems: Foundations of harmony theory. Colorado Univ at Boulder Dept of Computer Science.
Hinton, G. E. (2002). Training products of experts by minimizing contrastive divergence. Neural computation, 14(8), 1771-1800.
Salakhutdinov, R., Hinton, G. (2009). Deep Boltzmann Machines. AISTATS.
