A fast learning algorithm for deep belief nets

2020

With the advent of deep learning, the number of works proposing new methods or improving existent ones has grown exponentially in the last years. In this scenario, “very deep” models were emerging, once they were expected to extract more intrinsic and abstract features while supporting a better performance. However, such models suffer from the gradient vanishing problem, i.e., backpropagation values become too close to zero in their shallower layers, ultimately causing learning to stagnate. Such an issue was overcome in the context of convolution neural networks by creating “shortcut connections” between layers, in a so-called deep residual learning framework. Nonetheless, a very popular deep learning technique called Deep Belief Network still suffers from gradient vanishing when dealing with discriminative tasks. Therefore, this paper proposes the Residual Deep Belief Network, which considers the information reinforcement layer-by-layer to improve the feature extraction and knowled...

We propose a Multi-Layer Network based on the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional lattice. The Latent Variable Model (LVM) is the basic building block of a quadtree hierarchy built on top of a bottom layer of random variables that represent pixels of an image, a feature map, or more generally a collection of spatially distributed discrete variables. The multi-layer architecture implements a hierarchical data representation that, via belief propagation, can be used for learning and inference. Typical uses are pattern completion, correction and classification. The FGrn paradigm provides great flexibility and modularity and appears as a promising candidate for building deep networks: the system can be easily extended by introducing new and different (in cardinality and in type) variables. Prior knowledge, or supervised information, can be introduced at different scales. The FGrn paradigm provides a handy way for building all kinds of architectures by interconnecting only three types of units: Single Input Single Output (SISO) blocks, Sources and Replicators. The network is designed like a circuit diagram and the belief messages flow bidirectionally in the whole system. The learning algorithms operate only locally within each block. The framework is demonstrated in this paper in a three-layer structure applied to images extracted from a standard data set.

2013

Designing a principled and effective algorithm for learning deep architectures is a challenging problem. The current approach involves two training phases: a fully unsupervised learning followed by a strongly discriminative optimization. We suggest a deep learning strategy that bridges the gap between the two phases, resulting in a three-phase learning procedure. We propose to implement the scheme using a method to regularize deep belief networks with top-down information. The network is constructed from building blocks of restricted Boltzmann machines learned by combining bottom-up and top-down sampled signals. A global optimization procedure that merges samples from a forward bottom-up pass and a top-down pass is used. Experiments on the MNIST dataset show improvements over the existing algorithms for deep belief networks. Object recognition results on the Caltech-101 dataset also yield competitive results.

PhD Thesis - Cambridge, 2018

arXiv: Learning, 2019

We present a novel adversarial framework for training deep belief networks (DBNs), which includes replacing the generator network in the methodology of generative adversarial networks (GANs) with a DBN and developing a highly parallelizable numerical algorithm for training the resulting architecture in a stochastic manner. Unlike the existing techniques, this framework can be applied to the most general form of DBNs with no requirement for back propagation. As such, it lays a new foundation for developing DBNs on a par with GANs with various regularization units, such as pooling and normalization. Foregoing back-propagation, our framework also exhibits superior scalability as compared to other DBN and GAN learning techniques. We present a number of numerical experiments in computer vision as well as neurosciences to illustrate the main advantages of our approach.

2009

We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent expectations are estimated using a variational approximation that tends to focus on a single mode, and dataindependent expectations are approximated using persistent Markov chains. The use of two quite different techniques for estimating the two types of expectation that enter into the gradient of the log-likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer "pre-training" phase that allows variational inference to be initialized with a single bottomup pass. We present results on the MNIST and NORB datasets showing that deep Boltzmann machines learn good generative models and perform well on handwritten digit and visual object recognition tasks.

Neural Computation, 2008

Deep Belief Networks (DBN) are generative neural network models with many layers of hidden explanatory factors, recently introduced by Hinton et al., along with a greedy layer-wise unsupervised learning algorithm. The building block of a DBN is a probabilistic model called a Restricted Boltzmann Machine (RBM), used to represent one layer of the model. Restricted Boltzmann Machines are interesting because inference is easy in them, and because they have been successfully used as building blocks for training deeper models. We first prove that adding hidden units yields strictly improved modeling power, while a second theorem shows that RBMs are universal approximators of discrete distributions. We then study the question of whether DBNs with more layers are strictly more powerful in terms of representational power. This suggests a new and less greedy criterion for training RBMs within DBNs.

IEEE transactions on neural networks and learning systems, 2019

This paper addresses the duality between deterministic feed-forward neural networks (FF-NNs), and linear Bayesian networks (LBNs), which are generative stochastic models representing probability distributions over the visible data based on a linear function of a set of latent (hidden) variables. The maximum entropy principle is used to define a unique generative model corresponding to each FF-NN, called projected belief network (PBN). The FF-NN exactly recovers the hidden variables of the dual PBN. The large-◆ asymptotic approximation to the PBN has the familiar structure of an LBN, with the addition of an invertible non-linear transformation operating on the latent variables. It is shown that the exact nature of the PBN depends on the range of the input (visible) data-details for three cases of input data range are provided. The likelihood function of the PBN is straightforward to calculate, allowing it to be used as a generative classifier. An example is provided in which a generative classifier based on the PBN has comparable performance to a deep belief network in classifying handwritten characters. In addition, several examples are provided that demonstrate the duality relationship, for example by training networks from either side of the duality.

2009 IEEE Conference on Computer Vision and Pattern Recognition, 2009

In this paper we present a method for learning classspecific features for recognition. Recently a greedy layerwise procedure was proposed to initialize weights of deep belief networks, by viewing each layer as a separate Restricted Boltzmann Machine (RBM). We develop the Convolutional RBM (C-RBM), a variant of the RBM model in which weights are shared to respect the spatial structure of images. This framework learns a set of features that can generate the images of a specific object class. Our feature extraction model is a four layer hierarchy of alternating filtering and maximum subsampling. We learn feature parameters of the first and third layers viewing them as separate C-RBMs. The outputs of our feature extraction hierarchy are then fed as input to a discriminative classifier. It is experimentally demonstrated that the extracted features are effective for object detection, using them to obtain performance comparable to the state-of-the-art on handwritten digit recognition and pedestrian detection.

Neural Computation, 2010

Deep Belief Networks (DBN) are generative models with many layers of hidden causal variables, recently introduced by Hinton et al. (2006), along with a greedy layer-wise unsupervised learning algorithm. Building on Le Roux and Bengio (2008) and Sutskever and Hinton , we show that deep but narrow generative networks do not require more parameters than shallow ones to achieve universal approximation. Exploiting the proof technique, we prove that deep but narrow feed-forward neural networks with sigmoidal units can represent any Boolean expression.

Entropy, 2016

Conventionally, the maximum likelihood (ML) criterion is applied to train a deep belief network (DBN). We present a maximum entropy (ME) learning algorithm for DBNs, designed specifically to handle limited training data. Maximizing only the entropy of parameters in the DBN allows more effective generalization capability, less bias towards data distributions, and robustness to over-fitting compared to ML learning. Results of text classification and object recognition tasks demonstrate ME-trained DBN outperforms ML-trained DBN when training data is limited.

Advances in neural information processing …, 2007

Motivated in part by the hierarchical organization of the cortex, a number of algorithms have recently been proposed that try to learn hierarchical, or "deep," structure from unlabeled data. While several authors have formally or informally compared their algorithms to computations performed in visual area V1 (and the cochlea), little attempt has been made thus far to evaluate these algorithms in terms of their fidelity for mimicking computations at deeper levels in the cortical hierarchy. This paper presents an unsupervised learning model that faithfully mimics certain properties of visual area V2. Specifically, we develop a sparse variant of the deep belief networks of . We learn two layers of nodes in the network, and demonstrate that the first layer, similar to prior work on sparse coding and ICA, results in localized, oriented, edge filters, similar to the Gabor functions known to model V1 cell receptive fields. Further, the second layer in our model encodes correlations of the first layer responses in the data. Specifically, it picks up both colinear ("contour") features as well as corners and junctions. More interestingly, in a quantitative comparison, the encoding of these more complex "corner" features matches well with the results from the Ito & Komatsu's study of biological V2 responses. This suggests that our sparse variant of deep belief networks holds promise for modeling more higher-order features.

2007

Abstract Unsupervised learning algorithms aim to discover the structure hidden in the data, and to learn representations that are more suitable as input to a supervised machine than the raw input. Many unsupervised methods are based on reconstructing the input from the representation, while constraining the representation to have certain desirable properties (eg low dimension, sparsity, etc). Others are based on approximating density by stochastically reconstructing the input from the representation.

—Training deep models are time consuming and face many local minima. For dealing with this problem, we can use DBN (Deep Belief Network) with Contrastive Divergence (CD). Sparse representations are more efficient. This paper aims to find the best structure of incorporating sparsity into discriminative DBN. We use a DBN architecture with 784 units as input, two layers each with 500 hidden units, one layer with 2000 hidden units, and 10 units as the final output. We argue that combining sparsity and discriminative DBN may increase the accuracy, but no previous studies suggest the best structure or configuration of that combination that can give the best accuracy. We took three stages of experiments to find the best configuration, namely preliminary, intermediate, and final stages. Each analysis of each stage serves as a background for consideration of the next experiment. We use normal sparse for generative DBN and discriminative DBN. Experimental studies on MNIST dataset show that the best structure or scenario to combine normal sparse into deep belief networks is as follows: input-generative (CD)-generative (CD)-normal sparse discriminative (CD).

ArXiv, 2017

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural network parameters using such tools. Our resulting variational Bayes algorithm generalizes well to new tasks, even when very few training examples are provided. Furthermore, this learned prior allows the model to extrapolate correctly far from a given task’s training data on a meta-dataset of periodic signals. 1 Learning a Rich Prior Bayesian Neural Networks [1, 2, 3, 4] are now scalable and can be used to estimate prediction uncertainty and model uncertainty [5]. While many efforts focus on better approximation of the posterior, we believe that the quality of the uncertainty highly depends on the choice of the prior. Hence, we consider learning a prior from previous tasks by learning a probability distribution p(w|α) over the weights w of a netw...