Continuous-valued probabilistic behavior in a VLSI generative model

This paper presents the VLSI implementation of the continuous restricted Boltzmann machine (CRBM), a probabilistic generative model that is able to model continuous-valued data with a simple and hardware-amenable training algorithm. The full CRBM system consists of stochastic neurons whose continuous-valued probabilistic behavior is mediated by injected noise. Integrating on-chip training circuits, the full CRBM system provides a platform for exploring computation with continuous-valued probabilistic behavior in VLSI. The VLSI CRBM's ability both to model and to regenerate continuous-valued data distributions is examined and limitations on its performance are highlighted and discussed.     

A GMM/HMM model for reconstruction of missing speech spectral components for continuous speech recognition

This paper presents a method for reconstructing unreliable spectral components of speech signals using the statistical distributions of the clean components. Our goal is to model the temporal patterns in speech signal and take advantage of correlations between speech features in both time and frequency domain simultaneously. In this approach, a hidden Markov model (HMM) is first trained on clean speech data to model the temporal patterns which appear in the sequences of the spectral components. Using this model and according to the probabilities of occurring noisy spectral component at each states, a probability distributions for noisy components are estimated. Then, by applying maximum a posteriori (MAP) estimation on the mentioned distributions, the final estimations of the unreliable spectral components are obtained. The proposed method is compared to a common missing feature method which is based on the probabilistic clustering of the feature vectors and also to a state of the art method based on sparse reconstruction. The experimental results exhibits significant improvement in recognition accuracy over a noise polluted Persian corpus.     

Functional abilities of a stochastic logic neural network

The authors have studied the information processing ability of stochastic logic neural networks, which constitute one of the pulse-coded artificial neural network families. These networks realize pseudoanalog performance with local learning rules using digital circuits, and therefore suit silicon technology. The synaptic weights and the outputs of neurons in stochastic logic are represented by stochastic pulse sequences. The limited range of the synaptic weights reduces the coding noise and suppresses the degradation of memory storage capacity. To study the effect of the coding noise on an optimization problem, the authors simulate a probabilistic Hopfield model (Gaussian machine) which has a continuous neuron output function and probabilistic behavior. A proper choice of the coding noise amplitude and scheduling improves the network's solutions of the traveling salesman problem (TSP). These results suggest that stochastic logic may be useful for implementing probabilistic dynamics as well as deterministic dynamics.     

Bayesian Robust PCA of Incomplete Data

We present a probabilistic model for robust factor analysis and principal component analysis in which the observation noise is modeled by Student-t distributions in order to reduce the negative effect of outliers. The Student-t distributions are modeled independently for each data dimensions, which is different from previous works using multivariate Student-t distributions. We compare methods using the proposed noise distribution, the multivariate Student-t and the Laplace distribution. Intractability of evaluating the posterior probability density is solved by using variational Bayesian approximation methods. We demonstrate that the assumed noise model can yield accurate reconstructions because corrupted elements of a bad quality sample can be reconstructed using the other elements of the same data vector. Experiments on an artificial dataset and a weather dataset show that the dimensional independency and the flexibility of the proposed Student-t noise model can make it superior in some applications.     

When response variability increases neural network robustness to synaptic noise

Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as detrimental noise that reduces the computational accuracy of neural circuits. Here we investigate the possibility that such response variability might in fact be beneficial, because it may partially compensate for a decrease in accuracy due to stochastic changes in the synaptic strengths of a network. We study the interplay between two kinds of noise, response (or neuronal) noise and synaptic noise, by analyzing their joint influence on the accuracy of neural networks trained to perform various tasks. We find an interesting, generic interaction: when fluctuations in the synaptic connections are proportional to their strengths (multiplicative noise), a certain amount of response noise in the input neurons can significantly improve network performance, compared to the same network without response noise. Performance is enhanced because response noise and multiplicative synaptic noise are in some ways equivalent. So if the algorithm used to find the optimal synaptic weights can take into account the variability of the model neurons, it can also take into account the variability of the synapses. Thus, the connection patterns generated with response noise are typically more resistant to synaptic degradation than those obtained without response noise. As a consequence of this interplay, if multiplicative synaptic noise is present, it is better to have response noise in the network than not to have it. These results are demonstrated analytically for the most basic network consisting of two input neurons and one output neuron performing a simple classification task, but computer simulations show that the phenomenon persists in a wide range of architectures, including recurrent (attractor) networks and sensorimotor networks that perform coordinate transformations. The results suggest that response variability could play an important dynamic role in networks that continuously learn.     

Classification in the presence of class noise using a probabilistic Kernel Fisher method

In machine learning, class noise occurs frequently and deteriorates the classifier derived from the noisy data set. This paper presents two promising classifiers for this problem based on a probabilistic model proposed by Lawrence and Schölkopf (2001). The proposed algorithms are able to tolerate class noise, and extend the earlier work of Lawrence and Schölkopf in two ways. First, we present a novel incorporation of their probabilistic noise model in the Kernel Fisher discriminant; second, the distribution assumption previously made is relaxed in our work. The methods were investigated on simulated noisy data sets and a real world comparative genomic hybridization (CGH) data set. The results show that the proposed approaches substantially improve standard classifiers in noisy data sets, and achieve larger performance gain in non-Gaussian data sets and small size data sets.     

A Generative Probabilistic Oriented Wavelet Model for Texture Segmentation

This Letter addresses image segmentation via a generative model approach. A Bayesian network (BNT) in the space of dyadic wavelet transform coefficients is introduced to model texture images. The model is similar to a Hidden Markov model (HMM), but with non-stationary transitive conditional probability distributions. It is composed of discrete hidden variables and observable Gaussian outputs for wavelet coefficients. In particular, the Gabor wavelet transform is considered. The introduced model is compared with the simplest joint Gaussian probabilistic model for Gabor wavelet coefficients for several textures from the Brodatz album [1]. The comparison is based on cross-validation and includes probabilistic model ensembles instead of single models. In addition, the robustness of the models to cope with additive Gaussian noise is investigated. We further study the feasibility of the introduced generative model for image segmentation in the novelty detection framework [2]. Two examples are considered: (i) sea surface pollution detection from intensity images and (ii) image segmentation of the still images with varying illumination across the scene.     

Predicting time series of railway speed restrictions with time-dependent machine learning techniques

In this paper, a hybrid approach to combine conditional restricted Boltzmann machines (CRBM) and echo state networks (ESN) for binary time series prediction is proposed. Both methods have demonstrated their ability to extract complex dynamic patterns from time-dependent data in several applications and benchmark studies. To the authors’ knowledge, it is the first time that the proposed combination of algorithms is applied for reliability prediction.The proposed approach is verified on a case study predicting the occurrence of railway operation disruptions based on discrete-event data, which is represented by a binary time series. The case study concerns speed restrictions affecting railway operations, caused by failures of tilting systems of railway vehicles. The overall prediction accuracy of the algorithm is 99.93%; the prediction accuracy for occurrence of speed restrictions within the foresight period is 98% (which corresponds to the sensitivity of the algorithm). The prediction results of the case study are compared to the prediction with a MLP trained with a Newton conjugate gradient algorithm. The proposed approach proves to be superior to MLP.     

Convolutional restricted Boltzmann machines learning for robust visual tracking

It is a critical step to choose visual features in object tracking. Most existing tracking approaches adopt handcrafted features, which greatly depend on people’s prior knowledge and easily become invalid in other conditions where the scene structures are different. On the contrary, we learn informative and discriminative features from image data of tracking scenes itself. Local receptive filters and weight sharing make the convolutional restricted Boltzmann machines (CRBM) suit for natural images. The CRBM is applied to model the distribution of image patches sampled from the first frame which shares same properties with other frames. Each hidden variable corresponding to one local filter can be viewed as a feature detector. Local connections to hidden variables and max-pooling strategy make the extracted features invariant to shifts and distortions. A simple naive Bayes classifier is used to separate object from background in feature space. We demonstrate the effectiveness and robustness of our tracking method in several challenging video sequences. Experimental results show that features automatically learned by CRBM are effective for object tracking.     

Stochastic tube MPC with state estimation

An output feedback Model Predictive Control (MPC) strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed. Given the probability distributions of the disturbance input, the measurement noise and the initial state estimation error, the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator. From these distributions, a set of deterministic constraints is computed for the predictions of a nominal model. The constraints are incorporated in a receding horizon optimization of an expected quadratic cost, which is formulated as a quadratic program. The constraints are constructed so as to provide a guarantee of recursive feasibility, and the closed loop system is stable in a mean-square sense. All uncertainties in this paper are taken to be bounded—in most control applications this gives a more realistic representation of process and measurement noise than the more traditional Gaussian assumption.     

Process monitoring through manifold regularization-based GMM with global/local information

The nonlinear and multimodal characteristics in many manufacturing processes have posed some difficulties to regular multivariate statistical process control (MSPC) (e.g., principal component analysis (PCA)-based monitoring method) because a fundamental assumption is that the process data follow unimodal and Gaussian distribution. To explicitly address these important data distribution characteristics in some complicated processes, a novel manifold learning algorithm, joint local intrinsic and global/local variance preserving projection (JLGLPP) is proposed for information extraction from process data. Based on the features extracted by JLGLPP, local/nonlocal manifold regularization-based Gaussian mixture model (LNGMM) is proposed to estimate process data distributions with nonlinear and multimodal characteristics. A probabilistic indicator for quantifying process states is further developed, which effectively combines local and global information extracted from a baseline GMM. Thus, the JLGLPP and LNGMM-based monitoring model can be used effectively for online process monitoring under complicated working conditions. The experimental results illustrate that the proposed method effectively captures meaningful information hidden in the process signals and shows superior process monitoring performance compared to regular monitoring methods.     

Generalization in probabilistic RAM nets

The probabilistic RAM (pRAM) is a hardware-realizable neural device which is stochastic in operation and highly nonlinear. Even small nets of pRAMs offer high levels of functionality. The means by which a pRAM network generalizes when trained in noise is shown and the results of this behavior are described.     

Detecting and estimating signals over noisy and unreliable synapses: information-theoretic analysis

The temporal precision with which neurons respond to synaptic inputs has a direct bearing on the nature of the neural code. A characterization of the neuronal noise sources associated with different sub-cellular components (synapse, dendrite, soma, axon, and so on) is needed to understand the relationship between noise and information transfer. Here we study the effect of the unreliable, probabilistic nature of synaptic transmission on information transfer in the absence of interaction among presynaptic inputs. We derive theoretical lower bounds on the capacity of a simple model of a cortical synapse under two different paradigms. In signal estimation, the signal is assumed to be encoded in the mean firing rate of the presynaptic neuron, and the objective is to estimate the continuous input signal from the postsynaptic voltage. In signal detection, the input is binary, and the presence or absence of a presynaptic action potential is to be detected from the postsynaptic voltage. The efficacy of information transfer in synaptic transmission is characterized by deriving optimal strategies under these two paradigms. On the basis of parameter values derived from neocortex, we find that single cortical synapses cannot transmit information reliably, but redundancy obtained using a small number of multiple synapses leads to a significant improvement in the information capacity of synaptic transmission.     

A statistical approach to sparse multi-scale phase-based stereo

In this study, a multi-scale phase based sparse disparity algorithm and a probabilistic model for matching uncertain phase are proposed. The features used are oriented edges extracted using steerable filters. Feature correspondences are estimated using phase-similarity at multiple scale using a magnitude weighting scheme. In order to achieve sub-pixel accuracy in disparity, we use a fine tuning procedure which employs the phase difference between corresponding feature points. We also derive a probabilistic model, where phase uncertainty is trained using data from a single image pair. The model is used to provide stable matches. The disparity algorithm and the probabilistic phase uncertainty model are verified on various stereo image pairs.     

Visualization of Tree-Structured Data Through Generative Topographic Mapping

In this paper, we present a probabilistic generative approach for constructing topographic maps of tree-structured data. Our model defines a low-dimensional manifold of local noise models, namely, (hidden) Markov tree models, induced by a smooth mapping from low-dimensional latent space. We contrast our approach with that of topographic map formation using recursive neural-based techniques, namely, the self-organizing map for structured data (SOMSD) (Hagenbuchner , 2003). The probabilistic nature of our model brings a number of benefits: 1) naturally defined cost function that drives the model optimization; 2) principled model comparison and testing for overfitting; 3) a potential for transparent interpretation of the map by inspecting the underlying local noise models; 4) natural accommodation of alternative local noise models implicitly expressing different notions of structured data similarity. Furthermore, in contrast with the recursive neural-based approaches, the smooth nature of the mapping from the latent space to the local model space allows for calculation of magnification factors—a useful tool for the detection of data clusters. We demonstrate our approach on three data sets: a toy data set, an artificially generated data set, and on a data set of images represented as quadtrees.      

MRF Reinforcer: A Probabilistic Element for Space Redundancy in Nanoscale Circuits

Shrinking devices to nanoscale, increasing integration densities, and reducing voltage levels to the thermal limit-all conspire to produce faulty systems. A possible solution is a fault-tolerant probabilistic framework based on Markov random fields. This article introduces a new redundancy element, the MRF reinforcer, which achieves significant immunity to single-event upsets and noise     

Representing Probabilistic Rules with Networks of Gaussian Basis Functions

There is great interest in understanding the intrinsic knowledge neural networks have acquired during training. Most work in this direction is focussed on the multi-layer perceptron architecture. The topic of this paper is networks of Gaussian basis functions which are used extensively as learning systems in neural computation. We show that networks of Gaussian basis functions can be generated from simple probabilistic rules. Also, if appropriate learning rules are used, probabilistic rules can be extracted from trained networks. We present methods for the reduction of network complexity with the goal of obtaining concise and meaningful rules. We show how prior knowledge can be refined or supplemented using data by employing either a Bayesian approach, by a weighted combination of knowledge bases, or by generating artificial training data representing the prior knowledge. We validate our approach using a standard statistical data set.     

A Normalized Probabilistic Expectation-Maximization Neural Network for Minimizing Bayesian Misclassification Cost Risk

In this paper, we propose a normalized semi-supervised probabilistic expectation-maximization neural network (PEMNN) that minimizes Bayesian misclassification cost risk. Using simulated and real-world datasets, we compare the proposed PEMNN with supervised cost sensitive probabilistic neural network (PNN), discriminant analysis (DA), mathematical integer programming (MIP) model and support vector machines (SVM) for different misclassification cost asymmetries and class biases. The results of our experiments indicate that the PEMNN performs better when class data distributions are normal or uniform. However, when class data distribution is exponential the performance of PEMNN deteriorates giving slight advantage to competing MIP, DA, PNN and SVM techniques. For real-world data with non-parametric distributions and mixed decision-making attributes (continuous and categorical), the PEMNN outperforms the PNN.     

2d numerical simulations of an electron–phonon hydrodynamical model based on the maximum entropy principle

2d numerical solutions of a new macroscopic model describing the electron transport in semiconductors coupled with the heating of the crystal lattice are presented. The model has been obtained with the use of the maximum entropy principle. Numerical simulations of a nanoscale MOSFET are presented and the influence of self heating on the electrical characteristics is analyzed.