Stochastic Neural Network Model Research Articles

Recognition of Human Activities Using Continuous Autoencoders with Wearable Sensors.

This paper provides an approach for recognizing human activities with wearable sensors. The continuous autoencoder (CAE) as a novel stochastic neural network model is proposed which improves the ability of model continuous data. CAE adds Gaussian random units into the improved sigmoid activation function to extract the features of nonlinear data. In order to shorten the training time, we propose a new fast stochastic gradient descent (FSGD) algorithm to update the gradients of CAE. The reconstruction of a swiss-roll dataset experiment demonstrates that the CAE can fit continuous data better than the basic autoencoder, and the training time can be reduced by an FSGD algorithm. In the experiment of human activities’ recognition, time and frequency domain feature extract (TFFE) method is raised to extract features from the original sensors’ data. Then, the principal component analysis (PCA) method is applied to feature reduction. It can be noticed that the dimension of each data segment is reduced from 5625 to 42. The feature vectors extracted from original signals are used for the input of deep belief network (DBN), which is composed of multiple CAEs. The training results show that the correct differentiation rate of 99.3% has been achieved. Some contrast experiments like different sensors combinations, sensor units at different positions, and training time with different epochs are designed to validate our approach.

Stability Analysis of Stochastic Neural Network with Depression and Facilitation Synapses

We investigate dynamical properties of a stochastic neural network model in which neurons are connected by dynamic synapses that undergo short-term depression and facilitation. In this model, the state of the neuron is described by a binary variable that represents the active or resting state of the neuron and changes stochastically. Synaptic transmission efficacy is described by variables that represent the releasable neurotransmitters and the calcium concentration of the synaptic terminal. Here, we focus on a neural network with uniform connections, and we elucidate its neural dynamics, which is influenced by dynamic synapses. We derive a macroscopic mean field model that approximates the overall behavior of the stochastic neural network. We apply stability and bifurcation analyses to the macroscopic mean field model, and we find that the network exhibits a variety of dynamical structures, including ferromagnetic and paramagnetic states, as well as an oscillatory uniform state according to the parameter...

Forecasting Crude Oil Price and Stock Price by Jump Stochastic Time Effective Neural Network Model

The interacting impact between the crude oil prices and the stock market indices in China is investigated in the present paper, and the corresponding statistical behaviors are also analyzed. The database is based on the crude oil prices of Daqing and Shengli in the 7‐year period from January 2003 to December 2009 and also on the indices of SHCI, SZCI, SZPI, and SINOPEC with the same time period. A jump stochastic time effective neural network model is introduced and applied to forecast the fluctuations of the time series for the crude oil prices and the stock indices, and we study the corresponding statistical properties by comparison. The experiment analysis shows that when the price fluctuation is small, the predictive values are close to the actual values, and when the price fluctuation is large, the predictive values deviate from the actual values to some degree. Moreover, the correlation properties are studied by the detrended fluctuation analysis, and the results illustrate that there are positive correlations both in the absolute returns of actual data and predictive data.

Instabilities in Associative Memory Model with Synaptic Depression and Switching Phenomena among Attractors

We investigated how the stability of macroscopic states in the associative memory model is affected by synaptic depression. To this model, we applied the dynamical mean-field theory, which has recently been developed in stochastic neural network models with synaptic depression. By introducing a sublattice method, we derived macroscopic equations for firing state variables and depression variables. By using the macroscopic equations, we obtained the phase diagram when the strength of synaptic depression and the correlation level among stored patterns were changed. We found that there is an unstable region in which both the memory state and mixed state cannot be stable and that various switching phenomena can occur in this region.

Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing state variable and a synaptic variable. In these equations, their average product is decoupled as the product of averaged them because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady state equations for a network with uniform connections and a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady state solutions. An oscillatory uniform state was observed in the network with uniform connections due to a Hopf instability. With the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previous unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

Forecasting model of global stock index by stochastic time effective neural network

In this paper, we investigate the statistical properties of the fluctuations of the Chinese Stock Index, and we study the statistical properties of HSI, DJI, IXIC and SP500 by comparison. According to the theory of artificial neural networks, a stochastic time effective function is introduced in the forecasting model of the indices in the present paper, which gives an improved neural network – the stochastic time effective neural network model. In this model, a promising data mining technique in machine learning has been proposed to uncover the predictive relationships of numerous financial and economic variables. We suppose that the investors decide their investment positions by analyzing the historical data on the stock market, and the historical data are given weights depending on their time, in detail, the nearer the time of the historical data is to the present, the stronger impact the data have on the predictive model, and we also introduce the Brownian motion in order to make the model have the effect of random movement while maintaining the original trend. In the last part of the paper, we test the forecasting performance of the model by using different volatility parameters and we show some results of the analysis for the fluctuations of the global stock indices using the model.

An information geometrical approach to the mean-field approximation for quantum Ising spin models

We study the mean-field approximation for a general class of quantum Ising spin states from an information geometrical point of view. The states we consider are assumed to have at most second-order interactions with arbitrary but deterministic coupling coefficients. We call such a state a quantum Boltzmann machine (QBM) for the reason that it can be regarded as a quantum extension of the equilibrium distribution of a (classical) Boltzmann machine (CBM), which is a well-known stochastic neural network model. The totality of QBMs is then shown to form a quantum exponential family and thus can be considered as a smooth manifold having similar geometrical structures to those of CBMs. We elaborate on the significance and usefulness of information geometrical concepts, in particular the e- and m-projections, in studying the naive mean-field approximation for QBMs. We also discuss the higher-order corrections to the naive mean-field approximation based on the idea of the Plefka expansion in statistical physics. We elucidate the geometrical essence of the corrections and provide the expansion coefficients with expressions in terms of information geometrical quantities. Here, one may note this work as the information geometrical interpretation of (Plefka T 2006 Phys. Rev. E 73 016129) and as the quantum extension of (Tanaka T 2000 Neural Comput. 12 1951–68).

Statistical mechanics of stochastic neural networks: Relationship between the self-consistent signal-to-noise analysis, Thouless-Anderson-Palmer equation, and replica symmetric calculation approaches.

We study the statistical mechanical aspects of stochastic analog neural network models for associative memory with correlation type learning. We take three approaches to derive the set of the order parameter equations for investigating statistical properties of retrieval states: the self-consistent signal-to-noise analysis (SCSNA), the Thouless-Anderson-Palmer (TAP) equation, and the replica symmetric calculation. On the basis of the cavity method the SCSNA can be generalized to deal with stochastic networks. We establish the close connection between the TAP equation and the SCSNA to elucidate the relationship between the Onsager reaction term of the TAP equation and the output proportional term of the SCSNA that appear in the expressions for the local fields.

Stochastic neural network model for spontaneous bursting in hippocampal slices.

A biologically plausible, stochastic, neural network model that exhibits spontaneous transitions between a low-activity (normal) state and a high-activity (epileptic) state is studied by computer simulation. Brief excursions of the network to the high-activity state lead to spontaneous population bursting similar to the behavior observed in hippocampal slices bathed in a high-potassium medium. Although the variability of interburst intervals in this model is due to stochasticity, first return maps of successive interburst intervals show trajectories that resemble the behavior expected near unstable periodic orbits (UPOs) of systems exhibiting deterministic chaos. Simulations of the effects of the application of chaos control, periodic pacing, and anticontrol to the network model yield results that are qualitatively similar to those obtained in experiments on hippocampal slices. Estimation of the statistical significance of UPOs through surrogate data analysis also leads to results that resemble those of similar analysis of data obtained from slice experiments and human epileptic activity. These results suggest that spontaneous population bursting in hippocampal slices may be a manifestation of stochastic bistable dynamics, rather than of deterministic chaos. Our results also question the reliability of some of the recently proposed, UPO-based, statistical methods for detecting determinism and chaos in experimental time-series data.

Stochastic Neural Networks With Applications to Nonlinear Time Series

We consider a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinear stochastic systems. We show how the expectation-maximization algorithm can be used to develop efficient estimation schemes that have much lower computational complexity than those for conventional neural networks. This enables us to carry out model selection procedures, such as the Bayesian information criterion, to choose the number of hidden units and the input variables for each hidden unit. Stochastic neural networks are shown to have the universal approximation property of neural networks. Other important properties of the proposed model are given, and model-based multistep-ahead forecasts are provided. We fit stochastic neural network models to several real and simulated time series. Results show that the fitted models improve postsample forecasts over conventional neural networks and other nonlinear and nonparametric models.

On the effect of synaptic fluctuations during retrieval processes in neural network models

We studied stochastic neural network models in which, in addition to long term learning, fast fluctuations of the synaptic intensities occur so that the neuron activity update takes place assuming a set of synaptic intensities taken at random from a given distribution. The influence of this distribution on the performance of the retrieval process and on the general behavior of the network is discussed.

Neural Networks in Which Synaptic Patterns Fluctuate with Time

We study a stochastic neural-network model in which neurons and synapses change with a priori probability p and 1−p, respectively, in the limit p→0. This implies neuron activity competing with fast fluctuations of the synaptic connections—in fact, random oscillations around values given by a learning (for example, Hebb's) rule. The consequences for the system performance of a dynamics constantly checking at random the set of memorized patterns is thus studied both analytically and numerically. We describe various nonequilibrium phase transitions whose nature depends on the properties of fluctuations. We find, in particular, that under rather general conditions locally stable mixture states do not occur, and pattern recognition and retrieval processes are substantially improved for some classes of synaptic fluctuations.

Nonequilibrium neural network with competing dynamics

A stochastic neural-network model with superposition of neuron and synapse kinetics with a priori probabilities p and 1− p, respectively, is presented. We report on exact and approximate results for p→0. This includes Hopfield-like models in which synaptic intensities locally fluctuate around Hebbian values. It is illustrated how fluctuations influence the phase diagram and, in particular, that an appropriate choice of details may significantly improve the retrieval process.

A reinforcement learning neural network for adaptive control of Markov chains

In this paper we consider the problem of reinforcement learning in a dynamically changing environment. In this context, we study the problem of adaptive control of finite-state Markov chains with a finite number of controls. The transition and payoff structures are unknown. The objective is to find an optimal policy which maximizes the expected total discounted payoff over the infinite horizon. A stochastic neural network model is suggested for the controller. The parameters of the neural net, which determine a random control strategy, are updated at each instant using a simple learning scheme. This learning scheme involves estimation of some relevant parameters using an adaptive critic. It is proved that the controller asymptotically chooses an optimal action in each state of the Markov chain with a high probability.

Asymptotic Stationarity of Discrete-time Stochastic Neural Networks

This paper deals with a class of synchronous discrete-time stochastic neural network models. Dynamic stabilities (or asymptotic stationarities) are analysed for two sub-classes of the models, i.e., a class of stochasticized models from Little, and a class of Hopfield-type stochastic models. Copyright © 1996 Elsevier Science Ltd.

Evidence for a cooperative learning mechanism in the vestibulo-ocular reflex.

The vestibulo-ocular reflex (VOR) stabilizes vision by producing eye rotations that counterbalance head rotations. It receives input from a pair of vestibular receptors, and becomes unbalanced when input from one side is removed, producing spontaneous eye rotation in the absence of head rotation (SVOR). SVOR can be eliminated by the process of vestibular compensation. In mammals, SVOR elimination occurs over a period of days, and follows an exponential time course. We show that SVOR elimination in goldfish occurs in a matter of minutes, and its time course is not exponential but is characterized by a sigmoid function suggesting a cooperative mechanism. This time course is reproduced in a stochastic neural network model that has nonspecific reinforcement related to the level of VOR imbalance.

A new stochastic neural network model and its application to grouping parts and tools in flexible manufacturing systems

Recently, some stochastic neural network models have been presented for the purpose of overcoming the defect that the deterministic neural network models do not have the ability to escape from a local optimal solution. However, the specification of the values of various parameters and weights in these stochastic neural network models is more complicated than that in the deterministic neural network models. In this paper, a new stochastic neural network model is proposed in order to reduce the complication of specifying the values of parameters and weights. For a practical purpose, the proposed model is applied to the problem of grouping parts and tools in flexible manufacturing systems (FMSs).

Synchronization of firing times in a stochastic neural network model with excitatory connections

We investigate a finite, stochastic, completely neural network model with excitatory couplings. The dynamics of the moments of firing in the net is described by a Markov chain. We derive exponential bounds for its transition probabilities. Moreover, the exponential fast synchronization of the moments of firing is proved. The results are illustrated by computer simulations.

Scheduling for minimizing total actual flow time by neural networks

SUMMARY Scheduling problems are considered as combinatorial optimization problems. Hopfield and Tank (1985) showed that some combinatorial optimization problems can be solved using artificial neural network systems. However, their network model for solving the combinatorial optimization problems often attains a local optimum solution depending on the initial state of the network. Recently, some stochastic neural network models have been proposed for the purpose of avoiding convergence to a local optimum solution. In this paper a scheduling problem for minimizing the total actual flow time is solved by using the Gaussian machine model which is one of the stochastic neural network models.