White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

Generalization in a linear perceptron in the presence of noise

Abstract: The authors study the evolution of the generalization ability of a simple linear perceptron with N inputs which learns to imitate a 'teacher perceptron'. The system is trained on p= alpha N example inputs drawn from some distribution and the generalization ability is measured by the average agreement with the teacher on test examples drawn from the same distribution. The dynamics may be solved analytically and exhibits a phase transition from imperfect to perfect generalization at alpha =1, when there are no errors (static noise) in the training examples. If the examples are produced by an erroneous teacher, overfitting is observed, i.e. the generalization error starts to increase after a finite time of training. It is shown that a weight decay of the same size as the variance of the noise (errors) on the teacher improves on the generalization and suppresses the overfitting. The generalization error as a function of time is calculated numerically for various values of the parameters. Finally dynamic noise in the training is considered. White noise on the input corresponds on average to a weight decay, and can thus improve generalization, whereas white noise on the weights or the output degrades generalization. Generalization is particularly sensitive to noise on the weights (for alpha (1) where it makes the error constantly increase with time, but this effect is also shown to be damped by a weight decay. Weight noise and output noise acts similarly above the transition at alpha =1.

Synaptic Shot Noise and Conductance Fluctuations Affect the Membrane Voltage with Equal Significance

Abstract: The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductancebased synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Harmonic noise: Effect on bistable systems

Abstract: The coordinate of a white noise driven harmonic oscillator is used as a stochastic source term in bistable dynamics. This new kind of Gaussian colored noise gives rise to resonance phenomena due to a peak in the spectrum. We investigate its effect on linear and bistable systems. We derive a Markovian approximation for driven bistable oscillators and overdamped systems. In the resonance region computer simulations were carried out using an extension of Fox' algorithm procedure for colored noise. We find an increase of the transition rates in bistable systems as compared with the case of bistable systems driven by white and exponentially correlated noise.

Stochastic Maximum-Likelihood DOA Estimation in the Presence of Unknown Nonuniform Noise

Abstract: This correspondence investigates the direction-of-arrival (DOA) estimation of multiple narrowband sources in the presence of nonuniform white noise with an arbitrary diagonal covariance matrix. While both the deterministic and stochastic Cramer-Rao bound (CRB) and the deterministic maximum-likelihood (ML) DOA estimator under this model have been derived by Pesavento and Gershman, the stochastic ML DOA estimator under the same setting is still not available in the literature. In this correspondence, a new stochastic ML DOA estimator is derived. Its implementation is based on an iterative procedure which concentrates the log-likelihood function with respect to the signal and noise nuisance parameters in a stepwise fashion. A modified inverse iteration algorithm is also presented for the estimation of the noise parameters. Simulation results have shown that the proposed algorithm is able to provide significant performance improvement over the conventional uniform ML estimator in nonuniform noise environments and require only a few iterations to converge to the nonuniform stochastic CRB.