On the Noise Model of Support Vector Machine Regression

Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called Vapnik"s $epsilon$- insensitive loss function, which is similar to the "robust" loss functions introduced by Huber (Huber, 1981). The quadratic loss function is well justified under the assumption of Gaussian additive noise. However, the noise model underlying the choice of Vapnik's loss function is less clear. In this paper the use of Vapnik's loss function is shown to be equivalent to a model of additive and Gaussian noise, where the variance and mean of the Gaussian are random variables. The probability distributions for the variance and mean will be stated explicitly. While this work is presented in the framework of SVMR, it can be extended to justify non-quadratic loss functions in any Maximum Likelihood or Maximum A Posteriori approach. It applies not only to Vapnik's loss function, but to a much broader class of loss functions.

Thermal Noise Behavior of the Bridge Circuit

This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the deterministic terminal behavior reduces to that of a single linear resistor. This reduction of the deterministic terminal behavior, in which a natural frequency of a linear circuit does not appear in the driving-point impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper shows that, in addition to the reduction of the deterministic behavior, the thermal noise at the terminals of the network, arising from the usual Nyquist-Johnson noise model associated with each resistor in the network, is also exactly that of a single linear resistor. While this result for the linear time-invariant (LTI) case is a direct consequence of a well-known result for RLC circuits, the nonlinear result is novel. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying

Nonlinear Device Noise Models:Thermodynamic Requirements

This paper proposes three tests to determine whether a given nonlinear device noise model is in agreement with accepted thermodynamic principles. These tests are applied to several models. One conclusion is that every Gaussian noise model for any nonlinear device predicts thermodynamically impossible circuit behavior: these models should be abandoned. But the nonlinear shot-noise model predicts thermodynamically acceptable behavior under a constraint derived here. Further, this constraint specifies the current noise amplitude at each operating point from knowledge of the device v - i curve alone. For the Gaussian and shot-noise models, this paper shows how the thermodynamic requirements can be reduced to concise mathematical tests involving no approximatio

Neuroticism, intelligence, and intra-individual variability in elementary cognitive tasks : Testing the mental noise hypothesis. 'Neuroticismo, inteligencia y variabilidad intra-individual en tareas cognitivas elementales : contraste de la hip??tesis del ruido neuronal'

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Strial capillary permeability following noise exposure in mice

A study of strial capillary permeability using fluorescent microspheres and immunohistochemistry in mice that do or do not exhibit a reduction in endocochlear potential following a single, intense noise exposure.

Development of curriculum in noise awareness

This paper presents a curriculum in noise awareness developed for use in the second and fourth grades, to teach children about the harmful effects of elevated noise levels.

Speech intelligibility in noise-induced hearing loss: effects of high-frequency compensation

This dissertation examines the frequency response that results in the maximum level of speech intelligibility for persons with noise-induced hearing loss.

Noise exposure in the operating room

This paper discusses a study done to determine noise levels in operating rooms

A comparison of physical measurements of pure-tones, third-octave bands of noise and third-octave bands of speech to subjective judgments of audibility threshold, MCL and UCL for three normally hearing listeners

This study investigates the relation between physical measurements of pure-tones, third-octave bands of noise and third-octave bands of speech and subjective judgments of auditory threshold, most-comfortable listening level (MCL) and uncomfortable-listening level (UCL) for three normally hearing listeners.

Noise levels and hearing conservation in a water treatment facility

This paper describes a study assessing the sound levels and noise exposures of a municipal water treatment plant to determine the level of employee noise exposure dosages and to make any necessary recommendations regarding reducing the risk of noise induced hearing loss in employees.

Role of alpha synuclein in noise induced hearing loss

The recent discovery of the contribution of alpha synuclein in the auditory system prompted further investigation of its functional role. Auditory brainstem response (ABR) and gap detection testing were completed on wild-type and transgenic M83 mice to assess the role of alpha synuclein in noise-induced hearing loss and central auditory function.

The effectiveness of noise cancellation headphones for hearing impaired listeners

This paper discusses the use of noise cancellation headphones for hearing aid users to reduce background noise in order to improve speech discrimination.

Bone-conducted tones masked by air-conducted noise

This paper presents a study designed to develop and evaluate a method for obtaining monaural thresholds for bone-conducted signals masked by air-conducted noises.

Noise exposure in the fire department

This paper discusses noise exposure to firefighters on the job and whether this contributes to noise induced hearing loss.

Differences in performance in noise between conventional hearing aids and radiant multimicrophone beamforming technology

This paper discusses the results of a study to determine the differences between hearing aids and radiant beamforming technology.