A Stochastic Approximation Method

Robbins, Herbert; Monro, Sutton

doi:10.1214/aoms/1177729586

Cited by 7,168 publications

(3,273 citation statements)

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“…Step size was equal to the greater of two values, 25/n or 0.5 Hz, where n was the number of steps accumulated since the beginning of the test session (Robbins and Monro 1951;Levitt 1970). Tracks were allowed to continue for a minimum of 15 reversals in target frequency until two stability criteria were met: (1) the absolute difference in mean frequency between the final four reversals and the four preceding reversals was less than 5 Hz, and (2) the standard deviation of the frequency of the final eight reversals was less than 5 Hz.…”

Section: Behavioral Experimentsmentioning

confidence: 99%

Midbrain Synchrony to Envelope Structure Supports Behavioral Sensitivity to Single-Formant Vowel-Like Sounds in Noise

Henry

Abrams

Forst

et al. 2016

JARO

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Vowels make a strong contribution to speech perception under natural conditions. Vowels are encoded in the auditory nerve primarily through neural synchrony to temporal fine structure and to envelope fluctuations rather than through average discharge rate. Neural synchrony is thought to contribute less to vowel coding in central auditory nuclei, consistent with more limited synchronization to fine structure and the emergence of average-rate coding of envelope fluctuations. However, this hypothesis is largely unexplored, especially in background noise. The present study examined coding mechanisms at the level of the midbrain that support behavioral sensitivity to simple vowel-like sounds using neurophysiological recordings and matched behavioral experiments in the budgerigar. Stimuli were harmonic tone complexes with energy concentrated at one spectral peak, or formant frequency, presented in quiet and in noise. Behavioral thresholds for formant-frequency discrimination decreased with increasing amplitude of stimulus envelope fluctuations, increased in noise, and were similar between budgerigars and humans. Multiunit recordings in awake birds showed that the midbrain encodes vowel-like sounds both through response synchrony to envelope structure and through average rate. Whereas neural discrimination thresholds based on either coding scheme were sufficient to support behavioral thresholds in quiet, only synchrony-based neural thresholds could account for behavioral thresholds in background noise. These results reveal an incomplete transformation to average-rate coding of vowel-like sounds in the midbrain. Model simulations suggest that this transformation emerges due to modulation tuning, which is shared between birds and mammals. Furthermore, the results underscore the behavioral relevance of envelope synchrony in the midbrain for detection of small differences in vowel formant frequency under real-world listening conditions.

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Section: Behavioral Experimentsmentioning

confidence: 99%

Midbrain Synchrony to Envelope Structure Supports Behavioral Sensitivity to Single-Formant Vowel-Like Sounds in Noise

Henry

Abrams

Forst

et al. 2016

JARO

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“…The one used in this paper was inspired by the work of Atchadé (2006). It uses a Robbins-Monro type algorithm, widely used to calculate numerical solutions of differential equations (Robbins & Monro 1951).…”

Section: A2 Gaussian Proposal Covariance Matrix Adjustmentmentioning

confidence: 99%

The solar-like oscillations of HD 49933: a Bayesian approach

Benomar

Appourchaux

Baudin

2009

A&A

103

148

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Context. Asteroseismology has entered a new era with the availability of continuous observations from space-borne missions such as MOST, CoRoT and Kepler. However, the low amplitude and the complexity of the observed spectrum make the exploitation of these data sets difficult. Aims. The use of robust methods to estimate the parameters of stellar oscillation eigenmodes is necessary to fully exploit these new data sets. These parameters include in particular the frequency, the width and the energy of the eigenmodes, all being required for a seismic interpretation of the stellar internal structure or excitation of the eigenmodes. Methods. A Bayesian approach, coupled with a Markov chain Monte Carlo (MCMC) algorithm, is presented. Such a method allows the use of a priori knowledge to improve the parameter estimation. It also provides complete information on the probability distribution of the fitted parameters. The method is tested on simulated time series and then applied to CoRoT observations of HD 49933. Results. The simulated time series allow the validation of the method for conditions similar to those of the observations in terms of spectral complexity and signal-to-noise ratio. However, a very important problem in the analysis of the HD 49933 mode spectrum is the l degree identification of the modes. The degree identification has little impact on the large frequency separation, rotational splitting, energy and width estimation, whereas individual frequencies and the star inclination angle evaluation are strongly affected. From a statistical point of view, we provide a quantitative ranking of the four models considered. The most probable model includes only modes of degree 0 and 1. Two other models include modes with degree up to 2 and have a non negligible level of significance. The last model includes modes of degree 0 and 1 but has an alternate degree identification and can be definitively rejected. In conclusion, the significance of the resulting probabilities is not sufficient to draw a definite conclusion.

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“…Now, we interpret the operator k M as the expectation operator over k if k is given as a random integer which is distributed uniformly from 1 to M. Therefore, stochastic approximation [10] is applicable to the optimization of CSTRESS. Consequently, CSTRESS is minimized by repeating the following update equation:…”

Section: Linear Gmamentioning

confidence: 99%

“…In this paper, we propose a new stochastic gradient algorithm named "global mapping analysis" (GMA), which solves both the classical linear MDS [8], [9] and a non-linear MDS known as ALSCAL [5] efficiently. By using stochastic approximation [10], the computational cost of each update in the gradient descent is linear to the number of objects. So, GMA is expected to be efficient if the number of objects is large.…”

Section: Introductionmentioning

confidence: 99%

Global Mapping Analysis: Stochastic Gradient Algorithm in Multidimensional Scaling

Matsuda

Yamaguchi

2012

IEICE Trans. Inf. & Syst.

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SUMMARYIn order to implement multidimensional scaling (MDS) efficiently, we propose a new method named "global mapping analysis" (GMA), which applies stochastic approximation to minimizing MDS criteria. GMA can solve MDS more efficiently in both the linear case (classical MDS) and non-linear one (e.g., ALSCAL) if only the MDS criteria are polynomial. GMA separates the polynomial criteria into the local factors and the global ones. Because the global factors need to be calculated only once in each iteration, GMA is of linear order in the number of objects. Numerical experiments on artificial data verify the efficiency of GMA. It is also shown that GMA can find out various interesting structures from massive document collections.

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A Stochastic Approximation Method

Cited by 7,168 publications

References 0 publications

Midbrain Synchrony to Envelope Structure Supports Behavioral Sensitivity to Single-Formant Vowel-Like Sounds in Noise

Midbrain Synchrony to Envelope Structure Supports Behavioral Sensitivity to Single-Formant Vowel-Like Sounds in Noise

The solar-like oscillations of HD 49933: a Bayesian approach

Global Mapping Analysis: Stochastic Gradient Algorithm in Multidimensional Scaling

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