scholarly journals Does the neuronal noise in cortex help generalization?

2019 ◽  
Author(s):  
Brian Hu ◽  
Jiaqi Shang ◽  
Ramakrishnan Iyer ◽  
Josh Siegle ◽  
Stefan Mihalas

AbstractOne remarkable feature of neuronal activity in the mammalian cortex is the high level of variability in response to repeated stimuli. First, we used an open dataset, the Allen Brain Observatory, to quantify the distribution of responses to repeated presentations of natural movies. We find that even for their preferred moment in the movie clip, neurons have high variability which cannot be well captured by Gaussian or Poisson distributions. A large fraction of responses are better fit by log-normal or Gaussian mixture models with two components. These distributions are similar to activity distributions during training of deep neural networks using dropout. This poses the interesting hypothesis: is the role of cortical noise to help in generalization during learning?Second, to ensure the robustness of our results we analyzed electrophysiological recordings in the same areas of mouse visual cortex, again using repeated natural movie presentations and found similar response distributions. To make sure that the trial-by-trial variations we observe are not due exclusively to the result of changes in state, we constructed a population coupling model, where each neuron’s activity is coupled to a low-dimension version of the activity of all other simultaneously recorded neurons. The population coupling model can capture global, brain-wide activity fluctuations that are state-dependent. The residuals from this model also show non-Gaussian noise distributions.Third, we ask a more specific question: is the noise in the cortex more likely to move the representation of the stimulus in-class versus out-of-class? To address this question, we analyzed the responses of neurons across trials from multiple sections of different movie clips. We observe that the noise in the cortex better aligns to in-class variations. We argue that a useful noise for learning generalizations is to move from representations of different exemplars in-class, similar to cortical noise.

Sensors ◽  
2019 ◽  
Vol 19 (12) ◽  
pp. 2827 ◽  
Author(s):  
Danilo Pena ◽  
Carlos Lima ◽  
Matheus Dória ◽  
Luan Pena ◽  
Allan Martins ◽  
...  

In general, acoustic channels are not Gaussian distributed neither are second-order stationary. Considering them for signal processing methods designed for Gaussian assumptions is inadequate, consequently yielding in poor performance of such methods. This paper presents an analysis for audio signal corrupted by impulsive noise using non-Gaussian models. Audio samples are compared to the Gaussian, α -stable and Gaussian mixture models, evaluating the fitting by graphical and numerical methods. We discuss fitting properties as the window length and the overlap, finally concluding that the α -stable model has the best fit for all tested scenarios.


2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Till Massing

AbstractTewari et al. (Parametric characterization of multimodal distributions with non-Gaussian modes, pp 286–292, 2011) introduced Gaussian mixture copula models (GMCM) for clustering problems which do not assume normality of the mixture components as Gaussian mixture models (GMM) do. In this paper, we propose Student t mixture copula models (SMCM) as an extension of GMCMs. GMCMs require weak assumptions, yielding a flexible fit and a powerful cluster tool. Our SMCM extension offers, in a natural way, even more flexibility than the GMCM approach. We discuss estimation issues and compare Expectation-Maximization (EM)-based with numerical simplex optimization methods. We illustrate the SMCM as a tool for image segmentation.


2013 ◽  
Vol 141 (6) ◽  
pp. 1761-1785 ◽  
Author(s):  
Thomas Sondergaard ◽  
Pierre F. J. Lermusiaux

Abstract The properties and capabilities of the Gaussian Mixture Model–Dynamically Orthogonal filter (GMM-DO) are assessed and exemplified by applications to two dynamical systems: 1) the double well diffusion and 2) sudden expansion flows; both of which admit far-from-Gaussian statistics. The former test case, or twin experiment, validates the use of the Expectation-Maximization (EM) algorithm and Bayesian Information Criterion with GMMs in a filtering context; the latter further exemplifies its ability to efficiently handle state vectors of nontrivial dimensionality and dynamics with jets and eddies. For each test case, qualitative and quantitative comparisons are made with contemporary filters. The sensitivity to input parameters is illustrated and discussed. Properties of the filter are examined and its estimates are described, including the equation-based and adaptive prediction of the probability densities; the evolution of the mean field, stochastic subspace modes, and stochastic coefficients; the fitting of GMMs; and the efficient and analytical Bayesian updates at assimilation times and the corresponding data impacts. The advantages of respecting nonlinear dynamics and preserving non-Gaussian statistics are brought to light. For realistic test cases admitting complex distributions and with sparse or noisy measurements, the GMM-DO filter is shown to fundamentally improve the filtering skill, outperforming simpler schemes invoking the Gaussian parametric distribution.


Viruses ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 80
Author(s):  
Xinjie Li ◽  
Ling Pang ◽  
Yue Yin ◽  
Yuqi Zhang ◽  
Shuyun Xu ◽  
...  

The rate of decline in the levels of neutralizing antibodies (NAbs) greatly varies among patients who recover from Coronavirus disease 2019 (COVID-19). However, little is known about factors associated with this phenomenon. The objective of this study is to investigate early factors at admission that can influence long-term NAb levels in patients who recovered from COVID-19. A total of 306 individuals who recovered from COVID-19 at the Tongji Hospital, Wuhan, China, were included in this study. The patients were classified into two groups with high (NAbhigh, n = 153) and low (NAblow, n = 153) levels of NAb, respectively based on the median NAb levels six months after discharge. The majority (300/306, 98.0%) of the COVID-19 convalescents had detected NAbs. The median NAb concentration was 63.1 (34.7, 108.9) AU/mL. Compared with the NAblow group, a larger proportion of the NAbhigh group received corticosteroids (38.8% vs. 22.4%, p = 0.002) and IVIG therapy (26.5% vs. 16.3%, p = 0.033), and presented with diabetes comorbidity (25.2% vs. 12.2%, p = 0.004); high blood urea (median (IQR): 4.8 (3.7, 6.1) vs. 3.9 (3.5, 5.4) mmol/L; p = 0.017); CRP (31.6 (4.0, 93.7) vs. 16.3 (2.7, 51.4) mg/L; p = 0.027); PCT (0.08 (0.05, 0.17) vs. 0.05 (0.03, 0.09) ng/mL; p = 0.001); SF (838.5 (378.2, 1533.4) vs. 478.5 (222.0, 1133.4) μg/L; p = 0.035); and fibrinogen (5.1 (3.8, 6.4) vs. 4.5 (3.5, 5.7) g/L; p = 0.014) levels, but low SpO2 levels (96.0 (92.0, 98.0) vs. 97.0 (94.0, 98.0)%; p = 0.009). The predictive model based on Gaussian mixture models, displayed an average accuracy of 0.7117 in one of the 8191 formulas, and ROC analysis showed an AUC value of 0.715 (0.657–0.772), and specificity and sensitivity were 72.5% and 67.3%, respectively. In conclusion, we found that several factors at admission can contribute to the high level of NAbs in patients after discharge, and constructed a predictive model for long-term NAb levels, which can provide guidance for clinical treatment and monitoring.


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