For the stepsize αt in SGD and TG, we adopt a variable stepsize scheme (Zinkevich, 2003; Nemirovski et al., 2009), choosing αt = (D/G) √
2/t.
Sample text:```For seeking the optimal value of Wh of the sub-problems which corresponds to the h-th level, we can solve the problem by the smoothing proximal gradient (SPG) method [6] fortunately.```
Sample intent: background
Sample text:```Discrepancies analogous to those between our results and those of simulations have, indeed, recently been observed in the case of the binary perceptron [18], the pspin interaction spin glass [19], and in the case of fluctuating manifolds in random media [20], where dynamically frozen phases were observed in regions of parameter space in which static approaches yielded ergodic phases.```
Sample intent: result



Sample text:```For seeking the optimal value of Wh of the sub-problems which corresponds to the h-th level, we can solve the problem by the smoothing proximal gradient (SPG) method [6] fortunately.```
Sample intent: background



Sample text:```These are in keeping with earlier studies on the steadystate response (2, 5, 8), step-function response, (3, 5, 6, 14) and sinusoidal response ( 14) of the various vascular beds.```
Sample intent: result



Sample text:``` The GRS was then calculated by summing across all SNPs (the GRS could theoretically range from 0 to 58).```
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Sample text:```The merging is based on the increase in the weighted-bycounts entropy [1] and is stopped by a threshold indicating the minimum number of training samples required to estimate a weight distribution.```
Sample intent: method
Sample text:```For seeking the optimal value of Wh of the sub-problems which corresponds to the h-th level, we can solve the problem by the smoothing proximal gradient (SPG) method [6] fortunately.```
Sample intent: background



Sample text:``` The GRS was then calculated by summing across all SNPs (the GRS could theoretically range from 0 to 58).```
Sample intent: background



Sample text:```We used the stepwise multiple linear regression that accounts for repeated measurements in the same dog (4) first to test whether there was a difference among values for resistances and for elastances between control and emphysema at each mean Paw, considering the entire range of f and VT of forcing.```
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Sample text:```This section contains a generalisation of the basic results on multifractal products of stochastic processes developed in Kahane (1985), Kahane (1987) and Mannersalo et al (2002).```
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Sample text:```Following Baker et al. (2012), I include a constant and a linear time trend in xt.```
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Sample text:```Discrepancies analogous to those between our results and those of simulations have, indeed, recently been observed in the case of the binary perceptron [18], the pspin interaction spin glass [19], and in the case of fluctuating manifolds in random media [20], where dynamically frozen phases were observed in regions of parameter space in which static approaches yielded ergodic phases.```
Sample intent: result



Sample text:```This transition was introduced first by Prince and Elder (2007) and it simplifies formulas for parameter update on Mstep of EM algorithm.```
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Sample text:```In this study, we generalized previous results regarding the quasi-Gaussian shape and the scalar property using the SBF model [13,21,52].```
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Sample text:```Note that in their pioneering paper Calvet and Fisher (2002) proposed the simplified version of the construction of Mannersalo et al (2002).```
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Sample text:```In-between methods can be subdivided into linear approximations [12,24] and quadratic interpolation methods [22,23,25–27] based on the degree of the polynomial approximation employed.```
Sample intent: method