Since the Hessian of f(x) is not always positive semidefinite, we regularize the Hessian by computing its eigendecomposition and setting the negative eigenvalues to zeros [9].
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:```This seems to be the main drawback of the current implementation in comparison to the method of Black Jepson (“refined” in Table 1).```
Sample intent: result



Sample text:```Over the last few years, many different local interest point detectors (like Harris3D [16], Cuboid [6], Hessian [35] or Dense sampling [33]) and many spatio-temporal descriptors (like HOG [17], HOG3D [14], HOF [17], Cuboid [6] or ESURF [35]) have been proposed.```
Sample intent: method



Sample text:```The area under the curve represents the probability that the logistic regression model will rank a randomly chosen positive instance (i.e., an error) higher than a randomly chosen negative instance (i.e., nonerror; Fawcett, 2006; Macmillan & Creelman, 2005).```
Sample intent: method



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.```
Sample intent: background



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].```
Sample intent: result
Sample text:```Our results confi rm previous studies that reached the same conclusion (Boushey et al 1994; Vermeulen et al 2000; Till et al 2005; Marcucci et al 2005).```
Sample intent: result



Sample text:```…methods rely on some additional and often heuristic step to generate an initial solution, such as adversarially-trained neural networks [Conneau et al., 2018, Zhang et al., 2017a,b], robust self-learning [Artetxe et al., 2018b] or
5This can be easily verified by noting that the…```
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:```Following past work, we show that such basis models can be learned from 2D annotations using techniques adapted from nonrigid structure from motion (SFM) [20, 19].```
Sample intent: method



Sample text:```A rook pivoting scheme as in [3] and [11] can be implemented for tridiagonal matrices, but a full rook scheme for general banded matrices would probably lead to a ”chasing” scheme as in [5] or [15] .```
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.```
Sample intent: background



Sample text:```This seems to be the main drawback of the current implementation in comparison to the method of Black Jepson (“refined” in Table 1).```
Sample intent: result



Sample text:```To train our CNN for classification, we set initial learning rate to 0.01 and optimize cross-entropy loss with Adagrad [26].```
Sample intent: background



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].```
Sample intent: result



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