### Table 2. Word error rates for full covariance models with state dependent quadratic feature space transforms.

"... In PAGE 4: ... Further exploring the use of a quadratic feature space transform we considered using a different transform for each HMM state. Table2 shows the results with 680 and 10K gaussians respectively. In the case of 680 gaussians, where each gaussian has its own quadratic feature transform qj(Ajx), there was a substantial gain over the baseline full covariance model with 680 gaussians.... ..."

### Table 2. Word error rates for full covariance models with state dependent quadratic feature space transforms.

"... In PAGE 4: ... Further exploring the use of a quadratic feature space transform we considered using a different transform for each HMM state. Table2 shows the results with 680 and 10K gaussians respectively. In the case of 680 gaussians, where each gaussian has its own quadratic feature transform D5CYB4BTCYDCB5, there was a substantial gain over the baseline full covariance model with 680 gaussians.... ..."

### Table 1: Time and space for the BAliBASE benchmarks. For each alignment group and algorithm version, the statistics are for 20 random balanced splits of each alignment in the group, where a benchmark of k sequences was split into alignments with bk=2c and dk=2e sequences. Versions are: BDQ, bound and dominance pruning in quadratic space, and DL, dominance pruning in linear space.

2004

Cited by 5

### Table 1: Simulated coverage probabilities for a quadratic regression and locally weighted regression with 50 equally spaced points on [0; 1].

1994

"... In PAGE 5: ...2). Simulations of size 105 are then used to estimate the true coverage probabilities in the absence of bias; the results are shown in Table1 . As expected, the simulations indicate the true coverage slightly exceeds the nominal coverage in most cases.... In PAGE 5: ...7). Table1 About Here We show the results of a two dimensional simulation in Table 2. The design consisted of observations at the points ((i?1)=10; (j?1)=10); i; j = 1; .... In PAGE 9: ... In simulations reported in Section 5, this correction fails badly, sometimes being worse than no correction. A similar technique is used by Hardle and Marron (1991); their Table1 also suggests this bias correction is unsatisfactory. A more reasonable use of ^ m(x) may be to estimate certain global functionals of the bias; the maximum bias is useful in the con dence band setting.... ..."

Cited by 7

### Table 1. Reference quadrature data, quadratic spaces. The form ( ; )hk obtained by adding the local forms in (5.6) according to (5.3) is a generalization of the nodal inner product (u; v)k = h2 k Xni u(ni) v(ni) : (5.7)

1993

"... In PAGE 25: ... Each is the restriction to T of a single nodal basis function for Vk. Alternatively, de ne a basis f~ g for P(2)(T) according to the speci cations of Table1 . Associated with each ~ is a single element of a new local basis k for Vk.... In PAGE 25: ... Outline of reference triangle notations. For each ~ , we construct a linear functional, or \degree of freedom quot;, F ;T( ) acting on P(2)(T) and satisfying F ;T(~ ) = , see Table1 . If it is understood that for v 2 Vk, F ;T(v) F ;T(vjT), then each degree of freedom annihilates all but one element of the basis k.... In PAGE 26: ... A simple scaling argument proves the equivalence of kuk2 0;T and (u; u)hk;T , independently of T 2 k for quasi-uniform meshes k. If the weights !i;T are chosen according to Table1 , then ( ; )hk;T will also be suitably exact. In this case, for constants c (u; c)hk;T = 6 Xi=1 !i;T Fi;T(u)Fi;T(c) = 3 Xi=1 16jTju(ni) c + X 1 i lt;j 3 23jTj hu(nij) ? 14(u(ni) + u(nj))i h 1 2 c i = 1 3jTj X 1 i lt;j 3 u(nij) c : Recalling the standard quadrature formula ZT apos; dx = 13jTj X 1 i lt;j 3 apos;(nij) ; 8 apos; 2 P(2)(T) ; it follows that ET(u; v) = 0 for all fu; vg 2 P(2)(T) P(0)(T).... In PAGE 27: ... Assume that the hypotheses of Theorem 15 are valid. For example, use a scheme de ned by Table1 for m = 2, or by Table 2 for m = 3. In order to obtain inequalities (5.... In PAGE 29: ...11) associated with the modi ed Ciarlet-Raviart method, with piecewise-quadratic spaces, will be considered on the unit square, = [0; 1] [0; 1]. The discrete forms used in de ning this method are chosen from Table1 of Section 5. Consequently, Gauss-Seidel smoothing iterations may be used in the multigrid algorithms.... ..."

Cited by 9

### Table 2: The running time comparisons of Burns apos;, KO, YTO, Howard apos;s, HO, Karp apos;s, DG, Lawler apos;s, Karp2, and OA1 algorithms on the random graphs with n nodes and m arcs. For the cases marked with N/A, either we could not get a result in a day, or we ran out of memory because of the quadratic space complexity of the algorithm in context.

### Table 2. Error rates for the quadratic and linear classifiers in the one-dimensional space, where the transformed data has been obtained using the FDA, LD and RH methods.

"... In PAGE 6: ... For the linear classifier, again, LD and RH outperformed FDA, and also RH achieved the lowest error rate in six out of ten datasets, outperforming LD. In Table2 , the results for the dimensionality reduction and classification for dimen- sion d = 1 are shown. For the quadratic classifier, we observe that as in the previous case, LD and RH outperformed FDA, and that the latter did not obtained the lowest er- ror rate in any of the datasets.... ..."

### Table 1: Classi cation performance on a test set of 160 patterns of the combination rules of 3 classi ers in independent feature spaces. Classi ers are normal density based quadratic classi ers, P is the total number of train patterns, averaged on 25 runs.

1997

Cited by 14

### Table 3: Linear fits, quadratic fits and peak of the quadratic functions fit to the data in Experiment 2

"... In PAGE 12: ...Each of the three psychophysical roughness functions for active touch based on aggregated participant data was initially fit with linear and quadratic equations (see Table3 and Figure 3a). The r2linear values for the slow, medium and fast speeds were .... In PAGE 13: ... The three speed functions reversed themselves at about 1 mm on the interelement-spacing continuum. Each of the three psychophysical roughness functions based on aggregated participant data was initially fit with linear and quadratic equations (see Table3 and Figure 3b). The r2linear values for the slow, medium and fast speeds were .... In PAGE 14: ...he slow, medium and fast speeds were 2.28, 2.53, and 3.05 mm ( Table3 , Figure 3a), respectively. In the passive condition, the corresponding values were 2.... In PAGE 14: ...ondition, the corresponding values were 2.07, 2.67, and 3.28 mm ( Table3 , Figure 3b), respectively. Once again, there were several unusually high participant peak values in the high-speed conditions for both active and passive modes.... ..."

### Table 1 shows results on test and training set for the 3 models. Notice that the quadratic model performs best and the cubic model overfits the data. Quadratic model gains from 15% to 2% on test accuracy in comparison to the linear one.

"... In PAGE 4: ... Table1 : Performance of the regression mapping from XY lap sensor positions to the latent space positions. Quadratic regression performs best, cubic overfits.... ..."

Cited by 1