### Table 1 Properties of techniques for dimensionality reduction.

"... In PAGE 11: ...2. General properties In Table1 , the thirteen dimensionality reduction tech- niques are listed by four general properties: (1) the con- vexity of the optimization problem, (2) the main free... In PAGE 11: ... We discuss the four general properties below. For property 1, Table1 shows that most techniques for dimensionality reduction optimize a convex cost func- tion. This is advantageous, because it allows for find- ing the global optimum of the cost function.... In PAGE 11: ... Because of their nonconvex cost functions, autoencoders, LLC, and manifold charting may suffer from getting stuck in local optima. For property 2, Table1 shows that most nonlinear tech- niques for dimensionality reduction all have free param- eters that need to be optimized. By free parameters, we mean parameters that directly influence the cost func- tion that is optimized.... In PAGE 11: ... The main advantage of the presence of free parameters is that they provide more flexibility to the technique, whereas their main disadvantage is that they need to be tuned to optimize the performance of the di- mensionality reduction technique. For properties 3 and 4, Table1 provides insight into the computational and memory complexities of the com- putationally most expensive algorithmic components of the techniques. The computational complexity of a di- mensionality reduction technique is of importance to its applicability.... In PAGE 12: ...duction technique is determined by data properties such as the number of datapoints n, the original dimension- ality D, the target dimensionality d, and by parameters of the techniques, such as the number of nearest neigh- bors k (for techniques based on neighborhood graphs) and the number of iterations i (for iterative techniques). In Table1 , p denotes the ratio of nonzero elements in a sparse matrix to the total number of elements, m indi- cates the number of local models in a mixture of factor analyzers, and w is the number of weights in a neural network. Below, we discuss the computational complex- ity and the memory complexity of each of the entries in the table.... ..."

### Table 4. Run time of dimensionality reduction in seconds for dimensionality of 100. Run time for LSI and ICA is slightly faster than lin- ear function of dimensionality for the range tested (up to 300). Run time for DF is con-

"... In PAGE 9: ... The run time of DF is practically a constant func- tion of dimensionality, as the main computation is sorting the features according to their DF value. For comparing the run time of DF, ICA and LSI, the run time in seconds for dimensionality of 100 is shown in Table4 , on a Linux Pen- tium 4, 1.6GHz, with 1GB of RAM.... ..."

### Table 4 Base Regressions

1999

"... In PAGE 16: ... 4.1 Basic Estimates Table4 presents four variants of the basic regressions. 27 We include all the variables mentioned in Section 3 above, with a few exceptions for which sufficiently long time series data that are comparable across countries are not available (e.... In PAGE 21: ... But using individual data also raises problems. When we use the average grades of schooling by cohort as in Table4 , we average out the effect of personal characteristics and family background. But in the individual data their effects may be relevant but information to control for them is unavailable.... In PAGE 21: ... If the right-side variables move smoothly through time, the regression would confound the effect of macro variables with the impact of a better family background because the individual with higher education would exit the schooling system with secularly changed macro conditions. We include a time trend in the regression using individual data, as we did in Table4 , to attempt to control for this possibility. But the interpretation of some variables such as the demographic indicators and factor endowments is not as clear as in the case of Table 4 because they might be capturing part of the family background effect.... In PAGE 21: ... We include a time trend in the regression using individual data, as we did in Table 4, to attempt to control for this possibility. But the interpretation of some variables such as the demographic indicators and factor endowments is not as clear as in the case of Table4 because they might be capturing part of the family background effect. The coefficient estimates for the variables of primary interest in this paper -- the measure of volatility, GDP growth and the terms of trade -- are not likely to be subject to this problem.... In PAGE 21: ... We estimate the equations with Huber-White corrected standard errors and clustering for country, year of birth and grades of schooling. As in Table4 the first three regressions control for all country fixed effects, and refer to the total population, males and females, respectively and the fourth regression is for random effects. The main differences with Table 4 for the fixed-effects estimates include: ( i ) the coefficient for capital per worker becomes highly significant, for the whole population as well as for males and females separately; (ii) health conditions increase in significance and appear to have a larger effect on males; (iii) the coefficient for the proportion of urban population increases considerably in size (by a factor of about 10), and becomes highly significant; (iv) GDP per... In PAGE 21: ... As in Table 4 the first three regressions control for all country fixed effects, and refer to the total population, males and females, respectively and the fourth regression is for random effects. The main differences with Table4 for the fixed-effects estimates include: ( i ) the coefficient for capital per worker becomes highly significant, for the whole population as well as for males and females separately; (ii) health conditions increase in significance and appear to have a larger effect on males; (iii) the coefficient for the proportion of urban population increases considerably in size (by a factor of about 10), and becomes highly significant; (iv) GDP per... In PAGE 22: ...dependency rate increases in significance and becomes stronger for females than for males; and (v) trade openness becomes statistically insignificant. The main difference with Table4 for the variables emphasized in the random-effects estimates is that the size of the coefficient for the effect of latitude is now relatively small. Due to the potential correlation with family background, it is safer to interpret the effects of terms of trade, macro volatility and GDP growth as genuine macro effects, while the other variables, which move much more smoothly through time, are more likely to be contaminated by unobserved family background variables.... In PAGE 22: ... The right-side variables are the same as in Table 4. The estimates in Table 6 differ in relatively few respects from those in Table4 . One difference is that the impact of the volatility of GDP growth appears to be substantially greater, and the effect is greater for males than for females.... In PAGE 23: ... Decomposing the Changes in Attainment We here use the estimates from Section 4 to decompose the changes in schooling progress in the 18 LAC countries in our sample in order to assess the economic impact of the right-side variables on the patterns that we describe in Section 2. To decompose the changes, we use the regression coefficients in the first column in Table4 and the average values of the right-side variables (in Appendix Table D1) to predict the average grades of schooling of each birth cohort and how much of the changes in the grades of schooling is accounted for by each right-side variable. Table 7 summarizes the main results for the whole population, and for males and females separately.... In PAGE 25: ... The last two rows in Table 7 show our final simulations. The first predicts the change in attainment by using the regression coefficients in Table4 and mean values for the 1980s for factor endowments, health, urbanization and demography, as in previous simulations. But we use mean values of the 1970s for the terms of trade, volatility, GDP per capita growth and GDP per capita level, rather than the 1980s values.... ..."

Cited by 2

### Table 5 Base Regressions

1999

"... In PAGE 21: ... The coefficient estimates for the variables of primary interest in this paper -- the measure of volatility, GDP growth and the terms of trade -- are not likely to be subject to this problem. Table5 presents our results with the individual data, which refers to about 383,000 observations (some observations are dropped due to lack of macro variables for the early critical marginal schooling decision years). We estimate the equations with Huber-White corrected standard errors and clustering for country, year of birth and grades of schooling.... In PAGE 22: ... Due to the potential correlation with family background, it is safer to interpret the effects of terms of trade, macro volatility and GDP growth as genuine macro effects, while the other variables, which move much more smoothly through time, are more likely to be contaminated by unobserved family background variables. The results in Table5 clearly support the previous conclusion that macroeconomic shocks affect attainment significantly. These results are not changed by robustness tests parallel to those described in Section 4.... In PAGE 33: ... Similarly in Colombia, Ecuador, El Salvador, Mexico and Paraguay, early departure from school contributes to low primary completion rates. Perhaps the most striking feature of Table C5 is that even though there are declines in enrollment at around age 12 for several countries, enrollments are higher than might have been expected after looking at the results in Table5 where we showed that primary completion rates are below or around 80% in most countries in the region. This reflects that although individuals might find it relatively easy to enroll in school, they find it hard to actually complete grades.... ..."

Cited by 2

### Table 44. Pollock ICA, Catches Attributed to the ICA and Slack in the ICA in 1999-2002

2005

"... In PAGE 7: ...able 43. Discarded amp; Retained Non-Pollock amp; Pollock Catch of HT-CPs, 1999-2002 ................... 105 Table44 .... In PAGE 118: ...0 Source: Sector Profile Database Developed by Northern Economics from blend data supplied by NOAA Fisheries-Alaska Fisheries Science Center. In each of the last four years, the amount of pollock caught in the non-AFA pollock fishery has been less than the ICA ( Table44 ). During this time, non-AFA pollock fishery has used up to 92 percent of the ICA, leaving an average buffer of 3,200 mt.... In PAGE 119: ...BSAI Amendment 79 May 2005 While Table44 demonstrated that considerable slack exists between the pollock ICA and actual incidental pollock catches by all sectors, Table 45 shows that there is also considerable slack between pollock catches by the HT-CP sector and the amount that could be taken under the 20 percent MRA limit. The HT-CP sector during the 1999 to 2002 period, could have retained all of their pollock catch without exceeding the MRA based on an annual enforcement interval.... ..."

### Table 2. Equal error rates (EER) for ICA1 based face verification ICA1 EER (%)

"... In PAGE 4: ....2.2. Face Verification Using Independent Component Analysis As can be observed from the ROC curve in Figure 5, ICA1 performance results are very similar to those of PCA. See Table2 for equal error rates). Figure 5.... ..."

### Table 3. Size comparison among various regression sets Fault Numberof regressiontests Size reduction Size reduction

1997

"... In PAGE 6: ...4.1 Size reduction For each fault, Table3 lists the number of regression tests in T 0 on which the old and new programs produce different outputs and the number of tests in T 00 selected according to the modification-based technique. The size of subsequent prioritized #28T 00 P #29 and block minimized (T 00 MB )6 sets is also included.... In PAGE 6: ... Two reductions in size, with respect to T 0 and T 00 , respectively, were computed. Table3 lists the reductions for T 00 MB and Table 4 lists the reductions for T 00 P with three different N values. These values are defined as one-third of, two-thirds of, and the same as the size of T 00 MB , wherever possible.... ..."

Cited by 51

### Table 3. Equal error rates (EER) for ICA2 based face verification ICA2 EER (%)

### Table 2: Reduction in the problem size Circuit

"... In PAGE 5: ... The BN-based analysis was done using Bayesian Network Toolbox in MATLAB [1]. Table2 shows the reduction in gate sizes we obtain after per- forming Switching Window and Series Reduction transformations. We can obtain as much as 90% reduction in the circuit sizes and the average reduction obtained was 71%.... ..."

### Table 2. Optimal profile lengths for 3-grams and 4-grams when each of the listed dimen- sion reduction methods is applied.

"... In PAGE 7: ... N and Clustering Quality In order to investigate the ef- fect of N-gram length (N) on clustering quality, we choose the best profile length for 3-grams and 4-grams based on the results shown in the previous section. Table2 shows these best profile length for 3-grams and 4-grams when each of the three dimension reduction methods, LSI, ICA, or DF, is applied. Dimensionality and sparsity increase with N, as can be seen in Table 3.... ..."