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Network Generalization Prediction for Safety Critical Tasks in Novel Operating DomainsMolly O'Brien Mike Medoff Julia Bukowski Gregory D. HagerIEEE Winter Conference on Applications of Computer Vision
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ET
/S/Span<>BDC
BT
/F22 9.9626 Tf 97.029 498.75 Td [(g)]TJ/F19 9.9626 Tf 5.109 0 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F19 9.9626 Tf 4.423 0 Td [(\))-278(=)]TJ/F12 9.9626 Tf 18.353 14.346 Td [(P)]TJ/F21 6.9738 Tf 10.516 -2.463 Td [(N)]TJ 0 -7.998 Td [(i)]TJ/F18 6.9738 Tf 2.819 0 Td [(=1)]TJ/F63 9.9626 Tf 12.246 2.989 Td [(I)]TJ/F19 9.9626 Tf 3.874 0 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 -1.494 Td [(i)]TJ/F22 9.9626 Tf 3.317 1.494 Td [(;)]TJ/F66 9.9626 Tf 4.428 0 Td [(c)]TJ/F19 9.9626 Tf 4.423 0 Td [(\))]TJ/F25 9.9626 Tf 6.088 0 Td [<03>]TJ/F22 9.9626 Tf 7.195 0 Td [(l)]TJ/F19 9.9626 Tf 3.169 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(f)]TJ/F19 9.9626 Tf 5.95 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(y)]TJ/F21 6.9738 Tf 9.312 -1.494 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.494 Td [(\))]TJ
ET
q
1 0 0 1 128.789 501.241 cm
[]0 d 0 J 0.398 w 0 0 m 109.46 0 l S
Q
BT
/F12 9.9626 Tf 156.622 497.543 Td [(P)]TJ/F21 6.9738 Tf 10.516 -2.463 Td [(N)]TJ 0 -7.997 Td [(i)]TJ/F18 6.9738 Tf 2.819 0 Td [(=1)]TJ/F63 9.9626 Tf 12.245 2.988 Td [(I)]TJ/F19 9.9626 Tf 3.875 0 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F21 6.9738 Tf 4.424 -1.494 Td [(i)]TJ/F22 9.9626 Tf 3.316 1.494 Td [(;)]TJ/F66 9.9626 Tf 4.428 0 Td [(c)]TJ/F19 9.9626 Tf 4.424 0 Td [(\))]TJ
ET
EMC
BT
/F67 9.9626 Tf 274.746 498.75 Td [(\(2\))]TJ/F25 9.9626 Tf -224.634 -31.328 Td [(L)]TJ/F24 6.9738 Tf 6.871 3.616 Td [(T)]TJ/F67 9.9626 Tf 9.342 -3.616 Td [(can)-250(equi)25(v)25(alently)-250(be)-250(computed)-250(as:)]TJ
ET
/S/Span<>BDC
BT
/F25 9.9626 Tf 126.05 443.525 Td [(L)]TJ/F24 6.9738 Tf 6.872 4.114 Td [(T)]TJ/F19 9.9626 Tf 9.618 -4.114 Td [(=)]TJ/F12 9.9626 Tf 10.516 9.465 Td [(X)]TJ/F66 6.9738 Tf 0.445 -21.41 Td [(c)]TJ/F24 6.9738 Tf 3.096 0 Td [(2)]TJ/F66 6.9738 Tf 5.369 0 Td [(C)]TJ/F22 9.9626 Tf 7.141 11.945 Td [(p)]TJ/F24 6.9738 Tf 5.012 -1.494 Td [(T)]TJ/F19 9.9626 Tf 6.851 1.494 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F19 9.9626 Tf 4.424 0 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(g)]TJ/F19 9.9626 Tf 5.109 0 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F19 9.9626 Tf 4.423 0 Td [(\))]TJ
ET
EMC
BT
/F67 9.9626 Tf 274.746 443.525 Td [(\(3\))]TJ -224.634 -31.542 Td [(Lik)10(e)25(wise,)-293(we)-284(can)-285(no)25(w)-284(e)15(xpress)-285(the)-284(Netw)10(ork)-285(Generalization)]TJ 0 -11.955 Td [(Prediction,)]TJ/F19 9.9626 Tf 48.266 2.518 Td [(^)]TJ/F25 9.9626 Tf -2.329 -2.518 Td [(L)]TJ/F24 6.9738 Tf 6.872 3.615 Td [(O)]TJ/F67 9.9626 Tf 7.029 -3.615 Td [(,)-250(as:)]TJ
ET
/S/Span<>BDC
BT
/F19 9.9626 Tf 128.2 380.308 Td [(^)]TJ/F25 9.9626 Tf -2.329 -2.519 Td [(L)]TJ/F24 6.9738 Tf 6.872 4.114 Td [(O)]TJ/F19 9.9626 Tf 9.797 -4.114 Td [(=)]TJ/F12 9.9626 Tf 10.516 9.465 Td [(X)]TJ/F66 6.9738 Tf 0.445 -21.41 Td [(c)]TJ/F24 6.9738 Tf 3.096 0 Td [(2)]TJ/F66 6.9738 Tf 5.369 0 Td [(C)]TJ/F22 9.9626 Tf 7.141 11.945 Td [(p)]TJ/F24 6.9738 Tf 5.012 -1.494 Td [(O)]TJ/F19 9.9626 Tf 7.03 1.494 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F19 9.9626 Tf 4.424 0 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(g)]TJ/F19 9.9626 Tf 5.109 0 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F19 9.9626 Tf 4.423 0 Td [(\))]TJ
ET
EMC
BT
/F67 9.9626 Tf 274.746 377.789 Td [(\(4\))]TJ -224.634 -31.542 Td [(This)-223(formulation)-224(holds)-223(theoretically)-224(for)-223(an)15(y)-224(number)-223(of)-224(con-)]TJ 0 -11.955 Td [(te)15(xt)-333(features)]TJ/F22 9.9626 Tf 52.962 0 Td [(J)]TJ/F67 9.9626 Tf 6.483 0 Td [(.)-559(Ho)25(we)25(v)15(er)40(,)-354(as)]TJ/F22 9.9626 Tf 61.162 0 Td [(J)]TJ/F67 9.9626 Tf 9.801 0 Td [(gro)25(ws)-333(linearly)65(,)-354(computing)]TJ -130.408 -11.956 Td [(Eqn.)-612(4)-351(requires)-351(e)15(xponentially)-351(more)-350(test)-351(samples)-351(to)-351(co)15(v)15(er)]TJ 0 -11.955 Td [(e)25(v)15(ery)-257(possible)]TJ/F66 9.9626 Tf 59.51 0 Td [(c)]TJ/F25 9.9626 Tf 7.324 0 Td [(2)]TJ/F66 9.9626 Tf 9.542 0 Td [(C)]TJ/F67 9.9626 Tf 7.193 0 Td [(.)-332(Thus,)-259(we)-257(introduce)-257(the)-257(Conte)15(xt)-257(Sub-)]TJ -83.569 -11.955 Td [(space,)]TJ/F66 9.9626 Tf 26.98 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 7.009 -3.399 Td [(,)-237(a)-234(lo)25(w-dimensional)-234(space,)-237(encoding)-234(the)-234(conte)15(xt)]TJ -46.074 -11.955 Td [(features)-250(most)-250(informati)25(v)15(e)-250(about)-250(the)-250(netw)10(ork)-250(performance.)]TJ/F66 10.9589 Tf 0 -20.406 Td [(3.2.)-250(De\002ning)-250(a)-250(Context)-250(Subspace)]TJ/F67 9.9626 Tf 11.955 -18.093 Td [(W)80(e)-225(are)-225(interested)-226(in)-225(selecting)-225(the)]TJ/F22 9.9626 Tf 132.734 0 Td [(K)]TJ/F67 9.9626 Tf 11.418 0 Td [(conte)15(xt)-225(features)-225(that)]TJ -156.107 -11.955 Td [(pro)15(vide)-264(the)-264(most)-264(information)-264(about)-264(the)-263(netw)10(ork)-264(loss,)-268(to)-264(in-)]TJ 0 -11.955 Td [(clude)-269(these)-269(features)-269(in)]TJ/F66 9.9626 Tf 92.056 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(S)]TJ/F20 4.9813 Tf 4.893 -1.002 Td [(K)]TJ/F67 9.9626 Tf 7.008 -3.399 Td [(.)-367(Let)]TJ/F22 9.9626 Tf 22.11 0 Td [(S)]TJ/F21 6.9738 Tf 6.109 -1.495 Td [(K)]TJ/F19 9.9626 Tf 10.8 1.495 Td [(=)]TJ/F25 9.9626 Tf 10.868 0 Td [(f)]TJ/F22 9.9626 Tf 4.981 0 Td [(s)]TJ/F21 6.9738 Tf 4.67 -1.495 Td [(k)]TJ/F25 9.9626 Tf 4.902 1.495 Td [(g)]TJ/F21 6.9738 Tf 4.982 3.615 Td [(K)]TJ 0 -6.437 Td [(k)]TJ/F18 6.9738 Tf 4.403 0 Td [(=1)]TJ/F67 9.9626 Tf 13.266 2.822 Td [(be)-269(the)-269(in-)]TJ -198.241 -12.985 Td [(dices)-260(of)-260(conte)15(xt)-260(features)-259(of)-260(interest)-260(and)]TJ/F66 9.9626 Tf 159.62 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.001 Td [(K)]TJ/F19 9.9626 Tf 9.958 -3.4 Td [(=)]TJ/F25 9.9626 Tf 10.698 0 Td [(f)]TJ/F22 9.9626 Tf 4.981 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.615 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.057 Td [(k)]TJ/F25 9.9626 Tf 4.854 -2.558 Td [(g)]TJ/F21 6.9738 Tf 4.981 3.615 Td [(K)]TJ 0 -6.436 Td [(k)]TJ/F18 6.9738 Tf 4.404 0 Td [(=1)]TJ/F67 9.9626 Tf 10.585 2.821 Td [(,)]TJ -233.759 -11.955 Td [(where)]TJ/F22 9.9626 Tf 26.634 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.615 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.057 Td [(k)]TJ/F19 9.9626 Tf 7.621 -2.558 Td [(=)]TJ/F25 9.9626 Tf 10.516 0 Td [(f)]TJ/F22 9.9626 Tf 4.981 0 Td [(c)]TJ/F21 6.9738 Tf 4.312 4.489 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.058 Td [(k)]TJ/F21 6.9738 Tf -3.76 -6.208 Td [(i)]TJ/F25 9.9626 Tf 8.613 2.777 Td [(g)]TJ/F21 6.9738 Tf 4.982 3.615 Td [(N)]TJ 0 -6.208 Td [(i)]TJ/F18 6.9738 Tf 2.818 0 Td [(=1)]TJ/F67 9.9626 Tf 12.881 2.593 Td [(are)-230(the)-231(annotated)-230(attrib)20(utes)-231(for)-230(each)]TJ -94.951 -11.955 Td [(e)15(xample)-282(in)-282(the)-283(test)-282(set)-282(for)-282(conte)15(xt)-283(feature)]TJ/F22 9.9626 Tf 169.382 0 Td [(s)]TJ/F21 6.9738 Tf 4.67 -1.495 Td [(k)]TJ/F67 9.9626 Tf 4.902 1.495 Td [(.)-407(T)80(o)-282(select)-282(the)]TJ -178.954 -11.955 Td [(conte)15(xt)-301(features)-302(to)-301(include)-301(in)]TJ/F66 9.9626 Tf 120.554 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 7.008 -3.399 Td [(,)-314(we)-302(1\))-301(rank)-301(the)-302(conte)15(xt)]TJ -139.647 -11.956 Td [(features)-340(by)-339(ho)25(w)-340(much)-339(information)-340(the)15(y)-340(pro)15(vide)-339(about)-340(the)]TJ 0 -11.955 Td [(netw)10(ork)-237(loss,)-240(2\))-237(select)-238(the)]TJ/F66 9.9626 Tf 105.545 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.001 Td [(K)]TJ/F67 9.9626 Tf 9.373 -3.4 Td [(dimensionality)]TJ/F22 9.9626 Tf 61.591 0 Td [(K)]TJ/F67 9.9626 Tf 11.539 0 Td [(to)-237(enable)]TJ -200.133 -11.955 Td [(accurate)-250(Netw)10(ork)-250(Generalization)-250(Prediction.)]TJ/F66 9.9626 Tf 0 -27.407 Td [(3.2.1)-1000(Ranking)-250(Context)-250(F)25(eatur)18(es)]TJ/F67 9.9626 Tf 0 -18.984 Td [(Recall,)-400(the)-369(Mutual)-370(Information)-369(is)-370(often)-370(used)-369(to)-370(rank)-370(fea-)]TJ 0 -11.955 Td [(tures)-305(in)-305(\002lter)-305(feature)-304(selection)-305(algorithms)-305(and)-305(is)-305(computed)]TJ
0 g 0 G
0 g 0 G
0 g 0 G
0 g 0 G
0 g 0 G
/F66 9.9626 Tf 371.05 618.676 Td [(Notation)]TJ/F22 9.9626 Tf -84.147 -11.967 Td [(X)]TJ/F19 9.9626 Tf 11.803 0 Td [(=)]TJ/F25 9.9626 Tf 10.516 0 Td [(f)]TJ/F22 9.9626 Tf 4.982 0 Td [(x)]TJ/F21 6.9738 Tf 5.694 -1.495 Td [(i)]TJ/F25 9.9626 Tf 3.317 1.495 Td [(g)]TJ/F21 6.9738 Tf 4.981 3.615 Td [(N)]TJ 0 -6.208 Td [(i)]TJ/F18 6.9738 Tf 2.819 0 Td [(=1)]TJ/F67 9.9626 Tf 40.035 2.593 Td [(The)-250(T)70(est)-250(Data)]TJ/F22 9.9626 Tf -83.223 -11.968 Td [(Y)]TJ/F19 9.9626 Tf 10.765 0 Td [(=)]TJ/F25 9.9626 Tf 10.516 0 Td [(f)]TJ/F22 9.9626 Tf 4.982 0 Td [(y)]TJ/F21 6.9738 Tf 4.884 -1.494 Td [(i)]TJ/F25 9.9626 Tf 3.317 1.494 Td [(g)]TJ/F21 6.9738 Tf 4.981 3.616 Td [(N)]TJ 0 -6.209 Td [(i)]TJ/F18 6.9738 Tf 2.819 0 Td [(=1)]TJ/F67 9.9626 Tf 40.959 2.593 Td [(The)-250(T)70(est)-250(Labels)]TJ/F22 9.9626 Tf -59.773 -11.955 Td [(f)]TJ/F67 9.9626 Tf 59.773 0 Td [(The)-250(trained)-250(netw)10(ork)]TJ/F22 9.9626 Tf -101.641 -11.967 Td [(L)]TJ/F19 9.9626 Tf 9.547 0 Td [(=)]TJ/F25 9.9626 Tf 10.516 0 Td [(f)]TJ/F22 9.9626 Tf 4.981 0 Td [(l)]TJ/F19 9.9626 Tf 3.169 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(f)]TJ/F19 9.9626 Tf 5.95 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 5.694 -1.495 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.495 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(y)]TJ/F21 6.9738 Tf 9.312 -1.495 Td [(i)]TJ/F19 9.9626 Tf 3.317 1.495 Td [(\))]TJ/F25 9.9626 Tf 3.874 0 Td [(g)]TJ/F21 6.9738 Tf 4.982 3.615 Td [(N)]TJ 0 -6.209 Td [(i)]TJ/F18 6.9738 Tf 2.818 0 Td [(=1)]TJ/F67 9.9626 Tf 22.541 2.594 Td [(The)-250(T)70(est)-250(Set)-250(Loss)]TJ
ET
q
1 0 0 1 313.543 648.033 cm
[]0 d 0 J 0.398 w 0 0 m 226.888 0 l S
Q
BT
/F66 9.9626 Tf 360.767 639.465 Td [(C)]TJ/F67 9.9626 Tf 60.395 0 Td [(The)-250(conte)15(xt)-250(features)]TJ/F66 9.9626 Tf -68.695 -11.955 Td [(c)]TJ/F25 9.9626 Tf 7.191 0 Td [(2)]TJ/F66 9.9626 Tf 9.409 0 Td [(C)]TJ/F67 9.9626 Tf 52.095 0 Td [(A)-250(conte)15(xt)-250(v)15(ector)]TJ/F22 9.9626 Tf -65.439 -11.955 Td [(g)]TJ/F19 9.9626 Tf 5.109 0 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F19 9.9626 Tf 4.423 0 Td [(\))]TJ/F67 9.9626 Tf 52.032 0 Td [(The)-250(e)15(xpected)-250(loss)-250(of)]TJ/F22 9.9626 Tf 84.512 0 Td [(f)]TJ/F67 9.9626 Tf 8.441 0 Td [(in)]TJ/F66 9.9626 Tf 10.241 0 Td [(c)]TJ -169.539 -12.754 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.402 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 54.26 -3.399 Td [(The)-250(Conte)15(xt)-250(Subspace)]TJ
ET
q
1 0 0 1 313.543 599.016 cm
[]0 d 0 J 0.398 w 0 0 m 226.888 0 l S
Q
BT
/F25 9.9626 Tf 360.385 590.448 Td [(T)]TJ/F67 9.9626 Tf 60.777 0 Td [(The)-250(T)70(esting)-250(Domain)]TJ/F25 9.9626 Tf -60.902 -11.955 Td [(O)]TJ/F67 9.9626 Tf 60.902 0 Td [(The)-250(Operating)-250(Domain)]TJ/F22 9.9626 Tf -83.414 -11.955 Td [(p)]TJ/F24 6.9738 Tf 5.013 -1.495 Td [(T)]TJ/F19 9.9626 Tf 6.85 1.495 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F19 9.9626 Tf 4.423 0 Td [(\))]TJ/F67 9.9626 Tf 3.874 0 Td [(,)]TJ/F22 9.9626 Tf 4.982 0 Td [(p)]TJ/F24 6.9738 Tf 5.012 -1.495 Td [(O)]TJ/F19 9.9626 Tf 7.03 1.495 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F19 9.9626 Tf 4.424 0 Td [(\))]TJ/F67 9.9626 Tf 34.057 0 Td [(The)-250(probability)-250(of)]TJ/F66 9.9626 Tf 74.988 0 Td [(c)]TJ/F67 9.9626 Tf 6.914 0 Td [(in)]TJ/F25 9.9626 Tf 10.242 0 Td [(T)]TJ/F67 9.9626 Tf 7.958 0 Td [(,)]TJ/F25 9.9626 Tf 4.981 0 Td [(O)]TJ -168.742 -11.968 Td [(L)]TJ/F24 6.9738 Tf 6.871 3.615 Td [(T)]TJ/F67 9.9626 Tf 56.788 -3.615 Td [(The)-250(observ)15(ed)-250(loss)-250(in)]TJ/F25 9.9626 Tf 84.522 0 Td [(T)]TJ/F19 9.9626 Tf -145.942 -10.505 Td [(^)]TJ/F25 9.9626 Tf -2.329 -2.518 Td [(L)]TJ/F24 6.9738 Tf 6.871 3.615 Td [(O)]TJ/F67 9.9626 Tf 56.878 -3.615 Td [(The)-250(predicted)-250(loss)-250(in)]TJ/F25 9.9626 Tf 85.777 0 Td [(O)]TJ/F67 8.9664 Tf -112.217 -20.661 Td [(T)80(able)-250(1.)-250(Notation.)]TJ
0 g 0 G
/F67 9.9626 Tf -85.86 -26.851 Td [(as)]TJ/F22 9.9626 Tf 10.789 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.616 Td [(j)]TJ/F19 9.9626 Tf 4.198 -3.616 Td [(\))]TJ/F67 9.9626 Tf 6.365 0 Td [(for)-250(loss)]TJ/F22 9.9626 Tf 32.099 0 Td [(L)]TJ/F67 9.9626 Tf 9.271 0 Td [(and)-250(conte)15(xt)-250(feature)]TJ/F22 9.9626 Tf 78.694 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.616 Td [(j)]TJ/F67 9.9626 Tf 4.198 -3.616 Td [(:)]TJ
ET
/S/Span<>BDC
BT
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/F22 9.9626 Tf 26.126 0 Td [(s)]TJ/F24 6.9738 Tf 4.67 3.615 Td [<03>]TJ/F21 6.9738 Tf 0 -6.437 Td [(k)]TJ/F25 9.9626 Tf 7.669 2.822 Td [( )]TJ/F22 9.9626 Tf 12.73 0 Td [(ar)-28(g)-36(max)]TJ/F21 6.9738 Tf 34.855 -1.495 Td [(j)]TJ/F19 9.9626 Tf 4.198 1.495 Td [([)]TJ/F22 9.9626 Tf 2.767 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.615 Td [(j)]TJ/F22 9.9626 Tf 4.197 -3.615 Td [(;)-167(L)]TJ/F19 9.9626 Tf 11.208 0 Td [(\))]TJ/F25 9.9626 Tf 6.089 0 Td [<00>]TJ/F12 9.9626 Tf 9.962 7.472 Td [(P)]TJ/F21 6.9738 Tf 10.516 -10.461 Td [(s)]TJ/F20 4.9813 Tf 3.761 -1.057 Td [(k)]TJ/F24 6.9738 Tf 4.355 1.057 Td [(2)]TJ/F21 6.9738 Tf 5.369 0 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F22 9.9626 Tf 8.669 3.991 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.615 Td [(j)]TJ/F22 9.9626 Tf 4.198 -3.615 Td [(;)-167(C)]TJ/F21 6.9738 Tf 12.261 3.615 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.057 Td [(k)]TJ/F19 9.9626 Tf 4.854 -2.558 Td [(\)])]TJ
0 g 0 G
/F67 7.9701 Tf -220.843 -11.956 Td [(4:)]TJ
0 g 0 G
/F25 9.9626 Tf 31.108 0 Td [(8)]TJ/F22 9.9626 Tf 5.534 0 Td [(j)]TJ/F25 9.9626 Tf 7.441 0 Td [(2)]TJ/F22 9.9626 Tf 9.409 0 Td [(J)]TJ/F25 9.9626 Tf 8.696 0 Td [(n)]TJ/F22 9.9626 Tf 7.196 0 Td [(S)]TJ/F21 6.9738 Tf 6.109 -1.494 Td [(K)]TJ
0 g 0 G
/F67 7.9701 Tf -75.493 -10.461 Td [(5:)]TJ
0 g 0 G
/F22 9.9626 Tf 26.126 0 Td [(S)]TJ/F21 6.9738 Tf 6.109 -1.494 Td [(K)]TJ/F19 9.9626 Tf 10.449 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(S)]TJ/F21 6.9738 Tf 6.109 -1.494 Td [(K)]TJ/F25 9.9626 Tf 9.895 1.494 Td [([)]TJ/F22 9.9626 Tf 8.855 0 Td [(s)]TJ/F24 6.9738 Tf 4.67 3.616 Td [<03>]TJ/F21 6.9738 Tf 0 -6.437 Td [(k)]TJ
0 g 0 G
/F67 7.9701 Tf -82.729 -9.134 Td [(6:)]TJ
0 g 0 G
/F66 9.9626 Tf 11.182 0 Td [(end)-250(f)25(or)]TJ
0 g 0 G
/F67 7.9701 Tf -11.182 -11.955 Td [(7:)]TJ
0 g 0 G
/F22 9.9626 Tf 11.182 0 Td [(g)]TJ/F19 9.9626 Tf 5.11 0 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.893 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.613 Td [(\))-278(=)]TJ/F22 9.9626 Tf 17.158 0 Td [(E)]TJ/F19 9.9626 Tf 7.928 0 Td [([)]TJ/F22 9.9626 Tf 2.768 0 Td [(l)]TJ/F19 9.9626 Tf 3.169 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(f)]TJ/F19 9.9626 Tf 5.95 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(X)]TJ/F19 9.9626 Tf 9.036 0 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(Y)]TJ/F25 9.9626 Tf 12.426 0 Td [(j)]TJ/F66 9.9626 Tf 2.767 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.893 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.613 Td [(\)])]TJ
0 g 0 G
ET
q
1 0 0 1 50.112 617.928 cm
[]0 d 0 J 0.398 w 0 0 m 236.25 0 l S
Q
BT
/F67 9.9626 Tf 50.112 586.681 Td [(Intuiti)25(v)15(ely)65(,)]TJ/F19 9.9626 Tf 52.971 0 Td [<01>]TJ/F22 9.9626 Tf 8.303 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.761 -0.996 Td [(1)]TJ/F22 9.9626 Tf 4.386 -2.619 Td [(;)-167(:::;)-166(C)]TJ/F21 6.9738 Tf 24.991 3.615 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.613 Td [(\))]TJ/F67 9.9626 Tf 12.383 0 Td [(subtracts)-854(the)-854(redun-)]TJ -145.64 -13.262 Td [(dant)-733(information)-733(in)]TJ/F22 9.9626 Tf 93.852 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.616 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.002 Td [(K)]TJ/F67 9.9626 Tf 7.008 -2.614 Td [(,)]TJ/F12 9.9626 Tf 10.994 7.472 Td [(P)]TJ/F21 6.9738 Tf 10.516 -2.463 Td [(K)]TJ/F24 6.9738 Tf 7.183 0 Td [<00>]TJ/F18 6.9738 Tf 6.227 0 Td [(1)]TJ/F21 6.9738 Tf -13.41 -7.998 Td [(k)]TJ/F18 6.9738 Tf 4.404 0 Td [(=1)]TJ/F22 9.9626 Tf 15.136 2.989 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.616 Td [(s)]TJ/F20 4.9813 Tf 3.761 -1.058 Td [(k)]TJ/F22 9.9626 Tf 4.853 -2.558 Td [(;)-167(C)]TJ/F21 6.9738 Tf 12.261 3.616 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.614 Td [(\))]TJ/F67 9.9626 Tf 3.874 0 Td [(,)-854(from)]TJ -205.889 -11.955 Td [(the)-560(information)-560(it)-560(pro)15(vides)-560(about)-559(the)-560(loss,)]TJ/F22 9.9626 Tf 191.04 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.615 Td [(s)]TJ/F20 4.9813 Tf 3.76 -1.001 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.614 Td [(\))]TJ/F67 9.9626 Tf 3.874 0 Td [(.)]TJ -233.759 -11.955 Td [(Note)-622(that)-621(the)-622(computational)-621(comple)15(xity)-622(of)-622(computing)]TJ/F19 9.9626 Tf 0 -11.955 Td [<01>]TJ/F22 9.9626 Tf 8.302 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(1)]TJ/F22 9.9626 Tf 4.386 -2.619 Td [(;)-167(:::;)-166(C)]TJ/F21 6.9738 Tf 24.991 3.615 Td [(s)]TJ/F20 4.9813 Tf 3.761 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.613 Td [(\))]TJ/F67 9.9626 Tf 6.031 0 Td [(gro)25(ws)-216(linearly)-217(with)]TJ/F22 9.9626 Tf 78.717 0 Td [(K)]TJ/F67 9.9626 Tf 9.174 0 Td [(.)-299(Lik)10(e)-216(the)-217(Inter)20(-)]TJ -174.207 -11.956 Td [(action)-250(Information,)]TJ/F19 9.9626 Tf 79.423 0 Td [<01>]TJ/F22 9.9626 Tf 8.302 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.616 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(1)]TJ/F22 9.9626 Tf 4.386 -2.62 Td [(;)-167(:::;)-166(C)]TJ/F21 6.9738 Tf 24.991 3.616 Td [(s)]TJ/F20 4.9813 Tf 3.761 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.614 Td [(\))]TJ/F67 9.9626 Tf 6.37 0 Td [(can)-251(be)-250(positi)25(v)15(e)-251(or)]TJ -166.078 -11.955 Td [(ne)15(g)5(ati)25(v)15(e.)-299(In)-216(Appendix)-216(A,)-216(we)-216(sho)25(w)-216(that)-216(for)-216(independent)-216(fea-)]TJ 0 -11.955 Td [(tures)-196(in)-196(the)-196(Conte)15(xt)-196(Subspace,)]TJ/F19 9.9626 Tf 120.679 0 Td [<01>]TJ/F22 9.9626 Tf 8.303 0 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(1)]TJ/F22 9.9626 Tf 4.387 -2.619 Td [(;)-167(C)]TJ/F21 6.9738 Tf 12.261 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(2)]TJ/F19 9.9626 Tf 4.386 -2.619 Td [(\))]TJ/F67 9.9626 Tf 5.826 0 Td [(approaches)]TJ/F22 9.9626 Tf -191.438 -11.955 Td [(I)]TJ/F19 9.9626 Tf 5.161 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(L;)-167(C)]TJ/F21 6.9738 Tf 19.041 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(1)]TJ/F22 9.9626 Tf 4.386 -2.619 Td [(;)-167(C)]TJ/F21 6.9738 Tf 12.261 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(2)]TJ/F19 9.9626 Tf 4.387 -2.619 Td [(\))]TJ/F67 9.9626 Tf 7.54 0 Td [(as)]TJ/F22 9.9626 Tf 11.964 0 Td [(C)]TJ/F21 6.9738 Tf 7.833 3.615 Td [(s)]TJ/F17 4.9813 Tf 3.76 -0.996 Td [(2)]TJ/F67 9.9626 Tf 8.052 -2.619 Td [(approaches)-368(perfect)-368(information)-368(on)]TJ/F22 9.9626 Tf -95.78 -11.955 Td [(L)]TJ/F67 9.9626 Tf 6.78 0 Td [(.)-488(W)80(e)-310(propose)-309(a)-309(greedy)-310(algorithm)-309(to)-309(iterati)25(v)15(ely)-310(select)-309(the)]TJ/F22 9.9626 Tf -6.78 -11.955 Td [(K)]TJ/F67 9.9626 Tf 12.995 0 Td [(most)-384(informati)25(v)15(e)-383(features)-384(from)-383(the)-384(conte)15(xt,)-417(see)-383(Algo-)]TJ -12.995 -11.956 Td [(rithm)-250(1.)]TJ/F66 9.9626 Tf 0 -29.715 Td [(3.2.2)-1000(Selecting)-250(the)-250(Context)-250(Subspace)-250(Dimensionality)]TJ/F67 9.9626 Tf 0 -19.782 Td [(Selecting)-318(the)-318(number)-318(of)-317(features,)]TJ/F22 9.9626 Tf 138.013 0 Td [(K)]TJ/F67 9.9626 Tf 9.174 0 Td [(,)-335(to)-318(include)-318(in)]TJ/F66 9.9626 Tf 60.158 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 10.175 -3.399 Td [(is)]TJ -229.605 -11.956 Td [(not)-341(tri)25(vial.)-582(Recall,)-363(the)-341(conte)15(xt)-341(features)-341(are)-340(discretized.)-583(If)]TJ 0 -11.955 Td [(each)-205(feature)-205(has)]TJ/F22 9.9626 Tf 65.319 0 Td [(n)]TJ/F67 9.9626 Tf 8.024 0 Td [(unique)-205(v)25(alues,)-214(the)-205(total)-206(number)-205(of)-205(unique)]TJ -73.343 -11.955 Td [(conte)15(xts)-279(is)]TJ/F22 9.9626 Tf 45.257 0 Td [(n)]TJ/F21 6.9738 Tf 5.98 3.615 Td [(K)]TJ/F67 9.9626 Tf 7.681 -3.615 Td [(:)-368(as)-279(you)-278(increase)-279(the)-279(number)-279(of)-279(conte)15(xt)-279(fea-)]TJ -58.918 -11.955 Td [(tures)]TJ/F22 9.9626 Tf 23.27 0 Td [(K)]TJ/F67 9.9626 Tf 9.174 0 Td [(,)-427(the)-392(number)-392(of)-391(unique)-392(conte)15(xts)-392(to)-391(describe)-392(with)]TJ -32.444 -11.955 Td [(the)-351(test)-350(data)-351(increases)-351(e)15(xponential)1(ly)65(.)-612(Including)-351(more)-351(fea-)]TJ 0 -11.956 Td [(tures)-296(can)-295(lead)-296(to)-295(a)-296(more)-295(descripti)25(v)15(e)]TJ/F66 9.9626 Tf 146.37 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.402 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 9.953 -3.399 Td [(b)20(ut)-296(can)-295(also)-296(lead)]TJ -168.408 -11.956 Td [(to)-321(man)15(y)-322(untested)-321(conte)15(xts)-321(in)]TJ/F66 9.9626 Tf 119.755 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.402 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 7.008 -3.4 Td [(.)-524(T)80(o)-321(select)]TJ/F22 9.9626 Tf 47.069 0 Td [(K)]TJ/F67 9.9626 Tf 9.173 0 Td [(,)-339(we)-321(com-)]TJ -195.09 -11.955 Td [(pute)-302(the)-302(e)15(xpected)-303(prediction)-302(error)-302(for)-302(a)-302(gi)25(v)15(en)-303(subspace)-302(di-)]TJ 0 -11.955 Td [(mensionality)65(,)]TJ/F22 9.9626 Tf 57.282 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.494 Td [(.)-664(Using)-369(the)]TJ/F22 9.9626 Tf 52.421 0 Td [(K)]TJ/F67 9.9626 Tf 12.842 0 Td [(most)-368(informati)25(v)15(e)-368(conte)15(xt)]TJ -134.27 -11.955 Td [(features,)]TJ/F22 9.9626 Tf 37.871 0 Td [(g)]TJ/F19 9.9626 Tf 5.109 0 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.613 Td [(\))-480(=)]TJ/F22 9.9626 Tf 21.182 0 Td [(E)]TJ/F19 9.9626 Tf 7.929 0 Td [([)]TJ/F22 9.9626 Tf 2.767 0 Td [(l)]TJ/F19 9.9626 Tf 3.169 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(f)]TJ/F19 9.9626 Tf 5.95 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(X)]TJ/F19 9.9626 Tf 9.036 0 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(Y)]TJ/F25 9.9626 Tf 12.426 0 Td [(j)]TJ/F66 9.9626 Tf 2.767 0 Td [(c)]TJ/F21 6.9738 Tf 4.424 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.613 Td [(\)])]TJ/F67 9.9626 Tf 10.219 0 Td [(can)-359(be)-359(computed)]TJ -166.57 -11.955 Td [(according)-336(to)-336(Eqn.)-568(2.)-569(where)]TJ/F66 9.9626 Tf 118.753 0 Td [(c)]TJ/F21 6.9738 Tf 4.424 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F67 9.9626 Tf 10.357 -2.613 Td [(is)-336(a)]TJ/F22 9.9626 Tf 17.765 0 Td [(K)]TJ/F67 9.9626 Tf 12.522 0 Td [(dimensional)-336(fea-)]TJ -168.713 -11.956 Td [(ture)-313(v)15(ector)-312(in)]TJ/F66 9.9626 Tf 57.333 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.402 Td [(S)]TJ/F20 4.9813 Tf 4.893 -1.002 Td [(K)]TJ/F67 9.9626 Tf 7.008 -3.4 Td [(.)-498(W)80(e)-313(ite)1(rati)25(v)15(ely)-313(compute)-313(the)-312(prediction)]TJ -76.427 -11.955 Td [(error)-210(within)-209(the)-210(test)-209(set,)]TJ/F22 9.9626 Tf 94.913 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.494 Td [(,)-218(to)-209(estimate)-210(the)-209(e)15(xpected)-210(predic-)]TJ -106.638 -11.955 Td [(tion)-226(error)]TJ/F19 9.9626 Tf 39.453 0 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.494 Td [(,)-231(see)-226(Algorithm)-227(2.)-302(First,)-231(we)-226(randomly)-226(partition)]TJ -51.093 -11.955 Td [(the)-345(test)-346(set)-345(into)-345(a)]TJ/F22 9.9626 Tf 74.205 0 Td [(f)-108(it)]TJ/F67 9.9626 Tf 16.42 0 Td [(set)-345(and)-346(a)]TJ/F22 9.9626 Tf 40.198 0 Td [(v)-36(al)]TJ/F67 9.9626 Tf 17.061 0 Td [(set:)]TJ/F22 9.9626 Tf 18.825 0 Td [(X)]TJ/F21 6.9738 Tf 9.035 3.615 Td [(f)-112(it)]TJ/F67 9.9626 Tf 10.993 -3.615 Td [(,)]TJ/F22 9.9626 Tf 6.168 0 Td [(Y)]TJ/F21 6.9738 Tf 7.998 3.615 Td [(f)-112(it)]TJ/F67 9.9626 Tf 10.993 -3.615 Td [(,)]TJ/F66 9.9626 Tf 6.168 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(f)-112(it)]TJ/F67 9.9626 Tf -225.257 -16.356 Td [(with)]TJ/F22 9.9626 Tf 21.016 0 Td [(N)]TJ/F21 6.9738 Tf 9.091 3.615 Td [(f)-112(it)]TJ/F67 9.9626 Tf 14.296 -3.615 Td [(samples)-331(and)]TJ/F22 9.9626 Tf 53.09 0 Td [(X)]TJ/F21 6.9738 Tf 9.035 3.615 Td [(v)-36(al)]TJ/F67 9.9626 Tf 11.615 -3.615 Td [(,)]TJ/F22 9.9626 Tf 5.996 0 Td [(Y)]TJ/F21 6.9738 Tf 7.998 3.615 Td [(v)-36(al)]TJ/F67 9.9626 Tf 11.615 -3.615 Td [(,)]TJ/F66 9.9626 Tf 5.996 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(v)-36(al)]TJ/F67 9.9626 Tf 14.918 -4.401 Td [(with)]TJ/F22 9.9626 Tf 21.016 0 Td [(N)]TJ/F21 6.9738 Tf 9.091 3.615 Td [(v)-36(al)]TJ/F67 9.9626 Tf 14.917 -3.615 Td [(sam-)]TJ -216.883 -11.955 Td [(ples)-284(respecti)25(v)15(ely)65(.)-412(W)80(e)-284(estimate)]TJ/F22 9.9626 Tf 124.458 0 Td [(g)]TJ/F21 6.9738 Tf 5.109 3.615 Td [(f)-112(it)]TJ/F19 9.9626 Tf 10.993 -3.615 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.613 Td [(\))]TJ/F67 9.9626 Tf 6.703 0 Td [(using)-284(the)]TJ/F22 9.9626 Tf 39.42 0 Td [(f)-108(it)]TJ/F67 9.9626 Tf 15.809 0 Td [(set.)]TJ -222.691 -11.956 Td [(W)80(e)-307(compute)-307(the)-306(observ)15(ed)-307(loss)-307(from)-307(the)]TJ/F22 9.9626 Tf 163.771 0 Td [(v)-36(al)]TJ/F67 9.9626 Tf 16.679 0 Td [(set,)]TJ/F25 9.9626 Tf 16.757 0 Td [(L)]TJ/F21 6.9738 Tf 6.871 3.616 Td [(v)-36(al)]TJ/F67 9.9626 Tf 11.615 -3.616 Td [(.)-480(Let)]TJ/F22 9.9626 Tf -215.693 -11.955 Td [(p)]TJ/F21 6.9738 Tf 5.012 3.616 Td [(v)-36(al)]TJ/F19 9.9626 Tf 11.615 -3.616 Td [(\()]TJ/F66 9.9626 Tf 3.875 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.616 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.614 Td [(\))]TJ/F67 9.9626 Tf 6.976 0 Td [(indicate)-311(the)-312(probability)-311(of)-312(encountering)-311(conte)15(xt)]TJ/F66 9.9626 Tf -43.802 -11.955 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.001 Td [(K)]TJ/F67 9.9626 Tf 9.671 -2.614 Td [(in)]TJ/F66 9.9626 Tf 10.414 0 Td [(C)]TJ/F21 6.9738 Tf 7.193 4.401 Td [(v)-36(al)]TJ/F67 9.9626 Tf 11.614 -4.401 Td [(.)-362(The)-267(prediction)-267(error)40(,)]TJ/F22 9.9626 Tf 91.464 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.494 Td [(,)-272(is)-267(the)-267(dif)25(ference)-267(be-)]TJ -151.396 -11.955 Td [(tween)-278(the)-277(observ)15(ed)-278(v)25(alidation)-278(loss,)]TJ/F25 9.9626 Tf 143.274 0 Td [(L)]TJ/F21 6.9738 Tf 6.872 3.615 Td [(v)-36(al)]TJ/F67 9.9626 Tf 11.614 -3.615 Td [(,)-285(and)-277(the)-278(predicted)]TJ -161.76 -11.955 Td [(v)25(alidation)-318(loss)-317(using)]TJ/F22 9.9626 Tf 86.184 0 Td [(g)]TJ/F21 6.9738 Tf 5.11 3.615 Td [(f)-112(it)]TJ/F19 9.9626 Tf 10.993 -3.615 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.613 Td [(\))]TJ/F67 9.9626 Tf 3.874 0 Td [(.)-513(This)-318(procedure)-317(can)-318(be)-317(it-)]TJ -126.359 -11.955 Td [(erated)-245(multiple)-245(times,)-247(and)-245(the)-245(subsequent)]TJ/F22 9.9626 Tf 167.136 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.495 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.495 Td [(')55(s)-245(a)20(v)15(eraged,)-246(to)]TJ -178.861 -11.956 Td [(estimate)-222(the)-223(e)15(xpected)-222(prediction)-223(error)40(,)]TJ/F19 9.9626 Tf 153.707 0 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.494 Td [(,)-228(for)-222(dif)25(ferent)-223(ran-)]TJ -165.347 -11.955 Td [(dom)]TJ/F22 9.9626 Tf 20.525 0 Td [(f)-108(it)]TJ/F67 9.9626 Tf 15.791 0 Td [(and)]TJ/F22 9.9626 Tf 17.198 0 Td [(v)-36(al)]TJ/F67 9.9626 Tf 16.433 0 Td [(partitions)-282(of)-282(the)-283(test)-282(set.)-406(W)80(e)-283(select)-282(the)]TJ/F22 9.9626 Tf 157.129 0 Td [(K)]TJ/F67 9.9626 Tf -227.076 -11.955 Td [(that)-250(minimizes)]TJ/F19 9.9626 Tf 61.523 0 Td [(~)]TJ/F22 9.9626 Tf -0.084 0 Td [<0f>]TJ/F21 6.9738 Tf 4.043 -1.494 Td [(K)]TJ/F67 9.9626 Tf 7.681 1.494 Td [(.)]TJ/F19 9.9626 Tf -61.123 -12.535 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.495 Td [(K)]TJ/F67 9.9626 Tf 12.309 1.495 Td [(measures)-465(the)-464(e)15(xpected)-465(prediction)-464(error)-465(within)]TJ/F25 9.9626 Tf 197.493 0 Td [(T)]TJ/F67 9.9626 Tf 7.958 0 Td [(.)]TJ
0 g 0 G
0 g 0 G
ET
q
1 0 0 1 308.862 719.601 cm
[]0 d 0 J 0.797 w 0 0 m 236.25 0 l S
Q
BT
/F66 9.9626 Tf 308.862 710.346 Td [(Algorithm)-250(2)]TJ/F67 9.9626 Tf 54.236 0 Td [(Conte)15(xt)-250(Subspace)-250(Dimensionality)-250(Selection)]TJ
ET
q
1 0 0 1 308.862 705.998 cm
[]0 d 0 J 0.398 w 0 0 m 236.25 0 l S
Q
0 g 0 G
0 g 0 G
BT
/F67 7.9701 Tf 314.616 696.334 Td [(1:)]TJ
0 g 0 G
/F19 9.9626 Tf 11.267 0 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.495 Td [(K)]TJ/F19 9.9626 Tf 10.449 1.495 Td [(=)]TJ/F25 9.9626 Tf 10.516 0 Td [(fg)]TJ
0 g 0 G
/F67 7.9701 Tf -36.191 -11.955 Td [(2:)]TJ
0 g 0 G
/F66 9.9626 Tf 11.182 0 Td [(f)25(or)]TJ/F22 9.9626 Tf 17.455 0 Td [(K)]TJ/F19 9.9626 Tf 11.941 0 Td [(=)-278(1)-278(:)]TJ/F22 9.9626 Tf 23.8 0 Td [(J)]TJ/F66 9.9626 Tf 8.973 0 Td [(do)]TJ
0 g 0 G
/F67 7.9701 Tf -73.351 -11.955 Td [(3:)]TJ
0 g 0 G
/F22 9.9626 Tf 26.126 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.495 Td [(K)]TJ/F22 9.9626 Tf 7.681 1.495 Td [(s)]TJ/F19 9.9626 Tf 7.437 0 Td [(=)-278([])]TJ
0 g 0 G
/F67 7.9701 Tf -45.288 -11.956 Td [(4:)]TJ
0 g 0 G
/F66 9.9626 Tf 26.126 0 Td [(f)25(or)]TJ/F22 9.9626 Tf 14.964 0 Td [(iter)-28(ation)]TJ/F66 9.9626 Tf 42.036 0 Td [(do)]TJ
0 g 0 G
/F67 7.9701 Tf -83.126 -11.955 Td [(5:)]TJ
0 g 0 G
/F67 9.9626 Tf 41.07 0 Td [(split)-250(test)-250(set)-250(into)]TJ/F22 9.9626 Tf 67.536 0 Td [(f)-108(it)]TJ/F67 9.9626 Tf 15.47 0 Td [(and)]TJ/F22 9.9626 Tf 16.877 0 Td [(v)-36(al)]TJ/F67 9.9626 Tf 16.112 0 Td [(set)]TJ
0 g 0 G
/F67 7.9701 Tf -157.065 -11.955 Td [(6:)]TJ
0 g 0 G
/F22 9.9626 Tf 41.07 0 Td [(g)]TJ/F21 6.9738 Tf 5.11 3.615 Td [(f)-112(it)]TJ/F19 9.9626 Tf 10.993 -3.615 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.001 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.614 Td [(\))-278(=)]TJ/F22 9.9626 Tf 17.158 0 Td [(E)]TJ/F19 9.9626 Tf 7.928 0 Td [([)]TJ/F22 9.9626 Tf 2.768 0 Td [(l)]TJ/F19 9.9626 Tf 3.168 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(f)]TJ/F19 9.9626 Tf 5.95 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(X)]TJ/F21 6.9738 Tf 9.036 3.615 Td [(f)-112(it)]TJ/F19 9.9626 Tf 10.993 -3.615 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(;)-167(Y)]TJ/F21 6.9738 Tf 12.426 3.615 Td [(f)-112(it)]TJ/F25 9.9626 Tf 10.993 -3.615 Td [(j)]TJ/F66 9.9626 Tf 2.767 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.892 -1.001 Td [(K)]TJ/F19 9.9626 Tf 7.009 -2.614 Td [(\)])]TJ
0 g 0 G
/F67 7.9701 Tf -188.505 -14.962 Td [(7:)]TJ
0 g 0 G
/F25 9.9626 Tf 41.07 0 Td [(L)]TJ/F21 6.9738 Tf 6.872 3.616 Td [(v)-36(al)]TJ/F19 9.9626 Tf 14.382 -3.616 Td [(=)]TJ/F18 6.9738 Tf 18.517 3.923 Td [(1)]TJ
ET
q
1 0 0 1 388.651 624.087 cm
[]0 d 0 J 0.398 w 0 0 m 17.583 0 l S
Q
BT
/F21 6.9738 Tf 388.651 618.037 Td [(N)]TJ/F20 4.9813 Tf 7.059 1.993 Td [(v)-36(al)]TJ/F12 9.9626 Tf 13.38 9.038 Td [(P)]TJ/F21 6.9738 Tf 10.517 -2.463 Td [(N)]TJ/F20 4.9813 Tf 7.058 3.007 Td [(v)-36(al)]TJ/F21 6.9738 Tf -7.058 -11.005 Td [(i)]TJ/F18 6.9738 Tf 2.818 0 Td [(=1)]TJ/F22 9.9626 Tf 16.923 2.989 Td [(l)]TJ/F19 9.9626 Tf 3.169 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [(f)]TJ/F19 9.9626 Tf 5.95 0 Td [(\()]TJ/F22 9.9626 Tf 3.875 0 Td [(x)]TJ/F21 6.9738 Tf 5.694 3.616 Td [(v)-36(al)]TJ 0 -6.209 Td [(i)]TJ/F19 9.9626 Tf 11.614 2.593 Td [(\))]TJ/F22 9.9626 Tf 3.875 0 Td [(;)-167(y)]TJ/F21 6.9738 Tf 9.669 3.616 Td [(v)-36(al)]TJ -0.357 -6.209 Td [(i)]TJ/F19 9.9626 Tf 11.972 2.593 Td [(\))]TJ
0 g 0 G
/F67 7.9701 Tf -184.067 -14.185 Td [(8:)]TJ
0 g 0 G
/F22 9.9626 Tf 41.07 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.495 Td [(K)]TJ/F19 9.9626 Tf 10.448 1.495 Td [(=)]TJ/F25 9.9626 Tf 10.517 0 Td [(jL)]TJ/F21 6.9738 Tf 9.638 3.615 Td [(v)-36(al)]TJ/F25 9.9626 Tf 13.14 -3.615 Td [<00>]TJ/F12 9.9626 Tf 9.274 7.472 Td [(P)]TJ/F66 6.9738 Tf 10.516 -10.461 Td [(c)]TJ/F20 4.9813 Tf 3.097 2.439 Td [(S)]TJ 4.265 -1.689 Td [(K)]TJ/F24 6.9738 Tf 7.008 -0.75 Td [(2)]TJ/F66 6.9738 Tf 5.369 0 Td [(C)]TJ/F20 4.9813 Tf 5.035 2.439 Td [(S)]TJ 4.266 -1.689 Td [(K)]TJ/F22 9.9626 Tf 9.167 2.239 Td [(p)]TJ/F21 6.9738 Tf 5.012 3.615 Td [(v)-36(al)]TJ/F19 9.9626 Tf 11.615 -3.615 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.893 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.613 Td [(\))]TJ/F22 9.9626 Tf 3.874 0 Td [(g)]TJ/F21 6.9738 Tf 5.11 4.787 Td [(f)-112(it)]TJ -0.358 -7.793 Td [(k)]TJ/F19 9.9626 Tf 11.351 3.006 Td [(\()]TJ/F66 9.9626 Tf 3.874 0 Td [(c)]TJ/F21 6.9738 Tf 4.423 3.615 Td [(S)]TJ/F20 4.9813 Tf 4.893 -1.002 Td [(K)]TJ/F19 9.9626 Tf 7.008 -2.613 Td [(\))]TJ/F25 9.9626 Tf 3.874 0 Td [(j)]TJ
0 g 0 G
/F67 7.9701 Tf -227.728 -11.956 Td [(9:)]TJ
0 g 0 G
/F22 9.9626 Tf 41.07 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F22 9.9626 Tf 7.681 1.494 Td [(s:append)]TJ/F19 9.9626 Tf 38.533 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F19 9.9626 Tf 7.681 1.494 Td [(\))]TJ
0 g 0 G
/F67 7.9701 Tf -110.912 -11.955 Td [(10:)]TJ
0 g 0 G
/F66 9.9626 Tf 30.111 0 Td [(end)-250(f)25(or)]TJ
0 g 0 G
/F67 7.9701 Tf -30.111 -11.955 Td [(11:)]TJ
0 g 0 G
/F19 9.9626 Tf 30.196 0 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F19 9.9626 Tf 10.448 1.494 Td [(=)]TJ/F22 9.9626 Tf 10.516 0 Td [(mean)]TJ/F19 9.9626 Tf 24.633 0 Td [(\()]TJ/F22 9.9626 Tf 3.874 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F22 9.9626 Tf 7.681 1.494 Td [(s)]TJ/F19 9.9626 Tf 4.67 0 Td [(\))]TJ
0 g 0 G
/F67 7.9701 Tf -100.021 -11.955 Td [(12:)]TJ
0 g 0 G
/F66 9.9626 Tf 15.167 0 Td [(end)-250(f)25(or)]TJ
0 g 0 G
/F67 7.9701 Tf -15.167 -11.955 Td [(13:)]TJ
0 g 0 G
/F22 9.9626 Tf 15.167 0 Td [(K)]TJ/F25 9.9626 Tf 11.942 0 Td [( )]TJ/F22 9.9626 Tf 12.73 0 Td [(ar)-28(g)-36(min)]TJ/F21 6.9738 Tf 33.306 -1.495 Td [(K)]TJ/F19 9.9626 Tf 17.728 1.495 Td [(~)]TJ/F22 9.9626 Tf -0.084 0 Td [<0f>]TJ/F21 6.9738 Tf 4.043 -1.495 Td [(K)]TJ
0 g 0 G
ET
q
1 0 0 1 308.862 541.513 cm
[]0 d 0 J 0.398 w 0 0 m 236.25 0 l S
Q
BT
/F67 9.9626 Tf 308.862 511.427 Td [(When)-461(the)-461(conte)15(xt)-462(is)-461(informati)25(v)15(e)-461(about)-461(the)-461(loss,)-514(we)-462(e)15(x-)]TJ 0 -11.955 Td [(pect)]TJ/F19 9.9626 Tf 19.717 0 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 10.716 1.494 Td [(to)-305(decrease)-304(as)]TJ/F22 9.9626 Tf 59.444 0 Td [(K)]TJ/F67 9.9626 Tf 12.208 0 Td [(increases)-305(until)-304(an)-305(optimal)]TJ/F22 9.9626 Tf 106.773 0 Td [(K)]TJ/F24 6.9738 Tf 9.173 3.616 Td [<03>]TJ/F67 9.9626 Tf 7.615 -3.616 Td [(is)]TJ -229.605 -11.955 Td [(reached,)-240(then)]TJ/F19 9.9626 Tf 55.452 0 Td [(~)]TJ/F22 9.9626 Tf -0.085 0 Td [<0f>]TJ/F21 6.9738 Tf 4.044 -1.494 Td [(K)]TJ/F67 9.9626 Tf 10.042 1.494 Td [(will)-237(be)15(gin)-237(to)-237(rise)-237(as)]TJ/F22 9.9626 Tf 79.727 0 Td [(K)]TJ/F67 9.9626 Tf 11.535 0 Td [(increases)-237(and)-237(there)]TJ -160.715 -11.955 Td [(are)-257(man)15(y)-257(untested)-257(conte)15(xts.)-331(If)]TJ/F19 9.9626 Tf 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