File size: 128,196 Bytes
6fa4bc9 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146 2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204 2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262 2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 2321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 2410 2411 2412 2413 2414 2415 2416 2417 2418 2419 2420 2421 2422 2423 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436 2437 2438 2439 2440 2441 2442 2443 2444 2445 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 | {
"paper_id": "D08-1017",
"header": {
"generated_with": "S2ORC 1.0.0",
"date_generated": "2023-01-19T16:30:48.391483Z"
},
"title": "Stacking Dependency Parsers",
"authors": [
{
"first": "Andr\u00e9",
"middle": [
"F T"
],
"last": "Martins",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "Carnegie Mellon University",
"location": {
"postCode": "15213",
"settlement": "Pittsburgh",
"region": "PA",
"country": "USA"
}
},
"email": ""
},
{
"first": "Dipanjan",
"middle": [],
"last": "Das",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "Carnegie Mellon University",
"location": {
"postCode": "15213",
"settlement": "Pittsburgh",
"region": "PA",
"country": "USA"
}
},
"email": "dipanjan@cs.cmu.edu"
},
{
"first": "Noah",
"middle": [
"A"
],
"last": "Smith",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "Carnegie Mellon University",
"location": {
"postCode": "15213",
"settlement": "Pittsburgh",
"region": "PA",
"country": "USA"
}
},
"email": "nasmith@cs.cmu.edu"
},
{
"first": "Eric",
"middle": [
"P"
],
"last": "Xing",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "Carnegie Mellon University",
"location": {
"postCode": "15213",
"settlement": "Pittsburgh",
"region": "PA",
"country": "USA"
}
},
"email": "epxing@cs.cmu.edu"
}
],
"year": "",
"venue": null,
"identifiers": {},
"abstract": "We explore a stacked framework for learning to predict dependency structures for natural language sentences. A typical approach in graph-based dependency parsing has been to assume a factorized model, where local features are used but a global function is optimized (McDonald et al., 2005b). Recently Nivre and McDonald (2008) used the output of one dependency parser to provide features for another. We show that this is an example of stacked learning, in which a second predictor is trained to improve the performance of the first. Further, we argue that this technique is a novel way of approximating rich non-local features in the second parser, without sacrificing efficient, model-optimal prediction. Experiments on twelve languages show that stacking transition-based and graphbased parsers improves performance over existing state-of-the-art dependency parsers.",
"pdf_parse": {
"paper_id": "D08-1017",
"_pdf_hash": "",
"abstract": [
{
"text": "We explore a stacked framework for learning to predict dependency structures for natural language sentences. A typical approach in graph-based dependency parsing has been to assume a factorized model, where local features are used but a global function is optimized (McDonald et al., 2005b). Recently Nivre and McDonald (2008) used the output of one dependency parser to provide features for another. We show that this is an example of stacked learning, in which a second predictor is trained to improve the performance of the first. Further, we argue that this technique is a novel way of approximating rich non-local features in the second parser, without sacrificing efficient, model-optimal prediction. Experiments on twelve languages show that stacking transition-based and graphbased parsers improves performance over existing state-of-the-art dependency parsers.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Abstract",
"sec_num": null
}
],
"body_text": [
{
"text": "In this paper we address a representation-efficiency tradeoff in statistical natural language processing through the use of stacked learning (Wolpert, 1992) . This tradeoff is exemplified in dependency parsing, illustrated in Fig. 1 , on which we focus in this paper:",
"cite_spans": [
{
"start": 141,
"end": 156,
"text": "(Wolpert, 1992)",
"ref_id": "BIBREF31"
}
],
"ref_spans": [
{
"start": 226,
"end": 232,
"text": "Fig. 1",
"ref_id": "FIGREF0"
}
],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "\u2022 Exact algorithms for dependency parsing (Eisner and Satta, 1999; McDonald et al., 2005b) are tractable only when the model makes very strong, linguistically unsupportable independence assumptions, such as \"arc factorization\" for nonprojective dependency parsing (McDonald and Satta, 2007) .",
"cite_spans": [
{
"start": 42,
"end": 66,
"text": "(Eisner and Satta, 1999;",
"ref_id": "BIBREF10"
},
{
"start": 67,
"end": 90,
"text": "McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 264,
"end": 290,
"text": "(McDonald and Satta, 2007)",
"ref_id": "BIBREF18"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "\u2022 Feature-rich parsers must resort to search or greediness, (Ratnaparkhi et al., 1994; Sagae and Lavie, 2005; , so that parsing solutions are inexact and learned models may be subject to certain kinds of bias (Lafferty et al., 2001) .",
"cite_spans": [
{
"start": 60,
"end": 86,
"text": "(Ratnaparkhi et al., 1994;",
"ref_id": "BIBREF25"
},
{
"start": 87,
"end": 109,
"text": "Sagae and Lavie, 2005;",
"ref_id": "BIBREF27"
},
{
"start": 209,
"end": 232,
"text": "(Lafferty et al., 2001)",
"ref_id": "BIBREF14"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "A solution that leverages the complementary strengths of these two approaches-described in detail by McDonald and Nivre (2007) -was recently and successfully explored by Nivre and McDonald (2008) . Our contribution begins by reinterpreting and generalizing their parser combination scheme as a stacking of parsers.",
"cite_spans": [
{
"start": 101,
"end": 126,
"text": "McDonald and Nivre (2007)",
"ref_id": "BIBREF16"
},
{
"start": 170,
"end": 195,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "We give a new theoretical motivation for stacking parsers, in terms of extending a parsing model's feature space. Specifically, we view stacked learning as a way of approximating non-local features in a linear model, rather than making empirically dubious independence (McDonald et al., 2005b) or structural assumptions (e.g., projectivity, Eisner, 1996) , using search approximations (Sagae and Lavie, 2005; , solving a (generally NP-hard) integer linear program (Riedel and Clarke, 2006) , or adding latent variables (Titov and Henderson, 2007) . Notably, we introduce the use of very rich non-local approximate features in one parser, through the output of another parser. Related approaches are the belief propagation algorithm of Smith and Eisner (2008) , and the \"trading of structure for features\" explored by Liang et al. those that assume each dependency decision is independent modulo the global structural constraint that dependency graphs must be trees. Such models are commonly referred to as edge-factored since their parameters factor relative to individual edges of the graph (Paskin, 2001; McDonald et al., 2005a) . Edge-factored models have many computational benefits, most notably that inference for nonprojective dependency graphs can be achieved in polynomial time (McDonald et al., 2005b) . The primary problem in treating each dependency as independent is that it is not a realistic assumption. Non-local information, such as arity (or valency) and neighbouring dependencies, can be crucial to obtaining high parsing accuracies (Klein and Manning, 2002; . However, in the data-driven parsing setting this can be partially adverted by incorporating rich feature representations over the input (McDonald et al., 2005a) .",
"cite_spans": [
{
"start": 269,
"end": 293,
"text": "(McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 341,
"end": 354,
"text": "Eisner, 1996)",
"ref_id": "BIBREF11"
},
{
"start": 385,
"end": 408,
"text": "(Sagae and Lavie, 2005;",
"ref_id": "BIBREF27"
},
{
"start": 464,
"end": 489,
"text": "(Riedel and Clarke, 2006)",
"ref_id": "BIBREF26"
},
{
"start": 519,
"end": 546,
"text": "(Titov and Henderson, 2007)",
"ref_id": "BIBREF29"
},
{
"start": 735,
"end": 758,
"text": "Smith and Eisner (2008)",
"ref_id": "BIBREF28"
},
{
"start": 1092,
"end": 1106,
"text": "(Paskin, 2001;",
"ref_id": null
},
{
"start": 1107,
"end": 1130,
"text": "McDonald et al., 2005a)",
"ref_id": "BIBREF19"
},
{
"start": 1287,
"end": 1311,
"text": "(McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 1456,
"end": 1468,
"text": "(or valency)",
"ref_id": null
},
{
"start": 1552,
"end": 1577,
"text": "(Klein and Manning, 2002;",
"ref_id": null
},
{
"start": 1716,
"end": 1740,
"text": "(McDonald et al., 2005a)",
"ref_id": "BIBREF19"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "The goal of this work is to further our current understanding of the computational nature of nonprojective parsing algorithms for both learning and inference within the data-driven setting. We start by investigating and extending the edge-factored model of McDonald et al. (2005b) . In particular, we appeal to the Matrix Tree Theorem for multi-digraphs to design polynomial-time algorithms for calculating both the partition function and edge expectations over all possible dependency graphs for a given sentence. To motivate these algorithms, we show that they can be used in many important learning and inference problems including min-risk decoding, training globally normalized log-linear models, syntactic language modeling, and unsupervised learning via the EM algorithm -none of which have previously been known to have exact non-projective implementations.",
"cite_spans": [
{
"start": 257,
"end": 280,
"text": "McDonald et al. (2005b)",
"ref_id": "BIBREF20"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "We then switch focus to models that account for non-local information, in particular arity and neighbouring parse decisions. For systems that model arity constraints we give a reduction from the Hamiltonian graph problem suggesting that the parsing problem is intractable in this case. For neighbouring parse decisions, we extend the work of and show that modeling vertical neighbourhoods makes parsing intractable in addition to modeling horizontal neighbourhoods. A consequence of these results is that it is unlikely that exact non-projective dependency parsing is tractable for any model assumptions weaker than those made by the edge-factored models.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "There has been extensive work on data-driven dependency parsing for both projective parsing (Eisner, 1996; Paskin, 2001; Yamada and Matsumoto, 2003; Nivre and Scholz, 2004; McDonald et al., 2005a) and non-projective parsing systems (Nivre and Nilsson, 2005; Hall and N\u00f3v\u00e1k, 2005; McDonald et al., 2005b) . These approaches can often be classified into two broad categories. In the first category are those methods that employ approximate inference, typically through the use of linear time shift-reduce parsing algorithms (Yamada and Matsumoto, 2003; Nivre and Scholz, 2004; Nivre and Nilsson, 2005) . In the second category are those that employ exhaustive inference algorithms, usually by making strong independence assumptions, as is the case for edge-factored models (Paskin, 2001; McDonald et al., 2005a; McDonald et al., 2005b) . Recently there have also been proposals for exhaustive methods that weaken the edge-factored assumption, including both approximate methods and exact methods through integer linear programming (Riedel and Clarke, 2006) or branch-and-bound algorithms (Hirakawa, 2006) .",
"cite_spans": [
{
"start": 92,
"end": 106,
"text": "(Eisner, 1996;",
"ref_id": "BIBREF11"
},
{
"start": 107,
"end": 120,
"text": "Paskin, 2001;",
"ref_id": null
},
{
"start": 121,
"end": 148,
"text": "Yamada and Matsumoto, 2003;",
"ref_id": "BIBREF32"
},
{
"start": 149,
"end": 172,
"text": "Nivre and Scholz, 2004;",
"ref_id": null
},
{
"start": 173,
"end": 196,
"text": "McDonald et al., 2005a)",
"ref_id": "BIBREF19"
},
{
"start": 232,
"end": 257,
"text": "(Nivre and Nilsson, 2005;",
"ref_id": null
},
{
"start": 258,
"end": 279,
"text": "Hall and N\u00f3v\u00e1k, 2005;",
"ref_id": null
},
{
"start": 280,
"end": 303,
"text": "McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 522,
"end": 550,
"text": "(Yamada and Matsumoto, 2003;",
"ref_id": "BIBREF32"
},
{
"start": 551,
"end": 574,
"text": "Nivre and Scholz, 2004;",
"ref_id": null
},
{
"start": 575,
"end": 599,
"text": "Nivre and Nilsson, 2005)",
"ref_id": null
},
{
"start": 771,
"end": 785,
"text": "(Paskin, 2001;",
"ref_id": null
},
{
"start": 786,
"end": 809,
"text": "McDonald et al., 2005a;",
"ref_id": "BIBREF19"
},
{
"start": 810,
"end": 833,
"text": "McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 1029,
"end": 1054,
"text": "(Riedel and Clarke, 2006)",
"ref_id": "BIBREF26"
},
{
"start": 1086,
"end": 1102,
"text": "(Hirakawa, 2006)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "For grammar based models there has been limited work on empirical systems for non-projective parsing systems, notable exceptions include the work of Wang and Harper (2004) . Theoretical studies of note include the work of Neuhaus and B\u00f6ker (1997) showing that the recognition problem for a mini- those that assume each dependency decision is independent modulo the global structural constraint that dependency graphs must be trees. Such models are commonly referred to as edge-factored since their parameters factor relative to individual edges of the graph (Paskin, 2001; McDonald et al., 2005a) . Edge-factored models have many computational benefits, most notably that inference for nonprojective dependency graphs can be achieved in polynomial time (McDonald et al., 2005b) . The primary problem in treating each dependency as independent is that it is not a realistic assumption. Non-local information, such as arity (or valency) and neighbouring dependencies, can be crucial to obtaining high parsing accuracies (Klein and Manning, 2002; . However, in the data-driven parsing setting this can be partially adverted by incorporating rich feature representations over the input (McDonald et al., 2005a) .",
"cite_spans": [
{
"start": 149,
"end": 171,
"text": "Wang and Harper (2004)",
"ref_id": null
},
{
"start": 222,
"end": 246,
"text": "Neuhaus and B\u00f6ker (1997)",
"ref_id": null
},
{
"start": 558,
"end": 572,
"text": "(Paskin, 2001;",
"ref_id": null
},
{
"start": 573,
"end": 596,
"text": "McDonald et al., 2005a)",
"ref_id": "BIBREF19"
},
{
"start": 753,
"end": 777,
"text": "(McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 1018,
"end": 1043,
"text": "(Klein and Manning, 2002;",
"ref_id": null
},
{
"start": 1182,
"end": 1206,
"text": "(McDonald et al., 2005a)",
"ref_id": "BIBREF19"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "The goal of this work is to further our current understanding of the computational nature of nonprojective parsing algorithms for both learning and inference within the data-driven setting. We start by investigating and extending the edge-factored model of McDonald et al. (2005b) . In particular, we appeal to the Matrix Tree Theorem for multi-digraphs to design polynomial-time algorithms for calculating both the partition function and edge expectations over all possible dependency graphs for a given sentence. To motivate these algorithms, we show that they can be used in many important learning and inference problems including min-risk decoding, training globally normalized log-linear models, syntactic language modeling, and unsupervised learning via the EM algorithm -none of which have previously been known to have exact non-projective implementations.",
"cite_spans": [
{
"start": 257,
"end": 280,
"text": "McDonald et al. (2005b)",
"ref_id": "BIBREF20"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "We then switch focus to models that account for non-local information, in particular arity and neighbouring parse decisions. For systems that model arity constraints we give a reduction from the Hamiltonian graph problem suggesting that the parsing problem is intractable in this case. For neighbouring parse decisions, we extend the work of and show that modeling vertical neighbourhoods makes parsing intractable in addition to modeling horizontal neighbourhoods. A consequence of these results is that it is unlikely that exact non-projective dependency parsing is tractable for any model assumptions weaker than those made by the edge-factored models.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "There has been extensive work on data-driven dependency parsing for both projective parsing (Eisner, 1996; Paskin, 2001; Yamada and Matsumoto, 2003; Nivre and Scholz, 2004; McDonald et al., 2005a) and non-projective parsing systems (Nivre and Nilsson, 2005; Hall and N\u00f3v\u00e1k, 2005; McDonald et al., 2005b) . These approaches can often be classified into two broad categories. In the first category are those methods that employ approximate inference, typically through the use of linear time shift-reduce parsing algorithms (Yamada and Matsumoto, 2003; Nivre and Scholz, 2004; Nivre and Nilsson, 2005) . In the second category are those that employ exhaustive inference algorithms, usually by making strong independence assumptions, as is the case for edge-factored models (Paskin, 2001; McDonald et al., 2005a; McDonald et al., 2005b) . Recently there have also been proposals for exhaustive methods that weaken the edge-factored assumption, including both approximate methods and exact methods through integer linear programming (Riedel and Clarke, 2006) or branch-and-bound algorithms (Hirakawa, 2006) .",
"cite_spans": [
{
"start": 92,
"end": 106,
"text": "(Eisner, 1996;",
"ref_id": "BIBREF11"
},
{
"start": 107,
"end": 120,
"text": "Paskin, 2001;",
"ref_id": null
},
{
"start": 121,
"end": 148,
"text": "Yamada and Matsumoto, 2003;",
"ref_id": "BIBREF32"
},
{
"start": 149,
"end": 172,
"text": "Nivre and Scholz, 2004;",
"ref_id": null
},
{
"start": 173,
"end": 196,
"text": "McDonald et al., 2005a)",
"ref_id": "BIBREF19"
},
{
"start": 232,
"end": 257,
"text": "(Nivre and Nilsson, 2005;",
"ref_id": null
},
{
"start": 258,
"end": 279,
"text": "Hall and N\u00f3v\u00e1k, 2005;",
"ref_id": null
},
{
"start": 280,
"end": 303,
"text": "McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 522,
"end": 550,
"text": "(Yamada and Matsumoto, 2003;",
"ref_id": "BIBREF32"
},
{
"start": 551,
"end": 574,
"text": "Nivre and Scholz, 2004;",
"ref_id": null
},
{
"start": 575,
"end": 599,
"text": "Nivre and Nilsson, 2005)",
"ref_id": null
},
{
"start": 771,
"end": 785,
"text": "(Paskin, 2001;",
"ref_id": null
},
{
"start": 786,
"end": 809,
"text": "McDonald et al., 2005a;",
"ref_id": "BIBREF19"
},
{
"start": 810,
"end": 833,
"text": "McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 1029,
"end": 1054,
"text": "(Riedel and Clarke, 2006)",
"ref_id": "BIBREF26"
},
{
"start": 1086,
"end": 1102,
"text": "(Hirakawa, 2006)",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "For grammar based models there has been limited work on empirical systems for non-projective parsing systems, notable exceptions include the work of Wang and Harper (2004) . Theoretical studies of note include the work of Neuhaus and B\u00f6ker (1997) showing that the recognition problem for a mini- This paper focuses on dependency parsing, which has become widely used in relation extraction (Culotta and Sorensen, 2004), machine translation (Ding and Palmer, 2005) , question answering (Wang et al., 2007) , and many other NLP applications. We show that stacking methods outperform the approximate \"second-order\" parser of on twelve languages and can be used within that approximation to achieve even better results. These results are similar in spirit to (Nivre and McDonald, 2008) , but with the following novel contributions:",
"cite_spans": [
{
"start": 149,
"end": 171,
"text": "Wang and Harper (2004)",
"ref_id": null
},
{
"start": 222,
"end": 246,
"text": "Neuhaus and B\u00f6ker (1997)",
"ref_id": null
},
{
"start": 440,
"end": 463,
"text": "(Ding and Palmer, 2005)",
"ref_id": "BIBREF8"
},
{
"start": 485,
"end": 504,
"text": "(Wang et al., 2007)",
"ref_id": "BIBREF30"
},
{
"start": 755,
"end": 781,
"text": "(Nivre and McDonald, 2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "\u2022 a stacking interpretation,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "\u2022 a richer feature set that includes non-local features (shown here to improve performance), and",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "\u2022 a variety of stacking architectures.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "Using stacking with rich features, we obtain results competitive with Nivre and McDonald (2008) while preserving the fast quadratic parsing time of arcfactored spanning tree algorithms. The paper is organized as follows. We discuss related prior work on dependency parsing and stacking in \u00a72. Our model is given in \u00a73. A novel analysis of stacking in linear models is given in \u00a74. Experiments are presented in \u00a75.",
"cite_spans": [
{
"start": 70,
"end": 95,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Related Work",
"sec_num": "1.1"
},
{
"text": "We briefly review work on the NLP task of dependency parsing and the machine learning framework known as stacked learning.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Background and Related Work",
"sec_num": "2"
},
{
"text": "Dependency syntax is a lightweight syntactic representation that models a sentence as a graph where the words are vertices and syntactic relationships are directed edges (arcs) connecting heads to their arguments and modifiers.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Dependency Parsing",
"sec_num": "2.1"
},
{
"text": "Dependency parsing is often viewed computationally as a structured prediction problem: for each input sentence x, with n words, exponentially many candidate dependency trees y \u2208 Y(x) are possible in principle. We denote each tree by its set of vertices and directed arcs, y = (V y , A y ). A legal dependency tree has n + 1 vertices, each corresponding to one word plus a \"wall\" symbol, $, assumed to be the hidden root of the sentence. In a valid dependency tree, each vertex except the root has exactly one parent. In the projective case, arcs cannot cross when depicted on one side of the sentence; in the nonprojective case, this constraint is not imposed (see Fig. 1 ).",
"cite_spans": [],
"ref_spans": [
{
"start": 665,
"end": 671,
"text": "Fig. 1",
"ref_id": "FIGREF0"
}
],
"eq_spans": [],
"section": "Dependency Parsing",
"sec_num": "2.1"
},
{
"text": "Most recent work on dependency parsing can be categorized as graph-based or transition-based. In graph-based parsing, dependency trees are scored by factoring the tree into its arcs, and parsing is performed by searching for the highest scoring tree (Eisner, 1996; McDonald et al., 2005b) . Transitionbased parsers model the sequence of decisions of a shift-reduce parser, given previous decisions and current state, and parsing is performed by greedily choosing the highest scoring transition out of each successive parsing state or by searching for the best sequence of transitions (Ratnaparkhi et al., 1994; Yamada and Matsumoto, 2003; Nivre et al., 2004; Sagae and Lavie, 2005; .",
"cite_spans": [
{
"start": 250,
"end": 264,
"text": "(Eisner, 1996;",
"ref_id": "BIBREF11"
},
{
"start": 265,
"end": 288,
"text": "McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 584,
"end": 610,
"text": "(Ratnaparkhi et al., 1994;",
"ref_id": "BIBREF25"
},
{
"start": 611,
"end": 638,
"text": "Yamada and Matsumoto, 2003;",
"ref_id": "BIBREF32"
},
{
"start": 639,
"end": 658,
"text": "Nivre et al., 2004;",
"ref_id": "BIBREF23"
},
{
"start": 659,
"end": 681,
"text": "Sagae and Lavie, 2005;",
"ref_id": "BIBREF27"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Graph-based vs. transition-based models",
"sec_num": "2.1.1"
},
{
"text": "Both approaches most commonly use linear models to assign scores to arcs or decisions, so that a score is a dot-product of a feature vector f and a learned weight vector w.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Graph-based vs. transition-based models",
"sec_num": "2.1.1"
},
{
"text": "In sum, these two lines of research use different approximations to achieve tractability. Transitionbased approaches solve a sequence of local problems in sequence, sacrificing global optimality guarantees and possibly expressive power (Abney et al., 1999) . Graph-based methods perform global inference using score factorizations that correspond to strong independence assumptions (discussed in \u00a72.1.2). Recently, Nivre and McDonald (2008) proposed combining a graph-based and a transitionbased parser and have shown a significant improvement for several languages by letting one of the parsers \"guide\" the other. Our stacked formalism (to be described in \u00a73) generalizes this approach.",
"cite_spans": [
{
"start": 236,
"end": 256,
"text": "(Abney et al., 1999)",
"ref_id": "BIBREF0"
},
{
"start": 415,
"end": 440,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Graph-based vs. transition-based models",
"sec_num": "2.1.1"
},
{
"text": "In the successful graph-based method of McDonald et al. (2005b) , an arc factorization independence assumption is used to ensure tractability. This assumption forbids any feature that depends on two or more arcs, permitting only \"arc-factored\" features (i.e. features that depend only on a single candidate arc a \u2208 A y and on the input sequence x). This induces a decomposition of the feature vector f (x, y) as:",
"cite_spans": [
{
"start": 40,
"end": 63,
"text": "McDonald et al. (2005b)",
"ref_id": "BIBREF20"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Arc factorization",
"sec_num": "2.1.2"
},
{
"text": "f (x, y) = a\u2208Ay f a (x).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Arc factorization",
"sec_num": "2.1.2"
},
{
"text": "Parsing amounts to solving arg max y\u2208Y(x) w f (x, y), where w is a weight vector. With a projectivity constraint and arc factorization, the parsing problem can be solved in cubic time by dynamic programming (Eisner, 1996) , and with a weaker \"tree\" constraint (permitting nonprojective parses) and arc factorization, a quadratic-time algorithm exists (Chu and Liu, 1965; Edmonds, 1967) , as shown by McDonald et al. (2005b) . In the projective case, the arc-factored assumption can be weakened in certain ways while maintaining polynomial parser runtime (Eisner and Satta, 1999) , but not in the nonprojective case (McDonald and Satta, 2007) , where finding the highest-scoring tree becomes NP-hard. adopted an approximation based on O(n 3 ) projective parsing followed by rearrangement to permit crossing arcs, achieving higher performance. In \u00a73 we adopt a framework that maintains O(n 2 ) runtime (still exploiting the Chu-Liu-Edmonds algorithm) while approximating non arc-factored features.",
"cite_spans": [
{
"start": 207,
"end": 221,
"text": "(Eisner, 1996)",
"ref_id": "BIBREF11"
},
{
"start": 351,
"end": 370,
"text": "(Chu and Liu, 1965;",
"ref_id": "BIBREF5"
},
{
"start": 371,
"end": 385,
"text": "Edmonds, 1967)",
"ref_id": "BIBREF9"
},
{
"start": 400,
"end": 423,
"text": "McDonald et al. (2005b)",
"ref_id": "BIBREF20"
},
{
"start": 554,
"end": 578,
"text": "(Eisner and Satta, 1999)",
"ref_id": "BIBREF10"
},
{
"start": 615,
"end": 641,
"text": "(McDonald and Satta, 2007)",
"ref_id": "BIBREF18"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Arc factorization",
"sec_num": "2.1.2"
},
{
"text": "Stacked generalization was first proposed by Wolpert (1992) and Breiman (1996) for regression. The idea is to include two \"levels\" of predictors. The first level, \"level 0,\" includes one or more predictors g 1 , . . . , g K :",
"cite_spans": [
{
"start": 45,
"end": 59,
"text": "Wolpert (1992)",
"ref_id": "BIBREF31"
},
{
"start": 64,
"end": 78,
"text": "Breiman (1996)",
"ref_id": "BIBREF2"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "R d \u2192 R; each receives input x \u2208 R d",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "and outputs a prediction g k (x). The second level, \"level 1,\" consists of a single function h :",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "R d+K \u2192 R that takes as input x, g 1 (x), . . . g K (x) and out- puts a final prediction\u0177 = h(x, g 1 (x), . . . g K (x)).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "The predictor, then, combines an ensemble (the g k ) with a meta-predictor (h).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "Training is done as follows: the training data are split into L partitions, and L instances of the level 0 predictor are trained in a \"leave-one-out\" basis. Then, an augmented dataset is formed by letting each instance output predictions for the partition that was left out. Finally, each level 0 predictor is trained using the original dataset, and the level 1 predictor is trained on the augmented dataset, simulating the test-time setting when h is applied to a new instance x concatenated with g k (x) k .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "This framework has also been applied to classification, for example with structured data. Some applications (including here) use only one classifier at level 0; recent work includes sequence labeling (Cohen and de Carvalho, 2005) and inference in conditional random fields (Kou and Cohen, 2007) . Stacking is also intuitively related to transformation-based learning (Brill, 1993) .",
"cite_spans": [
{
"start": 273,
"end": 294,
"text": "(Kou and Cohen, 2007)",
"ref_id": "BIBREF13"
},
{
"start": 367,
"end": 380,
"text": "(Brill, 1993)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Learning",
"sec_num": "2.2"
},
{
"text": "We next describe how to use stacked learning for efficient, rich-featured dependency parsing.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Stacked Dependency Parsing",
"sec_num": "3"
},
{
"text": "The architecture consists of two levels. At level 0 we include a single dependency parser. At runtime, this \"level 0 parser\" g processes an input sentence x and outputs the set of predicted edges that make up its estimation of the dependency tree,\u0177 0 = g(x). At level 1, we apply a dependency parser-in this work, always a graph-based dependency parser-that uses basic factored features plus new ones from the edges predicted by the level 0 parser. The final parser predicts parse trees as h(x, g(x)), so that the total runtime is additive in calculating h(\u2022) and g(\u2022).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Architecture",
"sec_num": "3.1"
},
{
"text": "The stacking framework is agnostic about the form of g and h and the methods used to learn them from data. In this work we use two well-known, publicly available dependency parsers, MSTParser (McDonald et al., 2005b) , 1 which implements ex-act first-order arc-factored nonprojective parsing ( \u00a72.1.2) and approximate second-order nonprojective parsing, and MaltParser , which is a state-of-the-art transition-based parser. 2 We do not alter the training algorithms used in prior work for learning these two parsers from data. Using the existing parsers as starting points, we will combine them in a variety of ways.",
"cite_spans": [
{
"start": 192,
"end": 216,
"text": "(McDonald et al., 2005b)",
"ref_id": "BIBREF20"
},
{
"start": 424,
"end": 425,
"text": "2",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Architecture",
"sec_num": "3.1"
},
{
"text": "Regardless of our choices for the specific parsers and learning algorithms at level 0 and level 1, training is done as sketched in \u00a72.2. Let D be a set of training examples ",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Training",
"sec_num": "3.2"
},
{
"text": "{ x i , y i } i . 1. Split training data D into L partitions D 1 , . . . , D L . 2. Train L",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Training",
"sec_num": "3.2"
},
{
"text": "= { x i , g(x i ), y i } i .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Training",
"sec_num": "3.2"
},
{
"text": "3. Train the level 0 parser g on the original training data D. 4. Train the level 1 parser h on the augmented training dataD.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Training",
"sec_num": "3.2"
},
{
"text": "The runtime of this algorithm is O(LT 0 +T 1 ), where T 0 and T 1 are the individual runtimes required for training level 0 and level 1 alone, respectively.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Training",
"sec_num": "3.2"
},
{
"text": "We next describe two motivations for stacking parsers: as a way of augmenting the features of a graph-based dependency parser or as a way to approximate higher-order models.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Two Views of Stacked Parsing",
"sec_num": "4"
},
{
"text": "Suppose that the level 1 classifier is an arc-factored graph-based parser. The feature vectors will take the form 3",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "f (x, y) = f 1 (x, y) f 2 (x,\u0177 0 , y) = a\u2208Ay f 1,a (x) f 2,a (x, g(x)),",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "2 http://w3.msi.vxu.se/\u02dcjha/maltparser 3 We use to denote vector concatenation.",
"cite_spans": [
{
"start": 39,
"end": 40,
"text": "3",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "where f 1 (x, y) = a\u2208Ay f 1,a (x) are regular arc-factored features, and f 2 (x,\u0177 0 , y) = a\u2208Ay f 2,a (x, g(x)) are the stacked features. An example of a stacked feature is a binary feature f 2,a (x, g(x)) that fires if and only if the arc a was predicted by g, i.e., if a \u2208 A g(x) ; such a feature was used by Nivre and McDonald (2008) .",
"cite_spans": [
{
"start": 311,
"end": 336,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "It is difficult in general to decide whether the inclusion of such a feature yields a better parser, since features strongly correlate with each other. However, a popular heuristic for feature selection consists of measuring the information gain provided by each individual feature. In this case, we may obtain a closed-form expression for the information gain that f 2,a (x, g(x)) provides about the existence or not of the arc a in the actual dependency tree y. Let A and A be binary random variables associated with the events a \u2208 A y and a \u2208 A g(x) , respectively. We have:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "I(A; A ) = a,a \u2208{0,1} p(a, a ) log 2 p(a, a ) p(a)p(a ) = H(A ) \u2212 a\u2208{0,1} p(a)H(A |A = a).",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "Assuming, for simplicity, that at level 0 the probability of false positives equals the probability of false negatives (i.e., P err p(a = 0|a = 1) = p(a = 1|a = 0)), and that the probability of true positives equals the probability of true negatives (1 \u2212 P err = p(a = 0|a = 0) = p(a = 1|a = 1)), the expression above reduces to: I(A; A ) = H(A ) + P err log 2 P err",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "+ (1 \u2212 P err ) log 2 (1 \u2212 P err ) = H(A ) \u2212 H err ,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "where H err denotes the entropy of the probability of error on each arc's prediction by the level 0 classifier. If P err \u2264 0.5 (i.e. if the level 0 classifier is better than random), then the information gain provided by this simple stacked feature increases with (a) the accuracy of the level 0 classifier, and (b) the entropy H(A ) of the distribution associated with its arc predictions.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Adding Input Features",
"sec_num": "4.1"
},
{
"text": "Another way of interpreting the stacking framework is as a means to approximate a higher order model, such as one that is not arc-factored, by using stacked features that make use of the predicted structure around a candidate arc. Consider a second-order model where the features decompose by arc and by arc pair:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "f (x, y) = a 1 \u2208Ay \uf8eb \uf8ed f a 1 (x) a 2 \u2208Ay f a 1 ,a 2 (x) \uf8f6 \uf8f8 .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "Exact parsing under such model, with arbitrary second-order features, is intractable (McDonald and Satta, 2007) . Let us now consider a stacked model in which the level 0 predictor outputs a parse\u0177. At level 1, we use arc-factored features that may be written as",
"cite_spans": [
{
"start": 85,
"end": 111,
"text": "(McDonald and Satta, 2007)",
"ref_id": "BIBREF18"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "f (x, y) = a 1 \u2208Ay \uf8eb \uf8ed f a 1 (x) a 2 \u2208A\u0177 f a 1 ,a 2 (x) \uf8f6 \uf8f8 ;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "this model differs from the previous one only by replacing A y by A\u0177 in the index set of the second summation. Since\u0177 is given, this makes the latter model arc-factored, and therefore, tractable. We can now viewf (x, y) as an approximation of f (x, y); indeed, we can bound the score approximation error,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "\u2206s(x, y) = w f (x, y) \u2212 w f (x, y) ,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "wherew and w stand respectively for the parameters learned for the stacked model and those that would be learned for the (intractable) exact second order model. We can bound \u2206s(x, y) by spliting it into two terms:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "\u2206s(x, y) = (w \u2212 w) f (x, y) + w (f (x, y) \u2212 f (x, y)) \u2264 (w \u2212 w) f (x, y) \u2206str(x,y) + w (f (x, y) \u2212 f (x, y)) \u2206s dec (x,y) ;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "where we introduced the terms \u2206s tr and \u2206s dec that reflect the portion of the score approximation error that are due to training error (i.e., different parameterizations of the exact and approximate models) and decoding error (same parameterizations, but different feature vectors). Using H\u00f6lder's inequality, the former term can be bounded as:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "\u2206s tr (x, y) = (w \u2212 w) f (x, y) \u2264 w \u2212 w 1 \u2022 f (x, y) \u221e \u2264 w \u2212 w 1 ;",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "where . 1 and . \u221e denote the 1 -norm and supnorm, respectively, and the last inequality holds when the features are binary (so that f (x, y) \u221e \u2264 1). The proper way to bound the term w \u2212 w 1 depends on the training algorithm. As for the decoding error term, it can bounded for a given weight vector w, sentence x, candidate tree y, and level 0 prediction\u0177. Decomposing the weighted vector as w = w 1 w 2 , w 2 being the sub-vector associated with the second-order features, we have respectively:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "\u2206s dec (x, y) = w (f (x, y) \u2212 f (x, y)) = a 1 \u2208Ay w 2 \uf8eb \uf8ed a 2 \u2208A\u0177 f a 1 ,a 2 (x) \u2212 a 2 \u2208Ay f a 1 ,a 2 (x) \uf8f6 \uf8f8 \u2264 a 1 \u2208Ay a 2 \u2208A\u0177\u2206Ay w 2 f a 1 ,a 2 (x) \u2264 a 1 \u2208Ay |A\u0177\u2206A y | \u2022 max a 2 \u2208A\u0177\u2206Ay w 2 f a 1 ,a 2 (x) = a 1 \u2208Ay 2L(y,\u0177) \u2022 max a 2 \u2208A\u0177\u2206Ay w 2 f a 1 ,a 2 (x) ,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "where A\u0177\u2206A y (A\u0177 \u2212 A y ) \u222a (A y \u2212 A\u0177) denotes the symmetric difference of the sets A\u0177 and A y , which has cardinality 2L(y,\u0177), i.e., twice the Hamming distance between the sequences of heads that characterize y and the predicted parse\u0177. Using H\u00f6lder's inequality, we have both",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "w 2 f a 1 ,a 2 (x) \u2264 w 2 1 \u2022 f a 1 ,a 2 (x) \u221e and w 2 f a 1 ,a 2 (x) \u2264 w 2 \u221e \u2022 f a 1 ,a 2 (x) 1 .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "Assuming that all features are binary valued, we have that f a 1 ,a 2 (x) \u221e \u2264 1 and that f a 1 ,a 2 (x) 1 \u2264 N f,2 , where N f,2 denotes the maximum number of active second order features for any possible pair of arcs (a 1 , a 2 ). Therefore:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "\u2206s dec (x, y) \u2264 2nL(y,\u0177) min{ w 2 1 , N f,2 \u2022 w 2 \u221e },",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "where n is the sentence length. Although this bound can be loose, it suggests (intuitively) that the score approximation degrades as the predicted tree\u0177 gets farther away from the true tree y (in Hamming distance). It also degrades with the magnitude of weights associated with the second-order features, Table 2 : Combinations of features enumerated in Table 1 used for stacking. A is a replication of (Nivre and Mc-Donald, 2008) , except for the modifications described in footnote 4.",
"cite_spans": [
{
"start": 403,
"end": 430,
"text": "(Nivre and Mc-Donald, 2008)",
"ref_id": null
}
],
"ref_spans": [
{
"start": 305,
"end": 312,
"text": "Table 2",
"ref_id": null
},
{
"start": 354,
"end": 361,
"text": "Table 1",
"ref_id": "TABREF0"
}
],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "which suggests that a separate regularization of the first-order and stacked features might be beneficial in a stacking framework. As a side note, if we set each component of the weight vector to one, we obtain a bound on the 1 -norm of the feature vector difference,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "f (x, y) \u2212 f (x, y) 1 \u2264 2nL(y,\u0177)N f,2 .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Approximating Non-factored Features",
"sec_num": "4.2"
},
{
"text": "In the following experiments we demonstrate the effectiveness of stacking parsers. As noted in \u00a73.1, we make use of two component parsers, the graph-based MSTParser and the transition-based MaltParser.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Experiments",
"sec_num": "5"
},
{
"text": "The publicly available version of MSTParser performs parsing and labeling jointly. We adapted this system to first perform unlabeled parsing, then label the arcs using a log-linear classifier with access to the full unlabeled parse (McDonald et al., 2005a; McDonald et al., 2005b; . In stacking experiments, the arc labels from the level 0 parser are also used as a feature. 4 In the following subsections, we refer to our modification of the MSTParser as MST 1O (the arcfactored version) and MST 2O (the second-order arc-pair-factored version). All our experiments use the non-projective version of this parser. We refer to the MaltParser as Malt.",
"cite_spans": [
{
"start": 232,
"end": 256,
"text": "(McDonald et al., 2005a;",
"ref_id": "BIBREF19"
},
{
"start": 257,
"end": 280,
"text": "McDonald et al., 2005b;",
"ref_id": "BIBREF20"
},
{
"start": 375,
"end": 376,
"text": "4",
"ref_id": null
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Implementation and Experimental Details",
"sec_num": "5.1"
},
{
"text": "We report experiments on twelve languages from the CoNLL-X shared task (Buchholz and Marsi, 2006) . 5 All experiments are evaluated using the labeled attachment score (LAS), using the default settings. 6 Statistical significance is measured using Dan Bikel's randomized parsing evaluation comparator with 10,000 iterations. 7 The additional features used in the level 1 parser are enumerated in Table 1 and their various subsets are depicted in Table 2. The PredEdge features are exactly the six features used by Nivre and McDonald (2008) in their MST Malt parser; therefore, feature set A is a replication of this parser except for modifications noted in footnote 4. In all our experiments, the number of partitions used to createD is L = 2.",
"cite_spans": [
{
"start": 71,
"end": 97,
"text": "(Buchholz and Marsi, 2006)",
"ref_id": "BIBREF4"
},
{
"start": 100,
"end": 101,
"text": "5",
"ref_id": null
},
{
"start": 324,
"end": 325,
"text": "7",
"ref_id": null
},
{
"start": 513,
"end": 538,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [
{
"start": 395,
"end": 402,
"text": "Table 1",
"ref_id": "TABREF0"
}
],
"eq_spans": [],
"section": "Implementation and Experimental Details",
"sec_num": "5.1"
},
{
"text": "Our first experiment stacks the highly accurate MST 2O parser with itself. At level 0, the parser uses only the standard features ( \u00a75.1), and at level 1, these are augmented by various subsets of features of x along with the output of the level 0 parser, g(x) ( Table 2) . The results are shown in Table 3 . While we see improvements over the single-parser baseline 4 We made other modifications to MSTParser, implementing many of the successes described by . Our version of the code is publicly available at http: //www.ark.cs.cmu.edu/MSTParserStacked. The modifications included an approximation to lemmas for datasets without lemmas (three-character prefixes), and replacing morphology/word and morphology/lemma features with morphology/POS features.",
"cite_spans": [
{
"start": 367,
"end": 368,
"text": "4",
"ref_id": null
}
],
"ref_spans": [
{
"start": 263,
"end": 271,
"text": "Table 2)",
"ref_id": null
},
{
"start": 299,
"end": 306,
"text": "Table 3",
"ref_id": "TABREF2"
}
],
"eq_spans": [],
"section": "Experiment: MST 2O + MST 2O",
"sec_num": "5.2"
},
{
"text": "5 The CoNLL-X shared task actually involves thirteen languages; our experiments do not include Czech (the largest dataset), due to time constraints. Therefore, the average results plotted in the last rows of Tables 3, 4, and 5 are not directly comparable with previously published averages over thirteen languages. for nine languages, the improvements are small (less than 0.5%). One of the biggest concerns about this model is the fact that it stacks two predictors that are very similar in nature: both are graph-based and share the features f 1,a (x). It has been pointed out by Breiman (1996) , among others, that the success of ensemble methods like stacked learning strongly depends on how uncorrelated the individual decisions made by each predictor are from the others' decisions. 8 This experiment provides further evidence for the claim.",
"cite_spans": [
{
"start": 582,
"end": 596,
"text": "Breiman (1996)",
"ref_id": "BIBREF2"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Experiment: MST 2O + MST 2O",
"sec_num": "5.2"
},
{
"text": "M S T 2 O + M S T 2 O , A + M S T 2 O , B + M S T 2 O , C + M S T 2 O , D + M S T 2 O , E",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Experiment: MST 2O + MST 2O",
"sec_num": "5.2"
},
{
"text": "We next use MaltParser at level 0 and the secondorder arc-pair-factored MST 2O at level 1. This extends the experiments of Nivre and McDonald (2008) , replicated in our feature subset A. Table 4 enumerates the results. Note that the best-performing stacked configuration for each and every language outperforms MST 2O , corroborating results reported by Nivre and McDonald (2008) . The best performing stacked configuration outperforms Malt as well, except for Japanese and Turkish. Further, our non-arc-factored features largely outperform subset A, except on Bulgarian, Chinese, and Japanese. On average, the best feature configuration is E, which is statistically significant over Malt and MST 2O with p < 0.0001, and over feature subset A with p < 0.01.",
"cite_spans": [
{
"start": 123,
"end": 148,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
},
{
"start": 354,
"end": 379,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [
{
"start": 187,
"end": 194,
"text": "Table 4",
"ref_id": null
}
],
"eq_spans": [],
"section": "Experiment: Malt + MST 2O",
"sec_num": "5.3"
},
{
"text": "Finally, we consider stacking MaltParser with the first-order, arc-factored MSTParser. We view this approach as perhaps the most promising, since it is an exact parsing method with the quadratic runtime complexity of MST 1O . Table 5 enumerates the results. For all twelve languages, some stacked configuration outperforms MST 1O and also, surprisingly, MST 2O , the second order model. This provides empirical evidence that using rich features from MaltParser at level 0, a stacked level 1 first-order MSTParser can outperform the second-order MSTParser. 9 In only two cases (Japanese and Turkish), the MaltParser slightly outperforms the stacked parser.",
"cite_spans": [],
"ref_spans": [
{
"start": 226,
"end": 233,
"text": "Table 5",
"ref_id": null
}
],
"eq_spans": [],
"section": "Experiment: Malt + MST 1O",
"sec_num": "5.4"
},
{
"text": "On average, feature configuration D performs the best, and is statistically significant over Malt, MST 1O , and MST 2O with p < 0.0001, and over feature subset A with p < 0.05. Encouragingly, this configuration is barely outperformed by configura- Table 4 : Results of stacking Malt and MST 2O at level 0 and level 1, respectively. Columns 2-4 enumerate LAS for Malt, MST 2O and Malt + MST 2O as in Nivre and McDonald (2008) . Columns 5-8 enumerate results for four other stacked feature configurations. Bold indicates best result for a language. tion A of Malt + MST 2O (see Table 4 ), the difference being statistically insignificant (p > 0.05). This shows that stacking M alt with the exact, arcfactored MST 1O bridges the difference between the individual MST 1O and MST 2O models, by approximating higher order features, but maintaining an O(n 2 ) runtime and finding the model-optimal parse.",
"cite_spans": [
{
"start": 399,
"end": 424,
"text": "Nivre and McDonald (2008)",
"ref_id": "BIBREF22"
}
],
"ref_spans": [
{
"start": 248,
"end": 255,
"text": "Table 4",
"ref_id": null
},
{
"start": 576,
"end": 583,
"text": "Table 4",
"ref_id": null
}
],
"eq_spans": [],
"section": "Experiment: Malt + MST 1O",
"sec_num": "5.4"
},
{
"text": "In pipelines or semisupervised settings, it is useful when a parser can provide a confidence measure alongside its predicted parse tree. Because stacked predictors use ensembles with observable outputs, differences among those outputs may be used to estimate confidence in the final output. In stacked dependency parsing, this can be done (for example) by measuring the Hamming distance between the outputs of the level 0 and 1 parsers, L(g(x), h(x)). Indeed, the bound derived in \u00a74.2 suggests that the second-order approximation degrades for candidate parses y that are Hamming-far from g(x); therefore, if L(g(x), h(x)) is large, the best score s(x, h(x)) may well be \"biased\" due to misleading neighboring information provided by the level 0 parser.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Disagreement as a Confidence Measure",
"sec_num": "5.5"
},
{
"text": "We illustrate this point with an empirical analysis of the level 0/1 disagreement for the set of experiments described in \u00a75.3; namely, we compare the Figure 2 : Accuracy as a function of token disagreement between level 0 and level 1. The x-axis is the Hamming distance L(g(x), h(x)), i.e., the number of tokens where level 0 and level 1 disagree. The y-axis is the accuracy averaged over sentences that have the specified Hamming distance, both for level 0 and level 1. Table 5 : Results of stacking Malt and MST 1O at level 0 and level 1, respectively. Columns 2-4 enumerate LAS for Malt, MST 1O and MST 2O . Columns 5-9 enumerate results for five different stacked feature configurations. Bold indicates the best result for a language. level 0 and level 1 predictions under the best overall configuration (configuration E of M alt + M ST 2O ). Figure 2 depicts accuracy as a function of level 0level 1 disagreement (in number of tokens), averaged over all datasets.",
"cite_spans": [],
"ref_spans": [
{
"start": 151,
"end": 159,
"text": "Figure 2",
"ref_id": "FIGREF1"
},
{
"start": 472,
"end": 479,
"text": "Table 5",
"ref_id": null
},
{
"start": 848,
"end": 856,
"text": "Figure 2",
"ref_id": "FIGREF1"
}
],
"eq_spans": [],
"section": "Disagreement as a Confidence Measure",
"sec_num": "5.5"
},
{
"text": "We can see that performance degrades steeply when the disagreement between levels 0 and 1 increases in the range 0-4, and then behaves more irregularly but keeping the same trend. This suggests that the Hamming distance L(g(x), h(x)) is informative about parser performance and may be used as a confidence measure.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Disagreement as a Confidence Measure",
"sec_num": "5.5"
},
{
"text": "In this work, we made use of stacked learning to improve dependency parsing. We considered an architecture with two layers, where the output of a standard parser in the first level provides new features for a parser in the subsequent level. During learning, the second parser learns to correct mistakes made by the first one. The novelty of our approach is in the exploitation of higher-order predicted edges to simulate non-local features in the second parser. We provided a novel interpretation of stacking as feature approximation, and our experimental results show rich-featured stacked parsers outperforming stateof-the-art single-layer and ensemble parsers. No-tably, using a simple arc-factored parser at level 1, we obtain an exact O(n 2 ) stacked parser that outperforms earlier approximate methods .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusion",
"sec_num": "6"
},
{
"text": "http://sourceforge.net/projects/mstparser",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
},
{
"text": "http://nextens.uvt.nl/\u02dcconll/software.html 7 http://www.cis.upenn.edu/\u02dcdbikel/software. html",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
},
{
"text": "This claim has a parallel in the cotraining method(Blum and Mitchell, 1998), whose performance is bounded by the degree of independence between the two feature sets.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
},
{
"text": "Recall that MST 2O uses approximate search, as opposed to stacking, which uses approximate features.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
}
],
"back_matter": [
{
"text": "The authors thank the anonymous reviewers for helpful comments, Vitor Carvalho, William Cohen, and David Smith for interesting discussions, and Ryan McDonald and Joakim Nivre for providing us their code and preprocessed datasets. A.M. was supported by a grant from FCT through the CMU-Portugal Program and the Information and Communications Technologies Institute (ICTI) at CMU. N.S. was supported by NSF IIS-0713265 and an IBM faculty award. E.X. was supported by NSF DBI-0546594, DBI-0640543, and IIS-0713379.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Acknowledgments",
"sec_num": null
}
],
"bib_entries": {
"BIBREF0": {
"ref_id": "b0",
"title": "Relating probabilistic grammars and automata",
"authors": [
{
"first": "S",
"middle": [
"P"
],
"last": "References",
"suffix": ""
},
{
"first": "D",
"middle": [
"A"
],
"last": "Abney",
"suffix": ""
},
{
"first": "F",
"middle": [],
"last": "Mcallester",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Pereira",
"suffix": ""
}
],
"year": 1999,
"venue": "Proceedings of ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "References S. P. Abney, D. A. McAllester, and F. Pereira. 1999. Re- lating probabilistic grammars and automata. In Pro- ceedings of ACL.",
"links": null
},
"BIBREF1": {
"ref_id": "b1",
"title": "Combining labeled and unlabeled data with co-training",
"authors": [
{
"first": "A",
"middle": [],
"last": "Blum",
"suffix": ""
},
{
"first": "T",
"middle": [],
"last": "Mitchell",
"suffix": ""
}
],
"year": 1998,
"venue": "Proceedings of COLT",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "A. Blum and T. Mitchell. 1998. Combining labeled and unlabeled data with co-training. In Proceedings of COLT.",
"links": null
},
"BIBREF2": {
"ref_id": "b2",
"title": "Stacked regressions",
"authors": [
{
"first": "L",
"middle": [],
"last": "Breiman",
"suffix": ""
}
],
"year": 1996,
"venue": "Machine Learning",
"volume": "24",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "L. Breiman. 1996. Stacked regressions. Machine Learn- ing, 24:49.",
"links": null
},
"BIBREF3": {
"ref_id": "b3",
"title": "A Corpus-Based Approach to Language Learning",
"authors": [
{
"first": "E",
"middle": [],
"last": "Brill",
"suffix": ""
}
],
"year": 1993,
"venue": "",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "E. Brill. 1993. A Corpus-Based Approach to Language Learning. Ph.D. thesis, University of Pennsylvania.",
"links": null
},
"BIBREF4": {
"ref_id": "b4",
"title": "CoNLL-X shared task on multilingual dependency parsing",
"authors": [
{
"first": "S",
"middle": [],
"last": "Buchholz",
"suffix": ""
},
{
"first": "E",
"middle": [],
"last": "Marsi",
"suffix": ""
}
],
"year": 2006,
"venue": "Proceedings of CoNLL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "S. Buchholz and E. Marsi. 2006. CoNLL-X shared task on multilingual dependency parsing. In Proceedings of CoNLL.",
"links": null
},
"BIBREF5": {
"ref_id": "b5",
"title": "On the shortest arborescence of a directed graph",
"authors": [
{
"first": "Y",
"middle": [
"J"
],
"last": "Chu",
"suffix": ""
},
{
"first": "T",
"middle": [
"H"
],
"last": "Liu",
"suffix": ""
}
],
"year": 1965,
"venue": "Science Sinica",
"volume": "14",
"issue": "",
"pages": "1396--1400",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Y. J. Chu and T. H. Liu. 1965. On the shortest arbores- cence of a directed graph. Science Sinica, 14:1396- 1400.",
"links": null
},
"BIBREF6": {
"ref_id": "b6",
"title": "Stacked sequential learning",
"authors": [
{
"first": "W",
"middle": [
"W"
],
"last": "Cohen",
"suffix": ""
},
{
"first": "V",
"middle": [],
"last": "Rocha De Carvalho",
"suffix": ""
}
],
"year": 2005,
"venue": "Proceedings of IJCAI",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "W. W. Cohen and V. Rocha de Carvalho. 2005. Stacked sequential learning. In Proceedings of IJCAI.",
"links": null
},
"BIBREF7": {
"ref_id": "b7",
"title": "Dependency tree kernels for relation extraction",
"authors": [
{
"first": "A",
"middle": [],
"last": "Culotta",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Sorensen",
"suffix": ""
}
],
"year": 2004,
"venue": "Proceedings of ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "A. Culotta and J. Sorensen. 2004. Dependency tree ker- nels for relation extraction. In Proceedings of ACL.",
"links": null
},
"BIBREF8": {
"ref_id": "b8",
"title": "Machine translation using probabilistic synchronous dependency insertion grammar",
"authors": [
{
"first": "Y",
"middle": [],
"last": "Ding",
"suffix": ""
},
{
"first": "M",
"middle": [],
"last": "Palmer",
"suffix": ""
}
],
"year": 2005,
"venue": "Proceedings of ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Y. Ding and M. Palmer. 2005. Machine translation using probabilistic synchronous dependency insertion gram- mar. In Proceedings of ACL.",
"links": null
},
"BIBREF9": {
"ref_id": "b9",
"title": "Journal of Research of the National Bureau of Standards",
"authors": [
{
"first": "J",
"middle": [],
"last": "Edmonds",
"suffix": ""
}
],
"year": 1967,
"venue": "",
"volume": "71",
"issue": "",
"pages": "233--240",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Edmonds. 1967. Optimum branchings. Journal of Re- search of the National Bureau of Standards, 71B:233- 240.",
"links": null
},
"BIBREF10": {
"ref_id": "b10",
"title": "Efficient parsing for bilexical context-free grammars and head automaton grammars",
"authors": [
{
"first": "J",
"middle": [],
"last": "Eisner",
"suffix": ""
},
{
"first": "G",
"middle": [],
"last": "Satta",
"suffix": ""
}
],
"year": 1999,
"venue": "Proceedings of ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Eisner and G. Satta. 1999. Efficient parsing for bilex- ical context-free grammars and head automaton gram- mars. In Proceedings of ACL.",
"links": null
},
"BIBREF11": {
"ref_id": "b11",
"title": "Three new probabilistic models for dependency parsing: An exploration",
"authors": [
{
"first": "J",
"middle": [],
"last": "Eisner",
"suffix": ""
}
],
"year": 1996,
"venue": "Proceedings of COLING",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Eisner. 1996. Three new probabilistic models for de- pendency parsing: An exploration. In Proceedings of COLING.",
"links": null
},
"BIBREF12": {
"ref_id": "b12",
"title": "Discriminative classifiers for deterministic dependency parsing",
"authors": [
{
"first": "J",
"middle": [],
"last": "Hall",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Nivre",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Nilsson",
"suffix": ""
}
],
"year": 2006,
"venue": "Proceedings of ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Hall, J. Nivre, and J. Nilsson. 2006. Discriminative classifiers for deterministic dependency parsing. In Proceedings of ACL.",
"links": null
},
"BIBREF13": {
"ref_id": "b13",
"title": "Stacked graphical models for efficient inference in Markov random fields",
"authors": [
{
"first": "Z",
"middle": [],
"last": "Kou",
"suffix": ""
},
{
"first": "W",
"middle": [
"W"
],
"last": "Cohen",
"suffix": ""
}
],
"year": 2007,
"venue": "Proceedings of SDM",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Z. Kou and W. W. Cohen. 2007. Stacked graphical mod- els for efficient inference in Markov random fields. In Proceedings of SDM.",
"links": null
},
"BIBREF14": {
"ref_id": "b14",
"title": "Conditional random fields: Probabilistic models for segmenting and labeling sequence data",
"authors": [
{
"first": "J",
"middle": [],
"last": "Lafferty",
"suffix": ""
},
{
"first": "A",
"middle": [],
"last": "Mccallum",
"suffix": ""
},
{
"first": "F",
"middle": [],
"last": "Pereira",
"suffix": ""
}
],
"year": 2001,
"venue": "Proceedings of ICML",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Lafferty, A. McCallum, and F. Pereira. 2001. Con- ditional random fields: Probabilistic models for seg- menting and labeling sequence data. In Proceedings of ICML.",
"links": null
},
"BIBREF15": {
"ref_id": "b15",
"title": "Structure compilation: trading structure for features",
"authors": [
{
"first": "P",
"middle": [],
"last": "Liang",
"suffix": ""
},
{
"first": "H",
"middle": [],
"last": "Daum\u00e9",
"suffix": ""
},
{
"first": "D",
"middle": [],
"last": "Klein",
"suffix": ""
}
],
"year": 2008,
"venue": "Proceedings of ICML",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "P. Liang, H. Daum\u00e9, and D. Klein. 2008. Structure com- pilation: trading structure for features. In Proceedings of ICML.",
"links": null
},
"BIBREF16": {
"ref_id": "b16",
"title": "Characterizing the errors of data-driven dependency parsing models",
"authors": [
{
"first": "R",
"middle": [],
"last": "Mcdonald",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Nivre",
"suffix": ""
}
],
"year": 2007,
"venue": "Proceedings of EMNLP-CoNLL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "R. McDonald and J. Nivre. 2007. Characterizing the errors of data-driven dependency parsing models. In Proceedings of EMNLP-CoNLL.",
"links": null
},
"BIBREF17": {
"ref_id": "b17",
"title": "Online learning of approximate dependency parsing algorithms",
"authors": [
{
"first": "R",
"middle": [
"T"
],
"last": "Mcdonald",
"suffix": ""
},
{
"first": "F",
"middle": [
"C N"
],
"last": "Pereira",
"suffix": ""
}
],
"year": 2006,
"venue": "Proceedings of EACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "R. T. McDonald and F. C. N. Pereira. 2006. Online learn- ing of approximate dependency parsing algorithms. In Proceedings of EACL.",
"links": null
},
"BIBREF18": {
"ref_id": "b18",
"title": "On the complexity of non-projective data-driven dependency parsing",
"authors": [
{
"first": "R",
"middle": [],
"last": "Mcdonald",
"suffix": ""
},
{
"first": "G",
"middle": [],
"last": "Satta",
"suffix": ""
}
],
"year": 2007,
"venue": "Proceedings of IWPT",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "R. McDonald and G. Satta. 2007. On the complexity of non-projective data-driven dependency parsing. In Proceedings of IWPT.",
"links": null
},
"BIBREF19": {
"ref_id": "b19",
"title": "Online large-margin training of dependency parsers",
"authors": [
{
"first": "K",
"middle": [],
"last": "Mcdonald",
"suffix": ""
},
{
"first": "F",
"middle": [],
"last": "Crammer",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Pereira",
"suffix": ""
}
],
"year": 2005,
"venue": "Proceedings of ACL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "McDonald, K. Crammer, and F. Pereira. 2005a. On- line large-margin training of dependency parsers. In Proceedings of ACL.",
"links": null
},
"BIBREF20": {
"ref_id": "b20",
"title": "Non-projective dependency parsing using spanning tree algorithms",
"authors": [
{
"first": "R",
"middle": [
"T"
],
"last": "Mcdonald",
"suffix": ""
},
{
"first": "F",
"middle": [],
"last": "Pereira",
"suffix": ""
},
{
"first": "K",
"middle": [],
"last": "Ribarov",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Hajic",
"suffix": ""
}
],
"year": 2005,
"venue": "Proceedings of HLT-EMNLP",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "R. T. McDonald, F. Pereira, K. Ribarov, and J. Ha- jic. 2005b. Non-projective dependency parsing us- ing spanning tree algorithms. In Proceedings of HLT- EMNLP.",
"links": null
},
"BIBREF21": {
"ref_id": "b21",
"title": "Multilingual dependency analysis with a two-stage discriminative parser",
"authors": [
{
"first": "R",
"middle": [],
"last": "Mcdonald",
"suffix": ""
},
{
"first": "K",
"middle": [],
"last": "Lerman",
"suffix": ""
},
{
"first": "F",
"middle": [],
"last": "Pereira",
"suffix": ""
}
],
"year": 2006,
"venue": "Proceedings CoNLL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "R. McDonald, K. Lerman, and F. Pereira. 2006. Multi- lingual dependency analysis with a two-stage discrim- inative parser. In Proceedings CoNLL.",
"links": null
},
"BIBREF22": {
"ref_id": "b22",
"title": "Integrating graphbased and transition-based dependency parsers",
"authors": [
{
"first": "J",
"middle": [],
"last": "Nivre",
"suffix": ""
},
{
"first": "R",
"middle": [],
"last": "Mcdonald",
"suffix": ""
}
],
"year": 2008,
"venue": "Proceedings of ACL-HLT",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Nivre and R. McDonald. 2008. Integrating graph- based and transition-based dependency parsers. In Proceedings of ACL-HLT.",
"links": null
},
"BIBREF23": {
"ref_id": "b23",
"title": "Memory-based dependency parsing",
"authors": [
{
"first": "J",
"middle": [],
"last": "Nivre",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Hall",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Nilsson",
"suffix": ""
}
],
"year": 2004,
"venue": "Proceedings of CoNLL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Nivre, J. Hall, and J. Nilsson. 2004. Memory-based dependency parsing. In Proceedings of CoNLL.",
"links": null
},
"BIBREF24": {
"ref_id": "b24",
"title": "Labeled pseudo-projective dependency parsing with support vector machines",
"authors": [
{
"first": "J",
"middle": [],
"last": "Nivre",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Hall",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Nilsson",
"suffix": ""
},
{
"first": "G",
"middle": [],
"last": "Eryi\u01e7it",
"suffix": ""
},
{
"first": "S",
"middle": [],
"last": "Marinov",
"suffix": ""
}
],
"year": 2006,
"venue": "Proceedings of CoNLL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "J. Nivre, J. Hall, J. Nilsson, G. Eryi\u01e7it, and S. Marinov. 2006. Labeled pseudo-projective dependency pars- ing with support vector machines. In Proceedings of CoNLL.",
"links": null
},
"BIBREF25": {
"ref_id": "b25",
"title": "A maximum entropy model for parsing",
"authors": [
{
"first": "A",
"middle": [],
"last": "Ratnaparkhi",
"suffix": ""
},
{
"first": "S",
"middle": [],
"last": "Roukos",
"suffix": ""
},
{
"first": "R",
"middle": [
"T"
],
"last": "Ward",
"suffix": ""
}
],
"year": 1994,
"venue": "Proceedings of ICSLP",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "A. Ratnaparkhi, S. Roukos, and R. T. Ward. 1994. A maximum entropy model for parsing. In Proceedings of ICSLP.",
"links": null
},
"BIBREF26": {
"ref_id": "b26",
"title": "Incremental integer linear programming for non-projective dependency parsing",
"authors": [
{
"first": "S",
"middle": [],
"last": "Riedel",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Clarke",
"suffix": ""
}
],
"year": 2006,
"venue": "Proceedings of EMNLP",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "S. Riedel and J. Clarke. 2006. Incremental integer linear programming for non-projective dependency parsing. In Proceedings of EMNLP.",
"links": null
},
"BIBREF27": {
"ref_id": "b27",
"title": "A classifier-based parser with linear run-time complexity",
"authors": [
{
"first": "K",
"middle": [],
"last": "Sagae",
"suffix": ""
},
{
"first": "A",
"middle": [],
"last": "Lavie",
"suffix": ""
}
],
"year": 2005,
"venue": "Proceedings of IWPT",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "K. Sagae and A. Lavie. 2005. A classifier-based parser with linear run-time complexity. In Proceedings of IWPT.",
"links": null
},
"BIBREF28": {
"ref_id": "b28",
"title": "Dependency parsing by belief propagation",
"authors": [
{
"first": "D",
"middle": [
"A"
],
"last": "Smith",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Eisner",
"suffix": ""
}
],
"year": 2008,
"venue": "Proceedings of EMNLP",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "D. A. Smith and J. Eisner. 2008. Dependency parsing by belief propagation. In Proceedings of EMNLP.",
"links": null
},
"BIBREF29": {
"ref_id": "b29",
"title": "A latent variable model for generative dependency parsing",
"authors": [
{
"first": "I",
"middle": [],
"last": "Titov",
"suffix": ""
},
{
"first": "J",
"middle": [],
"last": "Henderson",
"suffix": ""
}
],
"year": 2007,
"venue": "Proceedings of IWPT",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "I. Titov and J. Henderson. 2007. A latent variable model for generative dependency parsing. In Proceedings of IWPT.",
"links": null
},
"BIBREF30": {
"ref_id": "b30",
"title": "What is the Jeopardy model? A quasi-synchronous grammar for QA",
"authors": [
{
"first": "M",
"middle": [],
"last": "Wang",
"suffix": ""
},
{
"first": "N",
"middle": [
"A"
],
"last": "Smith",
"suffix": ""
},
{
"first": "T",
"middle": [],
"last": "Mitamura",
"suffix": ""
}
],
"year": 2007,
"venue": "Proceedings of EMNLP-CoNLL",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "M. Wang, N. A. Smith, and T. Mitamura. 2007. What is the Jeopardy model? A quasi-synchronous grammar for QA. In Proceedings of EMNLP-CoNLL.",
"links": null
},
"BIBREF31": {
"ref_id": "b31",
"title": "Stacked generalization",
"authors": [
{
"first": "D",
"middle": [],
"last": "Wolpert",
"suffix": ""
}
],
"year": 1992,
"venue": "Neural Networks",
"volume": "5",
"issue": "2",
"pages": "241--260",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "D. Wolpert. 1992. Stacked generalization. Neural Net- works, 5(2):241-260.",
"links": null
},
"BIBREF32": {
"ref_id": "b32",
"title": "Statistical dependency analysis with support vector machines",
"authors": [
{
"first": "H",
"middle": [],
"last": "Yamada",
"suffix": ""
},
{
"first": "Y",
"middle": [],
"last": "Matsumoto",
"suffix": ""
}
],
"year": 2003,
"venue": "Proceedings of IWPT",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "H. Yamada and Y. Matsumoto. 2003. Statistical depen- dency analysis with support vector machines. In Pro- ceedings of IWPT.",
"links": null
}
},
"ref_entries": {
"FIGREF0": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "A projective dependency graph."
},
"FIGREF1": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "Non-projective dependency graph."
},
"FIGREF2": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "A projective dependency graph."
},
"FIGREF3": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "Non-projective dependency graph."
},
"FIGREF4": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "A projective dependency parse (top), and a nonprojective dependency parse (bottom) for two English sentences; examples from McDonald and Satta (2007). (2008)."
},
"FIGREF5": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "instances of the level 0 parser in the following way: the l-th instance, g l , is trained on D \u2212l = D \\ D l . Then use g l to output predictions for the (unseen) partition D l . At the end, an augmented datasetD = L l=1D l is built, so thatD"
},
"FIGREF6": {
"num": null,
"uris": null,
"type_str": "figure",
"text": "candidate edge was present, and what was its label. Sibling Lemma, POS, link label, distance and direction of attachment of the previous and and next predicted siblings GrandParents Lemma, POS, link label, distance and direction of attachment of the grandparent of the current modifier PredHead Predicted head of the candidate modifier (if PredEdge=0) AllChildren Sequence of POS and link labels of all the predicted children of the candidate head"
},
"TABREF0": {
"num": null,
"html": null,
"text": "Feature sets derived from the level 0 parser.",
"type_str": "table",
"content": "<table><tr><td colspan=\"2\">Subset Description</td></tr><tr><td>A</td><td>PredEdge</td></tr><tr><td>B</td><td>PredEdge+Sibling</td></tr><tr><td>C</td><td>PredEdge+Sibling+GrandParents</td></tr><tr><td>D</td><td>PredEdge+Sibling+GrandParents+PredHead</td></tr><tr><td>E</td><td>PredEdge+Sibling+GrandParents+PredHead+</td></tr><tr><td/><td>AllChildren</td></tr></table>"
},
"TABREF1": {
"num": null,
"html": null,
"text": "Arabic 67.88 66.91 67.41 67.68 67.37 68.02 Bulgarian 87.31 87.39 87.03 87.61 87.57 87.55 Chinese 87.57 87.16 87.24 87.48 87.42 87.48",
"type_str": "table",
"content": "<table><tr><td>Danish</td><td>85.27 85.39 85.61 85.57 85.43 85.57</td></tr><tr><td>Dutch</td><td>79.99 79.79 79.79 79.83 80.17 80.13</td></tr><tr><td>German</td><td>87.44 86.92 87.32 87.32 87.26 87.04</td></tr><tr><td>Japanese</td><td>90.93 91.41 91.21 91.35 91.11 91.19</td></tr><tr><td colspan=\"2\">Portuguese 87.12 87.26 86.88 87.02 87.04 86.98</td></tr><tr><td>Slovene</td><td>74.02 74.30 74.30 74.00 74.14 73.94</td></tr><tr><td>Spanish</td><td>82.43 82.17 82.35 82.81 82.53 82.75</td></tr><tr><td>Swedish</td><td>82.87 82.99 82.95 82.51 83.01 82.69</td></tr><tr><td>Turkish</td><td>60.11 59.47 59.25 59.47 59.45 59.31</td></tr><tr><td>Average</td><td>81.08 80.93 80.94 81.05 81.04 81.05</td></tr></table>"
},
"TABREF2": {
"num": null,
"html": null,
"text": "Results of stacking MST 2O with itself at both level 0 and level 1. Column 2 enumerates LAS for MST 2O . Columns 3-6 enumerate results for four different stacked feature subsets. Bold indicates best results for a particular language.",
"type_str": "table",
"content": "<table/>"
}
}
}
} |