File size: 93,168 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 | {
"paper_id": "P06-1012",
"header": {
"generated_with": "S2ORC 1.0.0",
"date_generated": "2023-01-19T09:24:42.339352Z"
},
"title": "Estimating Class Priors in Domain Adaptation for Word Sense Disambiguation",
"authors": [
{
"first": "Yee",
"middle": [
"Seng"
],
"last": "Chan",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "National University of Singapore",
"location": {
"addrLine": "3 Science Drive 2",
"postCode": "117543",
"country": "Singapore"
}
},
"email": "chanys@comp.nus.edu.sg"
},
{
"first": "Hwee",
"middle": [
"Tou"
],
"last": "Ng",
"suffix": "",
"affiliation": {
"laboratory": "",
"institution": "National University of Singapore",
"location": {
"addrLine": "3 Science Drive 2",
"postCode": "117543",
"country": "Singapore"
}
},
"email": ""
}
],
"year": "",
"venue": null,
"identifiers": {},
"abstract": "Instances of a word drawn from different domains may have different sense priors (the proportions of the different senses of a word). This in turn affects the accuracy of word sense disambiguation (WSD) systems trained and applied on different domains. This paper presents a method to estimate the sense priors of words drawn from a new domain, and highlights the importance of using well calibrated probabilities when performing these estimations. By using well calibrated probabilities, we are able to estimate the sense priors effectively to achieve significant improvements in WSD accuracy.",
"pdf_parse": {
"paper_id": "P06-1012",
"_pdf_hash": "",
"abstract": [
{
"text": "Instances of a word drawn from different domains may have different sense priors (the proportions of the different senses of a word). This in turn affects the accuracy of word sense disambiguation (WSD) systems trained and applied on different domains. This paper presents a method to estimate the sense priors of words drawn from a new domain, and highlights the importance of using well calibrated probabilities when performing these estimations. By using well calibrated probabilities, we are able to estimate the sense priors effectively to achieve significant improvements in WSD accuracy.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Abstract",
"sec_num": null
}
],
"body_text": [
{
"text": "Many words have multiple meanings, and the process of identifying the correct meaning, or sense of a word in context, is known as word sense disambiguation (WSD). Among the various approaches to WSD, corpus-based supervised machine learning methods have been the most successful to date. With this approach, one would need to obtain a corpus in which each ambiguous word has been manually annotated with the correct sense, to serve as training data.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "However, supervised WSD systems faced an important issue of domain dependence when using such a corpus-based approach. To investigate this, Escudero et al. (2000) conducted experiments using the DSO corpus, which contains sentences drawn from two different corpora, namely Brown Corpus (BC) and Wall Street Journal (WSJ). They found that training a WSD system on one part (BC or WSJ) of the DSO corpus and applying it to the other part can result in an accuracy drop of 12% to 19%. One reason for this is the difference in sense priors (i.e., the proportions of the different senses of a word) between BC and WSJ. For instance, the noun interest has these 6 senses in the DSO corpus: sense 1, 2, 3, 4, 5, and 8. In the BC part of the DSO corpus, these senses occur with the proportions: 34%, 9%, 16%, 14%, 12%, and 15%. However, in the WSJ part of the DSO corpus, the proportions are different: 13%, 4%, 3%, 56%, 22%, and 2%. When the authors assumed they knew the sense priors of each word in BC and WSJ, and adjusted these two datasets such that the proportions of the different senses of each word were the same between BC and WSJ, accuracy improved by 9%. In another work, Agirre and Martinez (2004) trained a WSD system on data which was automatically gathered from the Internet. The authors reported a 14% improvement in accuracy if they have an accurate estimate of the sense priors in the evaluation data and sampled their training data according to these sense priors. The work of these researchers showed that when the domain of the training data differs from the domain of the data on which the system is applied, there will be a decrease in WSD accuracy.",
"cite_spans": [
{
"start": 140,
"end": 162,
"text": "Escudero et al. (2000)",
"ref_id": "BIBREF5"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "To build WSD systems that are portable across different domains, estimation of the sense priors (i.e., determining the proportions of the different senses of a word) occurring in a text corpus drawn from a domain is important. McCarthy et al. (2004) provided a partial solution by describing a method to predict the predominant sense, or the most frequent sense, of a word in a corpus. Using the noun interest as an example, their method will try to predict that sense 1 is the predominant sense in the BC part of the DSO corpus, while sense 4 is the predominant sense in the WSJ part of the corpus.",
"cite_spans": [
{
"start": 227,
"end": 249,
"text": "McCarthy et al. (2004)",
"ref_id": "BIBREF8"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "In our recent work (Chan and Ng, 2005b) , we directly addressed the problem by applying machine learning methods to automatically estimate the sense priors in the target domain. For instance, given the noun interest and the WSJ part of the DSO corpus, we attempt to estimate the proportion of each sense of interest occurring in WSJ and showed that these estimates help to improve WSD accuracy. In our work, we used naive Bayes as the training algorithm to provide posterior probabilities, or class membership estimates, for the instances in the target domain. These probabilities were then used by the machine learning methods to estimate the sense priors of each word in the target domain.",
"cite_spans": [
{
"start": 19,
"end": 39,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "However, it is known that the posterior probabilities assigned by naive Bayes are not reliable, or not well calibrated (Domingos and Pazzani, 1996) . These probabilities are typically too extreme, often being very near 0 or 1. Since these probabilities are used in estimating the sense priors, it is important that they are well calibrated.",
"cite_spans": [
{
"start": 119,
"end": 147,
"text": "(Domingos and Pazzani, 1996)",
"ref_id": "BIBREF4"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "In this paper, we explore the estimation of sense priors by first calibrating the probabilities from naive Bayes. We also propose using probabilities from another algorithm (logistic regression, which already gives well calibrated probabilities) to estimate the sense priors. We show that by using well calibrated probabilities, we can estimate the sense priors more effectively. Using these estimates improves WSD accuracy and we achieve results that are significantly better than using our earlier approach described in (Chan and Ng, 2005b) .",
"cite_spans": [
{
"start": 522,
"end": 542,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "In the following section, we describe the algorithm to estimate the sense priors. Then, we describe the notion of being well calibrated and discuss why using well calibrated probabilities helps in estimating the sense priors. Next, we describe an algorithm to calibrate the probability estimates from naive Bayes. Then, we discuss the corpora and the set of words we use for our experiments before presenting our experimental results. Next, we propose using the well calibrated probabilities of logistic regression to estimate the sense priors, and perform significance tests to compare our various results before concluding.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Introduction",
"sec_num": "1"
},
{
"text": "To estimate the sense priors, or a priori probabilities of the different senses in a new dataset, we used a confusion matrix algorithm (Vucetic and Obradovic, 2001 ) and an EM based algorithm (Saerens et al., 2002) in (Chan and Ng, 2005b) . Our results in (Chan and Ng, 2005b) indicate that the EM based algorithm is effective in estimating the sense priors and achieves greater improvements in WSD accuracy compared to the confusion matrix algorithm. Hence, to estimate the sense priors in our current work, we use the EM based algorithm, which we describe in this section.",
"cite_spans": [
{
"start": 135,
"end": 163,
"text": "(Vucetic and Obradovic, 2001",
"ref_id": "BIBREF17"
},
{
"start": 192,
"end": 214,
"text": "(Saerens et al., 2002)",
"ref_id": "BIBREF16"
},
{
"start": 218,
"end": 238,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
},
{
"start": 256,
"end": 276,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Estimation of Priors",
"sec_num": "2"
},
{
"text": "Most of this section is based on (Saerens et al., 2002) . Assume we have a set of labeled data D with n classes and a set of N independent instances",
"cite_spans": [
{
"start": 33,
"end": 55,
"text": "(Saerens et al., 2002)",
"ref_id": "BIBREF16"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "\u00a1 \u00a2 \u00a3 \u00a5 \u00a4 \u00a7 \u00a6 \u00a6 \u00a7 \u00a6 \u00a9 \u00a4 \u00a2",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "from a new data set. The likelihood of these N instances can be defined as:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "\u00a1 \u00a2 \u00a3 \u00a4 \u00a6 \u00a7 \u00a6 \u00a7 \u00a6 \u00a4 \u00a2 \u00a3 ! \u00a1 \u00a2 \u00a3 \" $ # % & \u00a3 \u00a1 \u00a2 \u00a4 ( ' & 0 ) \u00a3 \" $ # % & \u00a3 \u00a1 \u00a2 2 1 ' & \u00a1 3 ' & 4 )",
"eq_num": "(1)"
}
],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "Assuming the within-class densities , do not change from the training set D to the new data set, we can define:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "\u00a1 \u00a2 6 1 ' & 7 \u00a1 \u00a2 5 1 ' & .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "To determine the a priori probability estimates 8 \u00a1 9 ' & of the new data set that will maximize the likelihood of (1) with respect to",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "\u00a1 3 ' & ,",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "we can apply the iterative procedure of the EM algorithm. In effect, through maximizing the likelihood of (1), we obtain the a priori probability estimates as a by-product.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "Let us now define some notations. When we apply a classifier trained on D on an instance \u00a2 drawn from the new data set D@ , we get",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "8 \u00a1 9 ' & 1 \u00a2",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": ", which we define as the probability of instance , the EM algorithm provides the following iterative steps:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "EQUATION",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [
{
"start": 0,
"end": 8,
"text": "EQUATION",
"ref_id": "EQREF",
"raw_str": "8 A B C \u00a1 9 ' & 1 \u00a2 8 \u00a1 9 ' & 1 \u00a2 8 \u00a1 \u00a3 \u00a2 \u00a5 \u00a4 \u00a7 \u00a6 \u00c4 \u00a9 C 8 \u00a1 \u00c4 \u00a9 C # \u00a9 \u00a3 8 \u00a1 3 ' 1 \u00a2 8 \u00a1 \u00a2 \u00a5 \u00a4 \u00a7 \u00a6 A C 8 \u00a1 A C (2) 8 A B \u00a3 C \u00a1 9 ' & % \u00a3 8 A B C \u00a1 3 ' & 1 \u00a2",
"eq_num": "(3)"
}
],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "where Equation 2represents the expectation Estep, Equation 3represents the maximization Mstep, and N represents the number of instances in D@ . Note that the probabilities",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "8 \u00a1 9 ' & 1 \u00a2 and 8 \u00a1 9 ' &",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "in Equation 2will stay the same throughout the iterations for each particular instance The denominator in Equation 2is simply a normalizing factor.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "The a posteriori",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "8 A B C \u00a1 3 ' & 1 \u00a2",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "and a priori probabilities . This iterative procedure will increase the likelihood of (1) at each step.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "EM Based Algorithm",
"sec_num": "2.1"
},
{
"text": "If a classifier estimates posterior class probabilities",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using A Priori Estimates",
"sec_num": "2.2"
},
{
"text": "8 \u00a1 3 ' & 1 \u00a2",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using A Priori Estimates",
"sec_num": "2.2"
},
{
"text": "when presented with a new instance \u00a2 from D@ , it can be directly adjusted according to estimated a priori probabilities",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using A Priori Estimates",
"sec_num": "2.2"
},
{
"text": "8 \u00a1 9 ' & on D@ : 8 ! \" $ # B & % \u00a1 3 ' & 1 \u00a2 8 \u00a1 9 ' & 1 \u00a2 8 \u00a1 A\u00a8 \u00a9 C 8 \u00a1 \u00c4 \u00a9 C 8 \u00a1 9 ' 1 \u00a2 8 \u00a1 A C 8 \u00a1 A C (4) where 8 \u00a1 9 ' & denotes the a priori probability of class ' & from D and 8 ' \" ( # B ) % \u00a1 9 ' & 1 \u00a2",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using A Priori Estimates",
"sec_num": "2.2"
},
{
"text": "denotes the adjusted predictions.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using A Priori Estimates",
"sec_num": "2.2"
},
{
"text": "In our eariler work (Chan and Ng, 2005b) , the posterior probabilities assigned by a naive Bayes classifier are used by the EM procedure described in the previous section to estimate the sense priors",
"cite_spans": [
{
"start": 20,
"end": 40,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Calibration of Probabilities",
"sec_num": "3"
},
{
"text": "8 \u00a1 9 ' &",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Calibration of Probabilities",
"sec_num": "3"
},
{
"text": "in a new dataset. However, it is known that the posterior probabilities assigned by naive Bayes are not well calibrated (Domingos and Pazzani, 1996) .",
"cite_spans": [
{
"start": 120,
"end": 148,
"text": "(Domingos and Pazzani, 1996)",
"ref_id": "BIBREF4"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Calibration of Probabilities",
"sec_num": "3"
},
{
"text": "It is important to use an algorithm which gives well calibrated probabilities, if we are to use the probabilities in estimating the sense priors. In this section, we will first describe the notion of being well calibrated before discussing why having well calibrated probabilities helps in estimating the sense priors. Finally, we will introduce a method used to calibrate the probabilities from naive Bayes.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Calibration of Probabilities",
"sec_num": "3"
},
{
"text": "Assume for each instance \u00a2 , a classifier outputs a probability S \u00a9 \u00a1 \u00a2 between 0 and 1, of",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "\u00a2 belonging to class ' & .",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "The classifier is wellcalibrated if the empirical class membership probability",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "\u00a1 9 ' & 1 S \u00a9 \u00a1 \u00a2 E 1 0 (",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "converges to the probability value S",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "\u00a9 \u00a1 \u00a2 2 0",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "as the number of examples classified goes to infinity (Zadrozny and Elkan, 2002) . Intuitively, if we consider all the instances to which the classifier assigns a probability S \u00a9 \u00a1 \u00a2 of say 0.6, then 60% of these instances should be members of class ' & .",
"cite_spans": [
{
"start": 54,
"end": 80,
"text": "(Zadrozny and Elkan, 2002)",
"ref_id": "BIBREF18"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Well Calibrated Probabilities",
"sec_num": "3.1"
},
{
"text": "To see why using an algorithm which gives well calibrated probabilities helps in estimating the sense priors, let us rewrite Equation 3, the Mstep of the EM procedure, as the following: . Let BS , for",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "8 A B 3 \u00a3 C \u00a1 9 ' & % % 4 5 6 \u00a9 % 4 7 9 8 A @5 B \u00a9 AC E D C % G F 8 A B C \u00a1 9 ' & 1 \u00a2 (5) where S \u00a9 = H 0 \u00a9 \u00a3 \u00a7 \u00a4 \u00a7 \u00a6 \u00a6 \u00a7 \u00a6 \u00a9 \u00a4 A 0 3 I P denotes",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "T \u00a4 \u00a6 \u00a6 \u00a7 \u00a6 \u00a9 \u00a4 Q",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": ", denote the set of instances in bin by definition and Equation (5) can be rewritten as:",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "T . Note that 1 B \u00a3 1 U W V \u00a3 V \u00a3 V X U 1 BS 1 U W V X V \u00a3 V \u00a3 U 1 B I 1 = . Now, let",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "8 A B \u00a3 C \u00a1 9 ' & \u00a1 0 \u00a9 \u00a3 1 B \u00a3 1 U 2 V \u00a3 V \u00a3 V a U 0 I 1 B I 1 \u00a1 \u00a3 1 B \u00a3 1 U b V X V \u00a3 V a U I 1 B I 1 \u00a9 (6) Input: training set \u00a1 \u00a3 \u00a2 \u00a4 \u00a5 \u00a6 \u00a2 \u00a7 sorted in ascending order of \u00a1 \u00a2 Initialize \u00a9 \u00a2 \u00a5 \u00a6 \u00a2 While k such that \u00a9 \u00a4 \u00a4 \u00a9 \u00a2 ! \u00a9 \u00a2 \u00a4 \u00a4 \u00a9 \"",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": ", where",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "\u00a9 # # # \u00a9 \u00a2 and \u00a9 \u00a2 # # # \u00a9 \" % $ ' & ) ( 1 0 ) 2 3 \u00a7 Set 4 6 5 7 9 8 @ B A 7 \" C Replace \u00a9 \u00a4 D \u00a4 \u00a9 \"",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "with m . Hence, using an algorithm which gives well calibrated probabilities helps in the estimation of sense priors.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Being Well Calibrated Helps Estimation",
"sec_num": "3.2"
},
{
"text": "Zadrozny and Elkan (2002) successfully used a method based on isotonic regression (Robertson et al., 1988) to calibrate the probability estimates from naive Bayes. To compute the isotonic regression, they used the pair-adjacent violators (PAV) (Ayer et al., 1955) algorithm, which we show in Figure 1 . Briefly, what PAV does is to initially view each data value as a level set. While there are two adjacent sets that are out of order (i.e., the left level set is above the right one) then the sets are combined and the mean of the data values becomes the value of the new level set.",
"cite_spans": [
{
"start": 82,
"end": 106,
"text": "(Robertson et al., 1988)",
"ref_id": "BIBREF15"
},
{
"start": 244,
"end": 263,
"text": "(Ayer et al., 1955)",
"ref_id": "BIBREF1"
}
],
"ref_spans": [
{
"start": 292,
"end": 300,
"text": "Figure 1",
"ref_id": null
}
],
"eq_spans": [],
"section": "Isotonic Regression",
"sec_num": "3.3"
},
{
"text": "PAV works on binary class problems. In a binary class problem, we have a positive class and a negative class. Now, let Figure 1 ) is associated with a lowest boundary value and a highest boundary value",
"cite_spans": [],
"ref_spans": [
{
"start": 119,
"end": 127,
"text": "Figure 1",
"ref_id": null
}
],
"eq_spans": [],
"section": "Isotonic Regression",
"sec_num": "3.3"
},
{
"text": "E \u00a1 \u00a4 \u00a2 \u00a4 G F I H P F , where \u00a2 \u00a3 \u00a5 \u00a4 \u00a7 \u00a6 \u00a6 \u00a7 \u00a6 \u00a9 \u00a4 \u00a2 represent N",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Isotonic Regression",
"sec_num": "3.3"
},
{
"text": ". We performed 10-fold crossvalidation on the training data to assign values to . We then applied the PAV algorithm to obtain values for T",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "S",
"sec_num": null
},
{
"text": ". To obtain the calibrated probability estimate for a test instance as the calibrated probability estimate. To apply PAV on a multiclass problem, we first reduce the problem into a number of binary class problems. For reducing a multiclass problem into a set of binary class problems, experiments in (Zadrozny and Elkan, 2002) suggest that the oneagainst-all approach works well. In one-againstall, a separate classifier is trained for each class is then learnt for each binary class problem and the probability estimates from each classifier are calibrated. Finally, the calibrated binary-class probability estimates are combined to obtain multiclass probabilities, computed by a simple normalization of the calibrated estimates from each binary classifier, as suggested by Zadrozny and Elkan (2002) .",
"cite_spans": [
{
"start": 300,
"end": 326,
"text": "(Zadrozny and Elkan, 2002)",
"ref_id": "BIBREF18"
},
{
"start": 775,
"end": 800,
"text": "Zadrozny and Elkan (2002)",
"ref_id": "BIBREF18"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "S",
"sec_num": null
},
{
"text": "In this section, we discuss the motivations in choosing the particular corpora and the set of words used in our experiments.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Selection of Dataset",
"sec_num": "4"
},
{
"text": "The DSO corpus (Ng and Lee, 1996) contains 192,800 annotated examples for 121 nouns and 70 verbs, drawn from BC and WSJ. BC was built as a balanced corpus and contains texts in various categories such as religion, fiction, etc. In contrast, the focus of the WSJ corpus is on financial and business news. Escudero et al. (2000) exploited the difference in coverage between these two corpora to separate the DSO corpus into its BC and WSJ parts for investigating the domain dependence of several WSD algorithms. Following their setup, we also use the DSO corpus in our experiments.",
"cite_spans": [
{
"start": 23,
"end": 33,
"text": "Lee, 1996)",
"ref_id": "BIBREF12"
},
{
"start": 304,
"end": 326,
"text": "Escudero et al. (2000)",
"ref_id": "BIBREF5"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "DSO Corpus",
"sec_num": "4.1"
},
{
"text": "The widely used SEMCOR (SC) corpus (Miller et al., 1994) is one of the few currently available manually sense-annotated corpora for WSD. SEMCOR is a subset of BC. Since BC is a balanced corpus, and training a classifier on a general corpus before applying it to a more specific corpus is a natural scenario, we will use examples from BC as training data, and examples from WSJ as evaluation data, or the target dataset.",
"cite_spans": [
{
"start": 35,
"end": 56,
"text": "(Miller et al., 1994)",
"ref_id": "BIBREF10"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "DSO Corpus",
"sec_num": "4.1"
},
{
"text": "Scalability is a problem faced by current supervised WSD systems, as they usually rely on manually annotated data for training. To tackle this problem, in one of our recent work (Ng et al., 2003) , we had gathered training data from parallel texts and obtained encouraging results in our evaluation on the nouns of SENSEVAL-2 English lexical sample task (Kilgarriff, 2001) . In another recent evaluation on the nouns of SENSEVAL-2 English all-words task (Chan and Ng, 2005a), promising results were also achieved using examples gathered from parallel texts. Due to the potential of parallel texts in addressing the issue of scalability, we also drew training data for our earlier sense priors estimation experiments (Chan and Ng, 2005b) from parallel texts. In addition, our parallel texts training data represents a natural domain difference with the test data of SENSEVAL-2 English lexical sample task, of which 91% is drawn from the British National Corpus (BNC).",
"cite_spans": [
{
"start": 178,
"end": 195,
"text": "(Ng et al., 2003)",
"ref_id": "BIBREF13"
},
{
"start": 354,
"end": 372,
"text": "(Kilgarriff, 2001)",
"ref_id": "BIBREF6"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Parallel Texts",
"sec_num": "4.2"
},
{
"text": "As part of our experiments, we followed the experimental setup of our earlier work (Chan and Ng, 2005b) , using the same 6 English-Chinese parallel corpora (Hong Kong Hansards, Hong Kong News, Hong Kong Laws, Sinorama, Xinhua News, and English translation of Chinese Treebank) , available from Linguistic Data Consortium. To gather training examples from these parallel texts, we used the approach we described in (Ng et al., 2003) and (Chan and Ng, 2005b) . We then evaluated our estimation of sense priors on the nouns of SENSEVAL-2 English lexical sample task, similar to the evaluation we conducted in (Chan and Ng, 2005b) . Since the test data for the nouns of SENSEVAL-3 English lexical sample task (Mihalcea et al., 2004) were also drawn from BNC and represented a difference in domain from the parallel texts we used, we also expanded our evaluation to these SENSEVAL-3 nouns.",
"cite_spans": [
{
"start": 83,
"end": 103,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
},
{
"start": 156,
"end": 276,
"text": "(Hong Kong Hansards, Hong Kong News, Hong Kong Laws, Sinorama, Xinhua News, and English translation of Chinese Treebank)",
"ref_id": null
},
{
"start": 414,
"end": 431,
"text": "(Ng et al., 2003)",
"ref_id": "BIBREF13"
},
{
"start": 436,
"end": 456,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
},
{
"start": 606,
"end": 626,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
},
{
"start": 705,
"end": 728,
"text": "(Mihalcea et al., 2004)",
"ref_id": "BIBREF9"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Parallel Texts",
"sec_num": "4.2"
},
{
"text": "Research by (McCarthy et al., 2004) highlighted that the sense priors of a word in a corpus depend on the domain from which the corpus is drawn. A change of predominant sense is often indicative of a change in domain, as different corpora drawn from different domains usually give different predominant senses. For example, the predominant sense of the noun interest in the BC part of the DSO corpus has the meaning \"a sense of concern with and curiosity about someone or something\". In the WSJ part of the DSO corpus, the noun interest has a different predominant sense with the meaning \"a fixed charge for borrowing money\", reflecting the business and finance focus of the WSJ corpus.",
"cite_spans": [
{
"start": 12,
"end": 35,
"text": "(McCarthy et al., 2004)",
"ref_id": "BIBREF8"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Choice of Words",
"sec_num": "4.3"
},
{
"text": "Estimation of sense priors is important when there is a significant change in sense priors between the training and target dataset, such as when there is a change in domain between the datasets. Hence, in our experiments involving the DSO corpus, we focused on the set of nouns and verbs which had different predominant senses between the BC and WSJ parts of the corpus. This gave us a set of 37 nouns and 28 verbs. For experiments involving the nouns of SENSEVAL-2 and SENSEVAL-3 English lexical sample task, we used the approach we described in (Chan and Ng, 2005b) of sampling training examples from the parallel texts using the natural (empirical) distribution of examples in the parallel texts. Then, we focused on the set of nouns having different predominant senses between the examples gathered from parallel texts and the evaluation data for the two SENSEVAL tasks. This gave a set of 6 nouns for SENSEVAL-2 and 9 nouns for SENSEVAL-3. For each noun, we gathered a maximum of 500 parallel text examples as training data, similar to what we had done in (Chan and Ng, 2005b) .",
"cite_spans": [
{
"start": 547,
"end": 567,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
},
{
"start": 1061,
"end": 1081,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Choice of Words",
"sec_num": "4.3"
},
{
"text": "Similar to our previous work (Chan and Ng, 2005b), we used the supervised WSD approach described in (Lee and Ng, 2002) for our experiments, using the naive Bayes algorithm as our classifier. Knowledge sources used include partsof-speech, surrounding words, and local collocations. This approach achieves state-of-the-art accuracy. All accuracies reported in our experiments are micro-averages over all test examples.",
"cite_spans": [
{
"start": 100,
"end": 118,
"text": "(Lee and Ng, 2002)",
"ref_id": "BIBREF7"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "In (Chan and Ng, 2005b), we used a multiclass naive Bayes classifier (denoted by NB) for each word. Following this approach, we noted the WSD accuracies achieved without any adjustment, in the column L under NB in Table 1 . The predictions",
"cite_spans": [],
"ref_spans": [
{
"start": 214,
"end": 221,
"text": "Table 1",
"ref_id": "TABREF1"
}
],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "8 \u00a1 9 ' & 1 \u00a2",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "of these naive Bayes classifiers are then used in Equation 2and (3) to estimate the sense priors 8 \u00a1 9 ' & , before being adjusted by these estimated sense priors based on Equation (4). The resulting WSD accuracies after adjustment are listed in the column EM \u00a1 in Table 1 , representing the WSD accuracies achievable by following the approach we described in (Chan and Ng, 2005b) .",
"cite_spans": [
{
"start": 360,
"end": 380,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [
{
"start": 265,
"end": 272,
"text": "Table 1",
"ref_id": "TABREF1"
}
],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "Next, we used the one-against-all approach to reduce each multiclass problem into a set of binary class problems. We trained a naive Bayes classifier for each binary problem and calibrated the probabilities from these binary classifiers. The WSD ",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "Classifier NB NBcal Method L EM \u00a2 \u00a1 EM \u00a3 A \u00a4 L EM \u00a2 \u00a1 \u00a5 \u00a7 \u00a6 \" EM \u00a3 A \u00a4 DSO",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "\u00a2 \u00a1 \u00a5 \u00a7 \u00a6 \" L EM \u00a3 A \u00a4 L DSO nouns",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "11.6 1.2 (10.3%) 5.3 (45.7%) DSO verbs 10.3 2.6 (25.2%) 3.9 (37.9%) SE2 nouns 3.0 0.9 (30.0%) 1.2 (40.0%) SE3 nouns 3.7 3.4 (91.9%) 3.0 (81.1%) The results show that calibrating the probabilities improves WSD accuracy. In particular, EM \u00a1 \u00a9 S achieves the highest accuracy among the methods described so far. To provide a basis for comparison, we also adjusted the calibrated probabilities by the true sense priors Table 2 . Note that this represents the maximum possible increase in accuracy achievable provided we know these true sense priors ",
"cite_spans": [],
"ref_spans": [
{
"start": 415,
"end": 423,
"text": "Table 2",
"ref_id": "TABREF2"
}
],
"eq_spans": [],
"section": "Experimental Results",
"sec_num": "5"
},
{
"text": "The experimental results show that the sense priors estimated using the calibrated probabilities of naive Bayes are effective in increasing the WSD accuracy. However, using a learning algorithm which already gives well calibrated posterior probabilities may be more effective in estimating the sense priors. One possible algorithm is logistic regression, which directly optimizes for getting approximations of the posterior probabilities. Hence, its probability estimates are already well calibrated (Zhang and Yang, 2004; Niculescu-Mizil and Caruana, 2005) .",
"cite_spans": [
{
"start": 500,
"end": 522,
"text": "(Zhang and Yang, 2004;",
"ref_id": "BIBREF19"
},
{
"start": 523,
"end": 557,
"text": "Niculescu-Mizil and Caruana, 2005)",
"ref_id": "BIBREF14"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Discussion",
"sec_num": "6"
},
{
"text": "In the rest of this section, we first conduct experiments to estimate sense priors using the predictions of logistic regression. Then, we perform significance tests to compare the various methods.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Discussion",
"sec_num": "6"
},
{
"text": "We trained logistic regression classifiers and evaluated them on the 4 datasets. However, the WSD accuracies of these unadjusted logistic regression classifiers are on average about 4% lower than those of the unadjusted naive Bayes classifiers. One possible reason is that being a discriminative learner, logistic regression requires more training examples for its performance to catch up to, and possibly overtake the generative naive Bayes learner (Ng and Jordan, 2001) .",
"cite_spans": [
{
"start": 450,
"end": 471,
"text": "(Ng and Jordan, 2001)",
"ref_id": "BIBREF11"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "Although the accuracy of logistic regression as a basic classifier is lower than that of naive Bayes, its predictions may still be suitable for estimating sense priors. To gauge how well the sense priors are estimated, we measure the KL divergence between the true sense priors and the sense priors estimated by using the predictions of (uncalibrated) multiclass naive Bayes, calibrated naive Bayes, and logistic regression. These results are shown in Table 3 and the column EM",
"cite_spans": [],
"ref_spans": [
{
"start": 452,
"end": 459,
"text": "Table 3",
"ref_id": "TABREF4"
}
],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "\u00a3 A \u00a4 vs. NB-EM \u00a2 \u00a1 NBcal-EM \u00a1 \u00a5 \u00a7 \u00a6 \" vs. NB-EM \u00a2 \u00a1 \u00a1 NBcal-EM \u00a1 \u00a5 \u00a7 \u00a6 \" vs. NB-EM \u00a3 A \u00a4 \u00a1 \u00a1 NBcal-EM \u00a3 A \u00a4 vs. NB-EM \u00a2 \u00a1 NBcal-EM \u00a3 A \u00a4 vs. NB-EM \u00a3 A \u00a4 \u00a1 NBcal-EM \u00a3 A \u00a4 vs. NBcal-EM \u00a2 \u00a1 \u00a5 \u00a7 \u00a6 \" \u00a1 \u00a1",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "\u00a2 \u00a4 \u00a3 \u00a5",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "shows that using the predictions of logistic regression to estimate sense priors consistently gives the lowest KL divergence.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "Results of the KL divergence test motivate us to use sense priors estimated by logistic regression on the predictions of the naive Bayes classifiers. To elaborate, we first use the probability estimates under NB. The relative improvements against using the true sense priors, based on the calibrated probabilities, are given in the column EM Table 2 . The results show that the sense priors provided by logistic regression are in general effective in further improving the results. In the case of DSO nouns, this improvement is especially significant.",
"cite_spans": [],
"ref_spans": [
{
"start": 342,
"end": 349,
"text": "Table 2",
"ref_id": "TABREF2"
}
],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "\u00a2 \u00a6 \u00a3 \u00a5 L in",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Using Logistic Regression",
"sec_num": "6.1"
},
{
"text": "Paired t-tests were conducted to see if one method is significantly better than another. The t statistic of the difference between each test instance pair is computed, giving rise to a p value. The results of significance tests for the various methods on the 4 datasets are given in Table 4 , where the symbols \" \u00a7 \", \"\u00a8\", and \"\u00a9 \" correspond to p-value\u00a80.05, (0.01, 0.05], and F 0.01 respectively. The methods in Table 4 are represented in the form a1-a2, where a1 denotes adjusting the pre-dictions of which classifier, and a2 denotes how the sense priors are estimated. As an example, NBcal-EM \u00a2 \u00a4 \u00a3 \u00a5 specifies that the sense priors estimated by logistic regression is used to adjust the predictions of the calibrated naive Bayes classifier, and corresponds to accuracies in column EM",
"cite_spans": [],
"ref_spans": [
{
"start": 283,
"end": 290,
"text": "Table 4",
"ref_id": "TABREF6"
},
{
"start": 414,
"end": 421,
"text": "Table 4",
"ref_id": "TABREF6"
}
],
"eq_spans": [],
"section": "Significance Test",
"sec_num": "6.2"
},
{
"text": "\u00a2 \u00a4 \u00a3 \u00a5",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Significance Test",
"sec_num": "6.2"
},
{
"text": "under NBcal in Table 1 . Based on the significance tests, the adjusted accuracies of EM \u00a1 and EM \u00a1 \u00a9 S in Table 1 are significantly better than their respective unadjusted L accuracies, indicating that estimating the sense priors of a new domain via the EM approach presented in this paper significantly improves WSD accuracy compared to just using the sense priors from the old domain.",
"cite_spans": [],
"ref_spans": [
{
"start": 15,
"end": 22,
"text": "Table 1",
"ref_id": "TABREF1"
},
{
"start": 106,
"end": 113,
"text": "Table 1",
"ref_id": "TABREF1"
}
],
"eq_spans": [],
"section": "Significance Test",
"sec_num": "6.2"
},
{
"text": "represents our earlier approach in (Chan and Ng, 2005b) . The significance tests show that our current approach of using calibrated naive Bayes probabilities to estimate sense priors, and then adjusting the calibrated probabilities by these estimates (NBcal-EM \u00a1 \u00a9 S ) performs significantly better than NB-EM \u00a1 (refer to row 2 of Table 4 ). For DSO nouns, though the results are similar, the p value is a relatively low 0.06.",
"cite_spans": [
{
"start": 35,
"end": 55,
"text": "(Chan and Ng, 2005b)",
"ref_id": "BIBREF3"
}
],
"ref_spans": [
{
"start": 331,
"end": 338,
"text": "Table 4",
"ref_id": "TABREF6"
}
],
"eq_spans": [],
"section": "\u00a1",
"sec_num": null
},
{
"text": "Using sense priors estimated by logistic regression further improves performance. For example, row 1 of Table 4 shows that adjusting the predictions of multiclass naive Bayes classifiers by sense priors estimated by logistic regression (NB-EM \u00a2 \u00a4 \u00a3 \u00a5 ) performs significantly better than using sense priors estimated by multiclass naive Bayes (NB-EM \u00a1 ). Finally, using sense priors estimated by logistic regression to adjust the predictions of calibrated naive Bayes (NBcal-EM \u00a2 \u00a4 \u00a3 \u00a5 ) in general performs significantly better than most other methods, achieving the best overall performance.",
"cite_spans": [],
"ref_spans": [
{
"start": 104,
"end": 111,
"text": "Table 4",
"ref_id": "TABREF6"
}
],
"eq_spans": [],
"section": "\u00a1",
"sec_num": null
},
{
"text": "In addition, we implemented the unsupervised method of (McCarthy et al., 2004) , which calculates a prevalence score for each sense of a word to predict the predominant sense. As in our earlier work (Chan and Ng, 2005b), we normalized the prevalence score of each sense to obtain estimated sense priors for each word, which we then used to adjust the predictions of our naive Bayes classifiers. We found that the WSD accuracies obtained with the method of (McCarthy et al., 2004) are on average 1.9% lower than our NBcal-EM \u00a2 \u00a4 \u00a3 \u00a5 method, and the difference is statistically significant.",
"cite_spans": [
{
"start": 55,
"end": 78,
"text": "(McCarthy et al., 2004)",
"ref_id": "BIBREF8"
},
{
"start": 456,
"end": 479,
"text": "(McCarthy et al., 2004)",
"ref_id": "BIBREF8"
}
],
"ref_spans": [],
"eq_spans": [],
"section": "\u00a1",
"sec_num": null
},
{
"text": "Differences in sense priors between training and target domain datasets will result in a loss of WSD accuracy. In this paper, we show that using well calibrated probabilities to estimate sense priors is important. By calibrating the probabilities of the naive Bayes algorithm, and using the probabilities given by logistic regression (which is already well calibrated), we achieved significant improvements in WSD accuracy over previous approaches.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "Conclusion",
"sec_num": "7"
},
{
"text": "Though not shown, we also calculated the accuracies of these binary classifiers without calibration, and found them to be similar to the accuracies of the multiclass naive Bayes shown in the column L under NB inTable 1.",
"cite_spans": [],
"ref_spans": [],
"eq_spans": [],
"section": "",
"sec_num": null
}
],
"back_matter": [],
"bib_entries": {
"BIBREF0": {
"ref_id": "b0",
"title": "Unsupervised WSD based on automatically retrieved examples: The importance of bias",
"authors": [
{
"first": "Eneko",
"middle": [],
"last": "Agirre",
"suffix": ""
},
{
"first": "David",
"middle": [],
"last": "Martinez",
"suffix": ""
}
],
"year": 2004,
"venue": "Proc. of EMNLP04",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Eneko Agirre and David Martinez. 2004. Unsuper- vised WSD based on automatically retrieved exam- ples: The importance of bias. In Proc. of EMNLP04.",
"links": null
},
"BIBREF1": {
"ref_id": "b1",
"title": "An empirical distribution function for sampling with incomplete information",
"authors": [
{
"first": "Miriam",
"middle": [],
"last": "Ayer",
"suffix": ""
},
{
"first": "H",
"middle": [
"D"
],
"last": "Brunk",
"suffix": ""
},
{
"first": "G",
"middle": [
"M"
],
"last": "Ewing",
"suffix": ""
},
{
"first": "W",
"middle": [
"T"
],
"last": "Reid",
"suffix": ""
},
{
"first": "Edward",
"middle": [],
"last": "Silverman",
"suffix": ""
}
],
"year": 1955,
"venue": "Annals of Mathematical Statistics",
"volume": "26",
"issue": "4",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Miriam Ayer, H. D. Brunk, G. M. Ewing, W. T. Reid, and Edward Silverman. 1955. An empirical distri- bution function for sampling with incomplete infor- mation. Annals of Mathematical Statistics, 26(4).",
"links": null
},
"BIBREF2": {
"ref_id": "b2",
"title": "Scaling up word sense disambiguation via parallel texts",
"authors": [
{
"first": "Yee",
"middle": [],
"last": "Seng Chan",
"suffix": ""
},
{
"first": "Hwee Tou",
"middle": [],
"last": "Ng",
"suffix": ""
}
],
"year": 2005,
"venue": "Proc. of AAAI05",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Yee Seng Chan and Hwee Tou Ng. 2005a. Scaling up word sense disambiguation via parallel texts. In Proc. of AAAI05.",
"links": null
},
"BIBREF3": {
"ref_id": "b3",
"title": "Word sense disambiguation with distribution estimation",
"authors": [
{
"first": "Yee",
"middle": [],
"last": "Seng Chan",
"suffix": ""
},
{
"first": "Hwee Tou",
"middle": [],
"last": "Ng",
"suffix": ""
}
],
"year": 2005,
"venue": "Proc. of IJCAI05",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Yee Seng Chan and Hwee Tou Ng. 2005b. Word sense disambiguation with distribution estimation. In Proc. of IJCAI05.",
"links": null
},
"BIBREF4": {
"ref_id": "b4",
"title": "Beyond independence: Conditions for the optimality of the simple Bayesian classifier",
"authors": [
{
"first": "Pedro",
"middle": [],
"last": "Domingos",
"suffix": ""
},
{
"first": "Michael",
"middle": [],
"last": "Pazzani",
"suffix": ""
}
],
"year": 1996,
"venue": "Proc. of ICML",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Pedro Domingos and Michael Pazzani. 1996. Beyond independence: Conditions for the optimality of the simple Bayesian classifier. In Proc. of ICML-1996.",
"links": null
},
"BIBREF5": {
"ref_id": "b5",
"title": "An empirical study of the domain dependence of supervised word sense disambiguation systems",
"authors": [
{
"first": "Gerard",
"middle": [],
"last": "Escudero",
"suffix": ""
},
{
"first": "Lluis",
"middle": [],
"last": "Marquez",
"suffix": ""
},
{
"first": "German",
"middle": [],
"last": "Rigau",
"suffix": ""
}
],
"year": 2000,
"venue": "Proc. of EMNLP/VLC00",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Gerard Escudero, Lluis Marquez, and German Rigau. 2000. An empirical study of the domain dependence of supervised word sense disambiguation systems. In Proc. of EMNLP/VLC00.",
"links": null
},
"BIBREF6": {
"ref_id": "b6",
"title": "English lexical sample task description",
"authors": [
{
"first": "Adam",
"middle": [],
"last": "Kilgarriff",
"suffix": ""
}
],
"year": 2001,
"venue": "Proc. of SENSEVAL-2",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Adam Kilgarriff. 2001. English lexical sample task description. In Proc. of SENSEVAL-2.",
"links": null
},
"BIBREF7": {
"ref_id": "b7",
"title": "An empirical evaluation of knowledge sources and learning algorithms for word sense disambiguation",
"authors": [
{
"first": "Yoong Keok",
"middle": [],
"last": "Lee",
"suffix": ""
},
{
"first": "Hwee Tou",
"middle": [],
"last": "Ng",
"suffix": ""
}
],
"year": 2002,
"venue": "Proc. of EMNLP02",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Yoong Keok Lee and Hwee Tou Ng. 2002. An empir- ical evaluation of knowledge sources and learning algorithms for word sense disambiguation. In Proc. of EMNLP02.",
"links": null
},
"BIBREF8": {
"ref_id": "b8",
"title": "Finding predominant word senses in untagged text",
"authors": [
{
"first": "Diana",
"middle": [],
"last": "Mccarthy",
"suffix": ""
},
{
"first": "Rob",
"middle": [],
"last": "Koeling",
"suffix": ""
},
{
"first": "Julie",
"middle": [],
"last": "Weeds",
"suffix": ""
},
{
"first": "John",
"middle": [],
"last": "Carroll",
"suffix": ""
}
],
"year": 2004,
"venue": "Proc. of ACL04",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Diana McCarthy, Rob Koeling, Julie Weeds, and John Carroll. 2004. Finding predominant word senses in untagged text. In Proc. of ACL04.",
"links": null
},
"BIBREF9": {
"ref_id": "b9",
"title": "The senseval-3 english lexical sample task",
"authors": [
{
"first": "Rada",
"middle": [],
"last": "Mihalcea",
"suffix": ""
},
{
"first": "Timothy",
"middle": [],
"last": "Chklovski",
"suffix": ""
},
{
"first": "Adam",
"middle": [],
"last": "Kilgarriff",
"suffix": ""
}
],
"year": 2004,
"venue": "Proc. of SENSEVAL-3",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Rada Mihalcea, Timothy Chklovski, and Adam Kilgar- riff. 2004. The senseval-3 english lexical sample task. In Proc. of SENSEVAL-3.",
"links": null
},
"BIBREF10": {
"ref_id": "b10",
"title": "Using a semantic concordance for sense identification",
"authors": [
{
"first": "George",
"middle": [
"A"
],
"last": "Miller",
"suffix": ""
},
{
"first": "Martin",
"middle": [],
"last": "Chodorow",
"suffix": ""
},
{
"first": "Shari",
"middle": [],
"last": "Landes",
"suffix": ""
},
{
"first": "Claudia",
"middle": [],
"last": "Leacock",
"suffix": ""
},
{
"first": "Robert",
"middle": [
"G"
],
"last": "Thomas",
"suffix": ""
}
],
"year": 1994,
"venue": "Proc. of ARPA Human Language Technology Workshop",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "George A. Miller, Martin Chodorow, Shari Landes, Claudia Leacock, and Robert G. Thomas. 1994. Using a semantic concordance for sense identifica- tion. In Proc. of ARPA Human Language Technol- ogy Workshop.",
"links": null
},
"BIBREF11": {
"ref_id": "b11",
"title": "On discriminative vs. generative classifiers: A comparison of logistic regression and naive Bayes",
"authors": [
{
"first": "Y",
"middle": [],
"last": "Andrew",
"suffix": ""
},
{
"first": "Michael",
"middle": [
"I"
],
"last": "Ng",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Jordan",
"suffix": ""
}
],
"year": 2001,
"venue": "Proc. of NIPS14",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Andrew Y. Ng and Michael I. Jordan. 2001. On dis- criminative vs. generative classifiers: A comparison of logistic regression and naive Bayes. In Proc. of NIPS14.",
"links": null
},
"BIBREF12": {
"ref_id": "b12",
"title": "Integrating multiple knowledge sources to disambiguate word sense: An exemplar-based approach",
"authors": [
{
"first": "Tou",
"middle": [],
"last": "Hwee",
"suffix": ""
},
{
"first": "Hian Beng",
"middle": [],
"last": "Ng",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Lee",
"suffix": ""
}
],
"year": 1996,
"venue": "Proc. of ACL96",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Hwee Tou Ng and Hian Beng Lee. 1996. Integrating multiple knowledge sources to disambiguate word sense: An exemplar-based approach. In Proc. of ACL96.",
"links": null
},
"BIBREF13": {
"ref_id": "b13",
"title": "Exploiting parallel texts for word sense disambiguation: An empirical study",
"authors": [
{
"first": "Bin",
"middle": [],
"last": "Hwee Tou Ng",
"suffix": ""
},
{
"first": "Yee Seng",
"middle": [],
"last": "Wang",
"suffix": ""
},
{
"first": "",
"middle": [],
"last": "Chan",
"suffix": ""
}
],
"year": 2003,
"venue": "Proc. of ACL03",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Hwee Tou Ng, Bin Wang, and Yee Seng Chan. 2003. Exploiting parallel texts for word sense disambigua- tion: An empirical study. In Proc. of ACL03.",
"links": null
},
"BIBREF14": {
"ref_id": "b14",
"title": "Predicting good probabilities with supervised learning",
"authors": [
{
"first": "Alexandru",
"middle": [],
"last": "Niculescu",
"suffix": ""
},
{
"first": "-",
"middle": [],
"last": "Mizil",
"suffix": ""
},
{
"first": "Rich",
"middle": [],
"last": "Caruana",
"suffix": ""
}
],
"year": 2005,
"venue": "Proc. of ICML05",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Alexandru Niculescu-Mizil and Rich Caruana. 2005. Predicting good probabilities with supervised learn- ing. In Proc. of ICML05.",
"links": null
},
"BIBREF15": {
"ref_id": "b15",
"title": "Chapter 1. Isotonic Regression",
"authors": [
{
"first": "Tim",
"middle": [],
"last": "Robertson",
"suffix": ""
},
{
"first": "F",
"middle": [
"T"
],
"last": "Wright",
"suffix": ""
},
{
"first": "R",
"middle": [
"L"
],
"last": "Dykstra",
"suffix": ""
}
],
"year": 1988,
"venue": "Order Restricted Statistical Inference",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Tim Robertson, F. T. Wright, and R. L. Dykstra. 1988. Chapter 1. Isotonic Regression. In Order Restricted Statistical Inference. John Wiley & Sons.",
"links": null
},
"BIBREF16": {
"ref_id": "b16",
"title": "Adjusting the outputs of a classifier to new a priori probabilities: A simple procedure",
"authors": [
{
"first": "Marco",
"middle": [],
"last": "Saerens",
"suffix": ""
},
{
"first": "Patrice",
"middle": [],
"last": "Latinne",
"suffix": ""
},
{
"first": "Christine",
"middle": [],
"last": "Decaestecker",
"suffix": ""
}
],
"year": 2002,
"venue": "Neural Computation",
"volume": "",
"issue": "1",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Marco Saerens, Patrice Latinne, and Christine De- caestecker. 2002. Adjusting the outputs of a clas- sifier to new a priori probabilities: A simple proce- dure. Neural Computation, 14(1).",
"links": null
},
"BIBREF17": {
"ref_id": "b17",
"title": "Classification on data with biased class distribution",
"authors": [
{
"first": "Slobodan",
"middle": [],
"last": "Vucetic",
"suffix": ""
},
{
"first": "Zoran",
"middle": [],
"last": "Obradovic",
"suffix": ""
}
],
"year": 2001,
"venue": "Proc. of ECML01",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Slobodan Vucetic and Zoran Obradovic. 2001. Clas- sification on data with biased class distribution. In Proc. of ECML01.",
"links": null
},
"BIBREF18": {
"ref_id": "b18",
"title": "Transforming classifier scores into accurate multiclass probability estimates",
"authors": [
{
"first": "Bianca",
"middle": [],
"last": "Zadrozny",
"suffix": ""
},
{
"first": "Charles",
"middle": [],
"last": "Elkan",
"suffix": ""
}
],
"year": 2002,
"venue": "Proc. of KDD02",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Bianca Zadrozny and Charles Elkan. 2002. Trans- forming classifier scores into accurate multiclass probability estimates. In Proc. of KDD02.",
"links": null
},
"BIBREF19": {
"ref_id": "b19",
"title": "Probabilistic score estimation with piecewise logistic regression",
"authors": [
{
"first": "Jian",
"middle": [],
"last": "Zhang",
"suffix": ""
},
{
"first": "Yiming",
"middle": [],
"last": "Yang",
"suffix": ""
}
],
"year": 2004,
"venue": "Proc. of ICML04",
"volume": "",
"issue": "",
"pages": "",
"other_ids": {},
"num": null,
"urls": [],
"raw_text": "Jian Zhang and Yiming Yang. 2004. Probabilistic score estimation with piecewise logistic regression. In Proc. of ICML04.",
"links": null
}
},
"ref_entries": {
"FIGREF1": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "timates of the new a priori and a posteriori probabilities at step s of the iterative EM procedure. Assuming we initialize"
},
"FIGREF2": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "step s in Equation(2)are simply the a posteriori probabilities in the conditions of the labeled data,"
},
"FIGREF4": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "the set of posterior probability values for class imagine that we have Q bins, where each bin is associated with a specific 0 value. Now, distribute all the instances in the new dataset D@ into the"
},
"FIGREF6": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "the proportion of instances in D@ with true class label ' &"
},
"FIGREF7": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "examples and is the probability of \u00a2 belonging to the positive class, as predicted by a classifier. Further, let Q represent the true label of \u00a2 . For a binary class problem, we let Q"
},
"FIGREF9": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "and all other examples are treated as negative examples. A separate classifier"
},
"FIGREF10": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "data. The increase in WSD accuracy thus obtained is given in the column True L in"
},
"FIGREF12": {
"type_str": "figure",
"uris": null,
"num": null,
"text": "Bayes classifier are then used in Equation (4) to obtain the adjusted predictions. The resulting WSD accuracy is shown in the column EM"
},
"TABREF1": {
"html": null,
"content": "<table><tr><td>Dataset</td><td>True\u00a8L EM</td></tr></table>",
"type_str": "table",
"num": null,
"text": "Micro-averaged WSD accuracies using the various methods. The different naive Bayes classifiers are: multiclass naive Bayes (NB) and naive Bayes with calibrated probabilities (NBcal)."
},
"TABREF2": {
"html": null,
"content": "<table><tr><td>: Relative accuracy improvement based on cali-</td></tr><tr><td>brated probabilities.</td></tr><tr><td>accuracies of these calibrated naive Bayes classi-</td></tr><tr><td>fiers (denoted by NBcal) are given in the column L</td></tr><tr><td>under NBcal. 1 The predictions of these classifiers &</td></tr><tr><td>are then used to estimate the sense priors before being adjusted by these estimates based on \u00a1 9 ' , 8</td></tr><tr><td>Equation (4). The resulting WSD accuracies after adjustment are listed in column EM \u00a1 \u00a9 in Table S 1.</td></tr></table>",
"type_str": "table",
"num": null,
"text": ""
},
"TABREF3": {
"html": null,
"content": "<table><tr><td>, we list the increase</td></tr><tr><td>in WSD accuracy when adjusted by the sense pri-&</td></tr><tr><td>ors ing the EM procedure. The relative improvements \u00a1 3 ' which were automatically estimated us-8 &</td></tr><tr><td>obtained with using & ing \u00a1 9 ' ) are given as percentages in brackets. \u00a1 3 ' (compared against us-8</td></tr><tr><td>As an example, according to Table 1 for the DSO verbs, EM \u00a1 \u00a9 gives an improvement of 49.5% S 46.9% = 2.6% in WSD accuracy, and the rela-</td></tr><tr><td>tive improvement compared to using the true sense</td></tr><tr><td>priors is 2.6/10.3 = 25.2%, as shown in Table 2.</td></tr></table>",
"type_str": "table",
"num": null,
"text": ""
},
"TABREF4": {
"html": null,
"content": "<table/>",
"type_str": "table",
"num": null,
"text": "KL divergence between the true and estimated sense distributions."
},
"TABREF6": {
"html": null,
"content": "<table/>",
"type_str": "table",
"num": null,
"text": "Paired t-tests between the various methods for the 4 datasets."
}
}
}
} |