10.1.1.66.9792

10.1.1.66.9792 - 6 4 0 T 2 B 0 E B 0 2 0 4 0 4 2 4 % i

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To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SIGIR'01, September 9-12, 2001, New Orleans, Louisiana, USA Copyright 2001 ACM 1-58113-331-6/01/0009 ... 5.00. % ) 0 6 E % $ 0 4 4 $ $ P 6 2 2 ) ) 2 E 2 3'FsXV39'&F"'t'H!!"u!!qbA3"AGD"0 2 E 0 ) % $ $ T c P 4 ) "!!X"9HA"d('3"fsW'35 gp om ) 4 ) % $ qW!'31&@! 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ABSTRACT INTRODUCTION School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 A Study of Smoothing Methods for Language Models Applied to Ad Hoc Information Retrieval Chengxiang Zhai School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 John Lafferty gp m q8y e! 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INTERPOLATION VS. BACKOFF 0.15 precision 0.35 0.3 recall 0.25 0.14 0.16 0.18 precision recall 0.6 0.7 0.8 0.22 0.24 0.26 0.28 0.1 0.2 0.4 0.2 0.3 0 0.2 Precision of Absolute Discounting (Large Collections) Precision of Absolute Discounting (Small Collections) 0.4 delta 0.6 0.8 1 fbis7T fbis8T ft7T ft8T la7T la8T fbis7L fbis8L ft7L ft8L la7L la8L 0.4 0.5 0.4 0.5 0.6 0.7 0.8 0 0.2 Recall of Absolute Discounting (Large Collections) Recall of Absolute Discounting (Small Collections) 0.4 delta 0.6 0.8 1 fbis7T fbis8T ft7T ft8T la7T la8T fbis7L fbis8L ft7L ft8L la7L la8L % % ) P % 4 2 2 0 4 2 6 4 ) i 0 4 4 0 4 2 4 B % 2 E 3'AW'AbS!D"!'sAQ33h3f'8'!v!''3A 4 2 % 4 g 0 ) % $ $ 0 4 4 4 % "!'b'3's!w5Shd('&"f"!!D"9Y'w!fs1AG$ P% B 2 2%4 % $ 04 2 6 442 4 % $% $ $ f9A3!a'3'31"R"!"'sAhR!'A3AQ'9''f" 42% 4 04 42 2 c2%4 % $ 04 "!&1b'd'!'b"AD'3'31""!'sA2 0 4 4 B 4 2 2 P % 2 ) % 6 % $ B % 4 % 0 4 4 0 "'w'f9'WAAeW!13D!#'7A3G!'A3'F"'D8'4 s d g 2 4 ) ) 4 2 4 B % 4 "Iu!'3!!p"!'b'h!'A3'% Y xSh!#AvD'9 i 2 % % B 2 2 0 4 4 B c 2 2 % B i u ) E % 0 4 2 13(Av"!A"'rH'8!C!A'3(u(1"YW"'f T 2 c z 4 ) 2 4 2 E c 2 % % $ 4 0 ) % c 0 4 !SQd("!'s"3A9&D'!At"'!'&fd9d!'WR&h'3 % ) % u v 2 0 4 0 4 2 2 E 4 $ % 4 % d'3ws"!!nY&"'3f!"'sA@A&!'9G'd'!f9 $ $ % 0 4 e 0 4 d g 4 % 0 4 4 "GD''#H"!3t"'RuS!'H!!#'"@'"!Vs ) 4 0 T ` ` i ) c 2 4 % &s"!'s!arBw"!"93"!r!&9'W&1A4 2 2) 42 % 0 % B2 6 2 % 4% $%4 E !kHA!'b!'p13(AF@'3'4 ! 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H8eep8$9eue j m w j k5ckxeXhf5kj xfx x m v%G vekkjvx jf m kCvkxkmq & ! @ 0 )1 5 @ !)1 F D 8EC $ " ( 0 9)1 'n )" 6n !1 " " & 4 v n v n v # # !! # 5 @ sD 'n 6n !)1 2 v n v n v P $ # # 5 s5 u x 8# o qy # 8" v % v 5 s# 6!#210 '#n A" n '% # v n# v n2 v s $ 5! s # u#fx 8$5C @ s 'n 6n !)1 v n44 v n 4 v s $ $ ## !! 3k u!fx "5C ( 4 & v n 85 s 6)3! !! 0v n ( v n4 v n v s $ e5# u# 8#m & ( 5 n" 0#v s# )! 6n )10 !e!5)0 # v n2 v n v s $ # $ u# 84" 00 "& s ! 'n !! 6n )1 # v n v n4 v P $ # e5 # u# 84kgj o s 67 'n ! 6|1 0% 0 n50 v n# v n2! v W $ "k u ! #m 0 ( & % s ! 'n 6n )' 2 v n" #v n 2 2 v s$ 3k !! #3k 4 u ! " s n # v # n v s # n n ! v "k u ! kgj o f n n fl e f n f n fle pH8ep8$9euf P 8ep8$9u Pe! j m w j k5ckxeXhf5kj xfx x m vv% vekkjvx jf m k5kxkmq @ % 0 'H1 )0 ! 0.05 0.15 0.25 0.35 0.1 precision precision precision 0.2 0.3 0.4 0 0 fbis8T fbis8T-bk fbis8L fbis8L-bk Precision of Interpolation vs. Backoff (Jelinek-Mercer) 0.2 0.4 lambda 0.6 0.8 1 0.05 0.15 0.25 0.35 0.1 0.2 0.3 0.4 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 prior Precision of Interpolation vs. Backoff (Dirichlet prior) 8. CONCLUSIONS AND FUTURE WORK g 0 2 A!9!&C!!VT 2 4 %42 T4 04 T4 E ) % i 04 c % 2 0) % $ $ !'81AbSg#'e3G#'3hWv"'U&'3F3"1('&" V8'l8fss!P!H!)'&WPf9AhH'dG&3!2#d!)VT 0 T 4 04 T u T c 4 ) 2 c 4) $ e 0 0 % 2 0 ) % $ $ 0 T 4 4 2 ) 2 ) P c P 4 % 4 c'33rd(' a"VWQ'A!hRW"Is'81Ab2 4 $ % 4 0 4 0 4 ) % 6 % $ 2 % T 2 B P 4 % 4 2 i !'9G'3's!Y"'t'R3"#'qA3GA'53(!t'81Abu u ) E 0 4 c % g 2 4 ) $ 2 2 B s1V'&y13"r'3"s&p!D"!!!"G#9A"3(!A2 2 % 0 4 2 4 ) %42 % 0 ) 0 T % 0 4 % 6 b'D'V'd9'Ab3'wd!Vc !9'R"'57z b X""GE v % $ $ % T 2 4 4 E P 2 0 4 c 0 4 W 4 dG""f3SH!p'Wr'f"&vGu#F!'uah"'dW "!'s"3) 2 4 2 E 0 4 4 ) s 2 2 2 P % ) 2 ) % i 0 b!p'!A"'!RsHW"!AIA!W'93I!p3"'3hW&FSi gH!'3!d!'WRF"3'3ws"!!w9FW99GAh!'9G'd'4 % % $ 4 0 ) % % ) % u P ) $ 2 c 4 $ % 6 4 04 04 %4 % $ 04 2 04 4 B 4 2 2 % !a5't'Qd'318f9'sAY'F'R(!'WA"AY' 2 ) % 6% $ i u ) E 0 4 4 0 4 s d g y % ` T 0 !R#'7A3GrdR'Q'#"IeU'&!C!@VHA2 % 2 4 2 % 0 i g z | 2 E6 i | 2 E6 cg g v y w o w 2 ) $ 4 '8V'!A'ISdr'!"7v'!"7! yy@(gd&Q!"'# 2 E4 A18" a` "'X"!A"&"'3'&'f!w7H'83) 0 4 2 2 0 4 % 0 4 % 6 % $ % P 4 % 4 2 4 $ % 4 0 4 P 4 % 4 2 i u ) E 0 '8'1Ab!'9G'd'!@'"3'1Abd@Si g 2 % B 4 $ % 4 $ 2 !A'3(wH'89G'3's!f"!&GA3'% % ) 0 4 0 4 P B 2 2 % % 4 % 0 4 4 A3F"'r"'r!3(!AA'f'u9'8H!!#'X'"!I3 ) 4 0 3su9's93ST '3'&'p"'!A'3((1"t'4 %4 4 2 4 2% B i u) E 0 T B y D IRRI g YR e B Iq Y dtt21 Cved$srvbTi WI F5qF 5 35 F I q0 1 b BbF5 e YR 3I WF5R e 8 5F B 9{R VrV5 TvevYtp 2IQ 9 9$w$Vs s6I2f09HVtd p HT9fgY a 7 Y ` X W fbis8T fbis8T-bk fbis8L fbis8L-bk 0.05 0.15 0.25 0.35 0.1 0.2 0.3 0.4 0 0 Precision of Interpolation vs. Backoff (Absolute Discounting) 0.2 0.4 delta 0.6 fbis8T fbis8T-bk fbis8L fbis8L-bk 0.8 1 REFERENCES # y 6 # !8 # v 2 2 v f "qWYI EDPrVWYI 9 I V f k#60 D#2 !vv)PGp5njhf kgkjkm j o o 5%5 F|88kxC5C%k5i 4 2e b 4x pf f 5nv kj n xx f w j y me jx j j l mx i o Skkkj!a% H n 2 2 x v x v x l D v v w 1 o Xs#3C 8dp & 4w &9 e 8e x n yj 4vv # g x ep l v D I S # A P#v C5w kg kjm ! 8 8 Di I BP 8s2 52 %9knx pvuP kx8kmkm e v dw n `HY``I EDG(aA X! #3CBTeWH Y DaXWf Y1I 43 v I vD # A { # gS f v 9 ! 8 # U S Q I % # HbD2aA v ef ! 2 A 8 HHDHWaV H DrGFnE6D! qtXen FDHDC78 @ &6 I f 4 2 0 ) ) ) ' %# ! keGXhW1eW"D kj w8kx5C56kC5kFD nm e j x j i j mx xl l m mx x !ai 8 p 8#R8Xvevl 6 Xs##3C%"85DqHqge8W I e 1 HDv! 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