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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SMOOTHING METHODS z t gv &X2x z 3 g S&5h2`v4d0 z t gv &D2x 2 4 ) B 4 % P E B 'sD(!'9'[email protected](! 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COMPARISON OF METHODS 0.15 precision 0.35 0.3 recall 0.25 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 0 500 1000 Precision of Dirichlet Prior (Large Collections) Precision of Dirichlet Prior (Small Collections) 1500 2000 2500 prior 3000 3500 4000 4500 5000 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 0 500 1000 Recall of Dirichlet Prior (Large Collections) Recall of Dirichlet Prior (Small Collections) 1500 2000 2500 prior 3000 3500 4000 4500 5000 fbis7T fbis8T ft7T ft8T la7T la8T fbis7L fbis8L ft7L ft8L la7L la8L 04 2 % T 2 04 6 24 ) 04 4 )2 T 0) 0 T '@R1A"'I's"'fA!&F1!"V! c 2 0 4 2 E 4 $ % 4 6 P % 4 ) 0 4 4 E % '3uHA!'9G'3's!SuA'8Hf't'w!Gq6 2 424 E %)2 B 0 T 4 04 2 04 % 04 0 [email protected]'b'wHG!'3AD8"pf8'Q'3D''YSi g P% x % 6 P% 9!&#A3"sI7tA8'2 2 ) 2 0 ) 0 T c 2 4 ) 2 2 % ) % 4 % $ 0 4 b3"I!r19V"'ssU!RA'3R3'd1"#"!"'sA2 e s 4 2 T c % ) % u 0 T c % 4 4 2 0 H&"D3ApShH3'3ws9!!F!!"Vh!'r!'8#9'b3p'4 % 6 E % 2 2 0 ) 0 T c P % 4 2 4 ) 6 0 4 0 4 7Y91WA&[email protected]!"V&s!!1'"Q's"s&'"!R'f'4 2 4 $ % % $ 4 0 ) % 2 c 2 2 2 u 2 2 0 4 P B 4 4 '&"f!'3!"1!'!IpUA"3AY(#rA!!"'rW(!'W"'sg g9!&wAd"sF!'D'IqsI!I3'3ws"!!j"'4 P % x 6 % 0 4 % 6 2 % ) % u 4 0 2 4 2 2 2 % x % 6 4 2 E 0 4 4 E c 2 % x 4 4 % 6 4 2 % 'b"A!'3"sp"97bGV"'!'3"sf!'!'7Sb'T 0 4 2 % 6 % $ % ) % u 4 0 4 4 ) 6 0 4 c % 4 'f'qA3GI3'3ws"!!j"'I3yD"'wh!'!'8# 4 2 0 4 % 6 2 4 4 0 4 2 4 2 2 2 % x 4 4 4 2 W'[email protected]'vqs#!#!f'#'b"A39'd"s!'W'#b3GE 0 4 2 % 6 % $ 0 4 % % $ 4 0 ) % 0 4 4 0 4 4 ) 6 0 4 c 2 0 ''7A3Gf"'dQ!'S3!"19'WR5"''3q5'&Si g1SX9'8#'7!#(H'`X3"'p76 2 % T ) B 4 % 6 P B 0 46 P 0 4 % P % x 6 % 0 4 P E ) % 2 4 ) i 0 "!!Ad"sSf!'D"'@sH""!'Y!R33h3F'4 c!'3"su"!v7H'3VS1Sw(!'8#'q&!g& 2 % x % 6 2 % 0 T c 2 % T ) B 4 % 6 % T 6 B 0 2 % x 4 4 0 4 2 4 % $ e % ) "t~3qw8"t39'd"sr!'!'@'f's!'3G&3v9r!A2 c!'!'8#9'b3Q"'f'!V'!33h3Q"'s!'3sx % 4 4 2 0 4 P E 4 % 2 4 ) i 0 4 c 2 % 4 4 % 6 c 4 g 0 4 2 6 2 % 0 4 E 6 4 ) i e !'W'tqQH& &"!"'sADt!''GDv3h3lH&We P % 2 B % 2 E T 4 0 4 0 4 2 6 4 ) i 0 W913"39 H('3AS8'!"'sA#3h3Si g2 % T ) 04 4% 4 &1S#R'D'813"3F'h& 4 ) ) 0 4 % P % T 2 4 ) 2 "9!'3!!3'D'YW's!9Vh's"3s!A") 3G"sA3"s"'!I&[email protected]'8!!'3A! 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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!"'[email protected]&!'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([email protected]'3'4 ! H'd''3's!eGH) 3I""9ss5"'hD9'sAV"'5'3"VI9F 4 ) 0 4 6 0 4 2 0 4 % 0 T % 6 B % 4 % % B % T c 4 Aq!'A3'S13"[email protected](!'3&wayt"93" dsH'sA#"!A"r!'A3'ws"!!(!!&Ad"s"'4 ) 04 2 2 B %4% 0 u P% x 0 4 % T % P g B %4 % 4 % 6 6 4 e 4 ) 04 "!'W'Q3'q39'Ad'!'#'q!v3's3"'!"! 0 4 2 6 E % $ 0 4 4 2 B 0 &'sAh&""9U !"'R'tH!"'bR(HIed 5R 3 Ib 1 i e0 3 i Y D g Y SRI I Db R 3 S Y tCvBst4a0 T9 f5$$viE Cve$9dEHVf5$vqfFY T B V 8 T ' V T U b b5 SR 5F0 W 5 S ) y b R e 5 D B q I i R e Y Y q 5 F i e y 0 t5 baR Ce 5pe D HB 2q TI uveY 7 I Y q i I T R 5 sD 6I i et5wF R W tb 9g t0aF T5 i 0 q 5 0 F 5 F v33 I Qrq e 5b 9I VS q YV5 b R F 5 xD XD 20p CAyrdtE4pT# H a0 9fIvbtH$W $9r tdtEt4pTPcX2R 0 TsvbYfIbeS fbctCCWS VEuvb$2H$VU2HVscE9HV29t!ttsT5yvetVtEsH4TeW i e Y 5F e Y Yq0 5 5 0R0 S 0 5 Sq0 F 5 10FB 55F SR 5 S y D IRRI b YF5 B g e i e0 WI b YF5 B 3 Y eI b i I SR5 g Y SRI I Db Q e I YF0 W D VHTcTA) Hdtt9x{1 tf5tCC TsfI3 $9X 9t{R tf5tCC f5tfRR 9E$pTVED Tve$2p&H9I stfb(a$EdI 8 f54a0 ) 31 Q S Q R I P $ v n2 v n4 v 5 ! # v n %ev n v s$ 4 6 [email protected] # v s# $ B n n v 9# 5 42 v n4 v n v ! $ 6## B e5 v n # v n 4 v s4 $ 6## !! !! # 2 v n5 #@#v n v s$ # 6# !)10 2 v ! $ 63! n n v 9s5 2 v n v n v ! $ 6! 5 4 v n! v n2 v s# $ 6# !" B5 2 v n v n# v s4 6# # $k f n p f n f l e 8H8p up8$9ePo l j f x m ek5s v{kgj C Cg 6 $ 2 ! # # v n2 v n4 v $ 5 v n 5 5 ! v n v ! #" 58" B5 s4 $ 'n n v 5 " $ ! v n v n ! v ! 1 )#1 "k # 5 # s# $ ( 5 'n ))0 1 n !)0 v 42 v ! $ 6## n 9n ## v n4 v n2 v s $ # 3 4 v n#4 v n2 v s# $ 3 # e53k 4 2 v n" ! v n v s$ # #3k !!1 $ v s# n n ! ! v !"k f n p f n f l e 8H8p eup8$9eueo l j f x m ekCW kgj 5 5g 6 F D 7EC $ )!1 6n 7" 9| " 0 v n v [email protected] 2(! v 8! n @ 2 5 v n v s$C6s5 $e n "0 s $ !)" 6n n )! v # % x 5# o Ey 5 ( v n v n"#v s e5# 9 s# $ % " 9e5 v" n 4 n ! 7 %#fx 5$5C 0 # v n4 v sw6 # n s$ # ! 6n 1 #! 5 & n &#v %!fx 3"5C ( v n# v n! v s 4 # !! ! $ )10 6n 7" 9|)10 n @ ( %# 5#m &! v n # v " 5 v s!#21 !8!(n !10 s# 6n $ 9n % 5# " s !9B80 n )! n"[email protected] @5 5 v n 2 v n v s$ )!1 B5 e5 # % 5# kgj o % % 0 8 s9"# 1v n 'n H! ! $ n H) v !0 e5# n4 v % 3! #m 0 s n 2 v !## n )! v &0 n2 v $ ! %!5(& n )0 ! %! 3" 2 v n v s 6B5 n ! 6n n v e5# %! 3kgj o f n f n fle f n f n fl e |H8eet8$9eue! 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'&[email protected] % 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! [email protected](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'[email protected]'"3'[email protected] 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$Vs s6I2f09HVtd p HT9fgY a 7 Y ` X W fbis8T fbis8T-bk fbis8L fbis8L-bk 0.05 0.15 0.25 0.35 0.1 0.2 0.3 0.4 0 0 Precision of Interpolation vs. Backoff (Absolute Discounting) 0.2 0.4 delta 0.6 fbis8T fbis8T-bk fbis8L fbis8L-bk 0.8 1 REFERENCES # y 6 # !8 # v 2 2 v f "qWYI EDPrVWYI 9 I V f k#60 D#2 !vv)PGp5njhf kgkjkm j o o 5%5 F|88kxC5C%k5i 4 2e b 4x pf f 5nv kj n xx f w j y me jx j j l mx i o Skkkj!a% H n 2 2 x v x v x l D v v w 1 o Xs#3C 8dp & 4w &9 e 8e x n yj 4vv # g x ep l v D I S # A P#v C5w kg kjm ! 8 8 Di I BP 8s2 52 %9knx pvuP kx8kmkm e v dw n `HY``I EDG(aA X! #3CBTeWH Y DaXWf Y1I 43 v I vD # A { # gS f v 9 ! 8 # U S Q I % # HbD2aA v ef ! 2 A 8 HHDHWaV H DrGFnE6D! qtXen FDHDC78 @ &6 I f 4 2 0 ) ) ) ' %# ! keGXhW1eW"D kj w8kx5C56kC5kFD nm e j x j i j mx xl l m mx x !ai 8 p 8#R8Xvevl 6 Xs##3C%"85DqHqge8W I e 1 HDv! H8& v 2 2 2 I S W Y#v ' A Y l # # U S Q I % I vH # 6bwpf f F ! 2 A 8 6 4 2 W$VD H 1PFfE!Geen DDHDCv8 @ &lke0 2 A v u ) ) ' %# ! th Wn tW"Da kj pkCkj85e&58kx6Wvai p n j m i wl m x f x j v 4 2E 2 j v n q m v ) m w l v 2 ev58se Xs##3CaXC %6y 81 uskx!Xf p ' Rewn8uekj 1 916 3 v 2 b# # n v n m s n xf j j i q jf !! #6De e e wvVvvkxf kC5 D2kxv( jx i x w m 8hf5vaR6 5E8q8e5 p n 5t o vvDxv88kxvCHq o v8CD f x xf e mx xf i x f m e j x l j e f n 2 2 q " kxm # v I e 8I 4 I 1 9c # Sv)|8kxC554ek5eai ) Xs#3C9!5f Vp D ' R DFhXCF8m We$ v v f 9 # ! v wm 5 4 px f R n i x j i j g x w f agWYI HDH8 #88Dkxeb CvCe!W5Bn hfC5 p 6kXts5ef n j 8 ek5sklvEwy Cfu s3 p kx!5f p ' h1 e) 8 E C 8 1 9eP" f l j w j x i x v # # 2 o q m v 2 m v c ! v j pk5hfkjm |8#v)f u 1 )vx8i m jfx n Sh8% V4Fv kun HrA f iFDDHDC2 DWHYaH f % f d v w j s9 2 ! IS # A # f EA9c|e8 H Xs#3C 5Chhy e8un p kxkjm p Px ' n @ 8 u j f o v 2 2 c v Xv8Rry y ve v 1 Pvk8 D v 1 pC5x o c8 p v 1' 3 ff d v v ngx nx m n g v @ 4 v 4 b v f f n # 2 n ng w yx # Duteu3fpe|% P5ECvCC n wfxgx 8 me jx j i vg m x v 8 q tX{85vcG88kxC5c8 kC5 ) [email protected] wv8v E BIe o ken ekX{85e89ek!eekf8kg!ahf5kgkjkmj o o 5 XP3C j l j wfxg l j ix j mx i j v #2 x v F Hhp n q # j 2 8 T v n g 8 v v5Ev & yXe8pvrCDxl oCUgp x c8 i8&% v RBt5CCvx o [email protected] v 1 $ x e v 2 s4#)n I f w88kx5Cvc8 k5CD nm e jx j i ) 9hf|% 8hfC58#v` E 6 Xs#3CvCx o Cx c8 8vA 8 @ h68 jl m jgg mf v 4 # 2 x l g j e v & 8 # v 4 2 0 % # ! n m e j x v C i b j pf f 1w f keihWPg w88kx5CvCk65D5! kyeCen Xts5ef j 89ekkjve!aB8 p e8#i6 Xs#3Ch"85qev ' v D e8BCWCv f l mx i xl l m v #22 x I S vH#5 eai`Y `PYvfR# 6 gx w p jg p 9 I 9g w f # X I U I 2 C e e CIvx w v w v s# 2 2 x U q j j 5H5Dg!x WXthCH8g%g F8 HP 5g v sex rPkgn D&e5v I p0 Xv #3CaCWCv 3 v # y I p I % U 6 # p 2kh# n ThI j FqHpDU 2 n l m x i x l l m j g w f g j g j f x x f x j eekkjve!ad8 p e8#EhfCC8uXCCGkvkxvveev)vedhfCCkgkjkmj o o 5ef l j g o v 2 2 g x Y# w h # e p ! x g 8 [email protected] # e Dn q v d k5 p f p CC1 H W5#36vD5WxSI vHehCB8 WYI 8dHvD5HCiaVsx HEU S3 Av n g v v 9 Q I % HT nv ee ! 2 A 8 6 4 2 0 ) ) ) ' % # ! 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