Learning Morphophonology From Morphology and MDL

Transcription

1 L Mphphlg F Mphlg MDL Jh A Glih Th Uivi f Chig hp://luii.uhig.u 17 Jul Uupvi l w f luii h 1. Hphi gi. T fu. 2. Hphi (vlui). D Div vi C g f pu D G Vifii vi Y,, N D G 1 G 2 Evlui i G 1 i b;, G 2 i b. Figu 1: Chk h pi f luii h D Bp vi G il hg G Evlui i Pf g G G N Hl? Y Hl! Figu 2: Uupvi l f g 1

2 2 Uupvi l f phlg: h Luii pj (2001) 2.1 Wk h uupvi l f ul lgug phlg. Wh? Wh i h k, h? Tk i w pu, pu phlg. Wh i phlg? Th w h p wh luii pbl w w lv. L wih h ipl: li f w i ph ( vull i ph). Slui lk lik FSA, h. Expl: Eglih, Fh, Swhili. A FSA i f vi ( ), f g, f h g lbl pbbili, wh h u f h pbbilii f h g lv h u Eglih phlg: ph g f fii- u pu, lu l l, h, fi hip ful/l/il buh, pil, pil g, b, gil uliv, lul jup, wlk, lv, v i,, i,, l Figu 3: Eglih phlg: ph g P h pbl piizi pbl: iiv h b u, bu pvi liivl pil pi i iuu wl f u. Tu hi i luii pj S il h MDL l; i lk bu h h h. W u h lgh (f h) h ub f bi = u f ifi pif i. Exp wh ii, h pbbili iibui() ivlv f xiu liklih l. Th lgh f FSA i h ub f bi pif i, i l h u f h h: 1. Li f ph: ig h phlgil f blih l l f ph. Avi u; iiiz ulipl u iil. Th pbbili iibui h i v ph (l). ph +1 lg p ph ( i i 1 ) i=1 2. Li f v: h f ph l lg p(v) v Vi 2

3 u: hi, li, h, f iig, v, uiv, pgl, g vlpp, gup, x i i i,, gl l l ux vb Figu 4: Fh 3. Li f g : h f phlgil uu: vi phlgil li xp wh i i hlpful. lg p(v 1 ) lg p(v 2 ) lg p() (v 1,v 2,) Eg (I lv ff h pifii f h pbbilii h FSA ilf, whih i l h i pifi i bi.) I ii, w g b h phlg i h ph hugh h FSA. P(w) = pu f h hi pbbilii f f w ph. S: f giv pu, Luii k h FSA f whih h ipi lgh f h pu giv h FSA i iiiz, whih i h h b i il lgug-ip uupvi fhi. wlk A B C jup 3

4 Ip hi gph: Th x-xi -xi bh ii u i bi. Th x-xi k hw bi w llw u wi g ib h : h bi w llw, h b u ipi will b, uil h pi wh w v-fi h. Thu h pi lg h x-xi p pibl g-lgh; bu f giv lgh l, w l bu h g g h ig h high pbbili h, i.., h b g. Th li ii hw bi f lf uxpli b h g, i whih i l -1 * lg pbbili f h ig b h g. Th blu li hw h u f h w ii (whih i h iil ipi lgh f h ). Th blk li giv h lgh f h g. Figu 5: MDL piizi bi g lgp( g(x)) iiu g(x) = lgh f g(x) lgp( g(x)) x Cpi (bi) 3Tp p f Luii upu f 600,000 w f Eglih: Sigu xpl u S u pg 20, Cbi 30, l zlu 14, il 6, ug 4, z 3, i wkl 2, l wful 2, bih 2, p viul wi L (ph)phlg f phlg I v z hw h i i vlp xplii lgih pf ipl luii k, v h i pul fl. Sul u i h k i j gl f luii. Mphlg h i i h lxi f lgug (fii ifii; l u fii k h h i). A giv li ivi h lxi up i i ub f ubgup. If h ubgup, h ll likl, i lxi f iz V (V f vbul), h k h w lg 2 V. (If h gup ll likl, h i h gup h i b, h k w b i h gup lg i 2 V = lg 2 V. Eh w i h i h gup i V b k, ll f h k gh i lg 2 i. If w llp w ubgup lill, h w v l f bi. Hw? If h w gup l-iz, h w v 1 bi f h i. Wh? Supp w hv w gup, g 1 g 2 f 100 w u f vbul f 1000 w. Eh i i h w 1000 gup i k i h lxi f lg bi; 200 uh w u bi = 664 bi. If h 200 w ll p f l g, h f pi h lg g wul b lg = 2.32 bi, w wul p l f = 464 bi. f l v f 200 bi. W ull pu hw plx li i. A h phlgil li h Luii pvi b hp b h ub f ii p i i, b (ph)phlg p f h phlg. Bu hw w iv i uill? 4

5 3.1 Eglih vb (1) Rgul vbl p jup wlk jup wlk jup wlk jup wlk (2) -fil vbl p v lv h v lv h v lv lv v lv lv -fil p C-ubl p -fil p (3) puh i v puh i v puh i v puh i v (4) p li g pp li gg pp li gg p li g (5) li* i i li l i i li Figu 6: S l pig S T R (S, T) jup jup jup jup wlk jup wlk jup wlk jup wlk jup Dfiii (l): Giv w S T wh lg iiil i ; S = + 1 ; T = + 1. Th R (S, T) = 1 1 Dfiii (igh): Giv lphb A. Dfi lli pi iv lphb A 1 : F h A h i l 1 i A 1 uh h 1 = 1 =. Dfi ug lphb A A A 1. A i h f ll w fa. If w h lli pi A, h w g f gup G i whih (.g.) b 1 1 b =. W ll h l i G b h h i A h p h. R (S, T) T 1 S. L (S, T) ST 1. E.g. R (jup, jup) (jup) 1 jup = () 1 (jup) 1 (jup)() = () 1 () = Sill, h ix i iil h. W fliz h bvi, if w k vg f h i f iff w fi ju bv. W x h fiii f L Σ Σ i hi w: L ( b, ) = L(, ) L (b, ) If w fi L ix h i-wi pplii f h pi h iiviul b, h w xp h iff bw 6 7 i hi w (wh w ii wih blk). S Figu 7,8 x w pg. 3.2 Hugi S Figu 10 blw. 3.3 Spih S Figu 9 blw. 4 Clui L P b f w (hik P[ig]) f lgh. W fi h i P Q f w P, Q f h lgh 2 2 ix, wh (6) P Q(i, j) L (p i, q j ) 5

6 jup jup jup jup puh puh puh puh jup jup jup jup puh puh puh puh,,,, v v v v li li li li v v v v,,, li li li li,,,,,,, i i i i i i i i i i i i, i,, i,, i, i,, Figu 7: Mix f iff I piul P P(i, j) L (p i, p j ) W p w pig h h iff: (P, Q) (P P) (Q Q) Thi i wh w hv xpl i hi hu. M phphlgil hg g h iff f ( pig ) f w. 6

7 jup:v jup:pli jup:puh jup: i i i i i 4. i Figu 8: Diff f iff: Eglih vb i i b b b bük bk b b ük b ük b bük bk b ük k ük k ük k ük k ük k k k k k ük k k k k k g g g gük gk g g ük g g gük gk g ük k ük k ük k ük ük k ük k k k k k ük k k k k k Diff f iff b b b b b b Figu 9: Hugi vwl h: uiv f gup 7

8 hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl ŕ ó ś á ń hbl hbl hbl hbl ś bu bu bu bu bu bu bu bu bu bu bu bu bu bu bu bu bu ś bu hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl hbl Figu 10: Diff f iff: Spih vb 8