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Query	Expansion	with	Locally-Trained
Word	Embeddings
Fernando Diaz Bhaskar Mitra Nick	Craswell
Microsoft
July	21, 2016
1 / 22
word	embedding: discriminatively	trained	vector
representation
2 / 22
L =
T∑
t=1
ωxt
term	weight


∑
y∈Vt
c
log σ(ϕ(xt) · ϕ(y))
observed	context
+
∑
y∈Vt
n
log σ(−ϕ(xt) · ϕ(y))
negative	context


3 / 22
ωxt needs	to	reflect	the	importance	of	the	term	at	evaluation
time.
4 / 22
T∑
t=1
ωxt=w ∝ p(w|C)
5 / 22
what	terms	are	important	at	query	time?
6 / 22
p(w|R) probability	of	the	term	in	the	relevant	documents.
7 / 22
how	different	is p(w|R) from p(w|C)?
8 / 22
KL(R, C)w = p(w|R) log
p(w|R)
p(w|C)
9 / 22
KL
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
rank
10 / 22
how	much	better	can	we	do	if	we	train	with∑T
t=1 ωxt ∝ p(w|R)?
11 / 22
Language	Model	Scoring
score(d, q) = KL(θq, θd)
θq maximum	likelihood	query	language	model
θd document	language	model
12 / 22
Query	Expansion	with	Word	Embeddings
˜θq = UUT
θq
U |V| × k term	embedding	matrix
13 / 22
Query	Expansion	with	Word	Embeddings
Uglobal embedding	trained	with p(w|C)
Ulocal embedding	trained	with p(w|R)
14 / 22
Getting p(w|R)
p(d) =
exp(−KL(θq, θd))
∑
d′ exp(−KL(θq, θd′ ))
15 / 22
Getting p(w|R)
p(d) =
exp(−KL(θq, θd))
∑
d′ exp(−KL(θq, θd′ ))
˜p(w|R) =
∑
d
p(w|θd)p(d)
15 / 22
Experiments
16 / 22
Data
docs words queries
trec12 469,949 438,338 150
robust 528,155 665,128 250
web 50,220,423 90,411,624 200
giga 9,875,524 2,645,367 -
wiki 3,225,743 4,726,862 -
17 / 22
Embeddings
• global
• public	embeddings	(GloVe, word2vec)
• word2vec	on	target	corpus
• local: word2vec	with	documents	sampled	by p(d)
18 / 22
• ten-fold	cross-validation
• metric: NDCG@10
19 / 22
Results
global local
wiki+giga gnews target target giga wiki
QL 50 100 200 300 300 400 400 400 400
trec12 0.514 0.518 0.518 0.530 0.531 0.530 0.545 0.535 0.563*
0.523
robust 0.467 0.470 0.463 0.469 0.468 0.472 0.465 0.475 0.517*
0.476
web 0.216 0.227 0.229 0.230 0.232 0.218 0.216 0.234 0.236 0.258*
20 / 22
global
local
top	words	by ˜p(w|R) (blue: query; red: top	words	by p(w|R))
21 / 22
Summary
• local	embedding	provides	a	stronger	representation
than	global	embedding
• potential	impact	for	other	topic-specific	natural
language	processing	tasks
• future	work
• effectiveness	improvements
• efficiency	improvements
22 / 22

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Query Expansion with Locally-Trained Word Embeddings (Neu-IR 2016)