lda2vec Text by the Bay 2016

lda2vec
(word2vec, and lda)
Christopher Moody
@ Stitch Fix

About
@chrisemoody
Caltech Physics
PhD. in astrostats supercomputing
sklearn t-SNE contributor
Data Labs at Stitch Fix
github.com/cemoody
Gaussian Processes t-SNE
chainer
deep learning
Tensor Decomposition

1. king - man + woman = queen
2. Huge splash in NLP world
3. Learns from raw text
4. Pretty simple algorithm
5. Comes pretrained
word2vec

1. Set up an objective function
2. Randomly initialize vectors
3. Do gradient descent
word2vec

w
ord2vec
word2vec: learn word vector w
from it’s surrounding context
w

w
ord2vec
P(fox|over)
What should this be?

w
ord2vec
P(vfox|vover)
Should depend on the word vectors.
P(fox|over)

w
ord2vec
P(w|c)
Extract pairs from context window around every input word.

w
ord2vec
c
P(w|c)

w
ord2vec
w
P(w|c)
c

w
ord2vec
P(w|c)
w c

w
ord2vec
P(w|c)
c w

w
ord2vec
P(w|c)
cw

objective
Measure loss between
w and c?
How should we deﬁne P(w|c)?

objective
w . c
How should we deﬁne P(w|c)?
Measure loss between
w and c?

w
ord2vec
w . c ~ 1
objective
w
c
vcanada . vsnow ~ 1

w
ord2vec
w . c ~ 0
objective
w
c
vcanada . vdesert ~0

w
ord2vec
w . c ~ -1
objective
w
c

w
ord2vec
w . c ∈ [-1,1]
objective

w
ord2vec
But we’d like to measure a probability.
w . c ∈ [-1,1]
objective

w
ord2vec
objective
∈ [0,1]σ(c·w)

w
ord2vec
objective
∈ [0,1]σ(c·w)
w
c
w
c
SimilarDissimilar

w
ord2vec
Loss function:
objective
L=σ(c·w)
Logistic (binary) choice.
Is the (context, word) combination from our dataset?

w
ord2vec
The skip-gram negative-sampling model
objective
Trivial solution is that context = word for all vectors
L=σ(c·w)
w
c

w
ord2vec
L = σ(c·w) + σ(-c·wneg)
objective
Draw random words in vocabulary.

w
ord2vec
objective
Discriminate positive from negative samples
Multiple Negative
L = σ(c·w) + σ(-c·wneg) +…+ σ(-c·wneg)

w
ord2vec
The SGNS Model
PM
I
ci·wj = PMI(Mij) - log k
…is extremely similar to matrix factorization!
Levy & Goldberg 2014

w
ord2vec
The SGNS Model
PM
I
‘traditional’ NLP
ci·wj = PMI(Mij) - log k
…is extremely similar to matrix factorization!

w
ord2vec
The SGNS Model
L = σ(c·w) + Σσ(-c·w)
PM
I
ci·wj = log
#(ci,wj)/n
k #(wj)/n #(ci)/n

w
ord2vec
The SGNS Model
L = σ(c·w) + Σσ(-c·w)
PM
I
ci·wj = log
popularity of c,w
k (popularity of c) (popularity of w)

w
ord2vec
PM
I
99% of word2vec
is counting.
And you can count
words in SQL

w
ord2vec
PM
I
Count how many times
you saw c·w
you saw c
you saw w

w
ord2vec
PM
I
…and this takes ~5 minutes to compute on a single core.
Computing SVD is a completely standard math library.

= ITEM_701333
= ITEM_901004
= ITEM_800456

LDA
on Client Item
Descriptions

LDA
on Item
Descriptions
(with Jay)

Bayesian Graphical ModelML Neural Model

word2vec is local:
one word predicts a nearby word
“I love ﬁnding new designer brands for jeans”

But text is usually organized.

In LDA, documents globally predict words.
doc 7681

typical word2vec vector
[ 0%, 9%, 78%, 11%]
typical LDA document vector
[ -0.75, -1.25, -0.55, -0.12, +2.2]
All sum to 100%All real values

5D word2vec vector
[ 0%, 9%, 78%, 11%]
5D LDA document vector
[ -0.75, -1.25, -0.55, -0.12, +2.2]
Sparse
All sum to 100%
Dimensions are absolute
Dense
All real values
Dimensions relative

100D word2vec vector
[ 0%0%0%0%0% … 0%, 9%, 78%, 11%]
[ -0.75, -1.25, -0.55, -0.27, -0.94, 0.44, 0.05, 0.31 … -0.12, +2.2]
Sparse
All sum to 100%
Dimensions are absolute
Dense
All real values
Dimensions relative
dense sparse

100D word2vec vector
[ 0%0%0%0%0% … 0%, 9%, 78%, 11%]
[ -0.75, -1.25, -0.55, -0.27, -0.94, 0.44, 0.05, 0.31 … -0.12, +2.2]
Similar in fewer ways
(more interpretable)
Similar in 100D ways
(very ﬂexible)
+mixture
+sparse

-1.9 0.85 -0.6 -0.3 -0.5
Lufthansa is a German airline and when
fox
#hidden units
Skip grams from
sentences
Word vector
Negative sampling loss
German
word2vec predicts locally:
one word predicts a nearby word

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units#hidden units
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
German
Document vector
predicts a word from
a global context
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
We’re missing
mixtures & sparsity!
German

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
We’re missing
mixtures & sparsity!

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
Now it’s a mixture.
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
Trinitarian
baptismal
Pentecostals
Bede
schismatics
excommunication
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
#topics
Document weight

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
topic 1 = “religion”
Trinitarian
baptismal
Pentecostals
Bede
schismatics
excommunication
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
#topics
Document weight

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
Milosevic
absentee
Indonesia
Lebanese
Isrealis
Karadzic
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
#topics
Document weight

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
topic 2 = “politics”
Milosevic
absentee
Indonesia
Lebanese
Isrealis
Karadzic
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
#topics
Document weight

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+

0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
Sparsity!
0.34 -0.1 0.17
41% 26% 34%
-1.4 -0.5 -1.4
-1.9-1.7 0.75
0.96-0.7 -1.9
-0.2-1.1 0.6
-0.7 -0.4 -0.7 -0.3 -0.3-1.9 0.85 -0.6 -0.3 -0.5
-2.6 0.45 -1.3 -0.6 -0.8
#topics
#topics
fox
#hiddenunits
#topics
#hidden units
Skip grams from
sentences
Word vector
Topic matrix
Document proportion
Document weight
Document vector
Context vector
x
+
34% 32% 34%
t=0
41% 26% 34%
t=10
99% 1% 0%
t=∞
tim
e

+ API docs
+ Examples
+ GPU
+ Tests
@chrisemoody
lda2vec.com

@chrisemoody
Example Hacker News comments
Topics:
http://nbviewer.jupyter.org/github/cemoody/lda2vec/blob/master/examples/
hacker_news/lda2vec/lda2vec.ipynb
Word vectors:
https://github.com/cemoody/
lda2vec/blob/master/examples/
hacker_news/lda2vec/
word_vectors.ipynb

@chrisemoody
lda2vec.com
human-interpretable doc topics, use LDA.
machine-useable word-level features, use word2vec.
if you like to experiment a lot, and have
topics over user / doc / region / etc. features, use lda2vec.
(and you have a GPU)
If you want…

?@chrisemoody
Multithreaded
Stitch Fix

Credit
Large swathes of this talk are from
previous presentations by:
• Tomas Mikolov
• David Blei
• Christopher Olah
• Radim Rehurek
• Omer Levy & Yoav Goldberg
• Richard Socher
• Xin Rong
• Tim Hopper

“PS! Thank you for such an awesome idea”
@chrisemoody
doc_id=1846
Can we model topics to sentences?
lda2lstm

Can we model topics to sentences?
lda2lstm
“PS! Thank you for such an awesome idea”doc_id=1846
@chrisemoody
Can we model topics to images?
lda2ae
TJ Torres

and now for something completely crazy
4
Fun
Stuﬀ

translation
(using just a rotation
matrix)
M
ikolov
2013
English
Spanish
Matrix
Rotation

deepwalk
Perozzi
etal2014
learn word vectors from
sentences
vOUT vOUT vOUT vOUT vOUTvOUT
‘words’ are graph vertices
‘sentences’ are random walks on the
graph
word2vec

Playlists at
Spotify
context
sequence
learning
‘words’ are song indices
‘sentences’ are playlists

Playlists at
Spotify
context
Erik
Bernhardsson
Great performance on ‘related artists’

Fixes at
Stitch Fix
sequence
learning
Let’s try:
‘words’ are items
‘sentences’ are ﬁxes

Fixes at
Stitch Fix
context
Learn similarity between styles
because they co-occur
Learn ‘coherent’ styles
sequence
learning

Fixes at
Stitch Fix?
context
sequence
learning
Got lots of structure!

Fixes at
Stitch Fix?
context
sequence
learning

Fixes at
Stitch Fix?
context
sequence
learning
Nearby regions are
consistent ‘closets’

context
dependent
Levy
&
G
oldberg
2014
Australian scientist discovers star with telescope
context +/- 2 words

context
dependent
context
Levy
&
G
oldberg
2014

context
dependent
context
context
Levy
&
G
oldberg
2014

context
dependent
context
BoW DEPS
topically-similar vs ‘functionally’ similar
Levy
&
G
oldberg
2014

Crazy
Approaches
Paragraph Vectors
(Just extend the context window)
Content dependency
(Change the window grammatically)
Social word2vec (deepwalk)
(Sentence is a walk on the graph)
Spotify
(Sentence is a playlist of song_ids)
Stitch Fix
(Sentence is a shipment of ﬁve items)

CBOW
Guess the word
given the context
~20x faster.
(this is the alternative.)
vOUT
vIN vINvIN vINvIN vIN
SkipGram
vOUT vOUT
vIN
vOUT vOUT vOUTvOUT
Guess the context
given the word
Better at syntax.
(this is the one we went over)

lda2vec
vDOC = a vtopic1 + b vtopic2 +…
Let’s make vDOC sparse

lda2vec
This works! 😀 But vDOC isn’t as
interpretable as the topic vectors. 😔
vDOC = topic0 + topic1
Let’s say that vDOC ads

lda2vec
softmax(vOUT * (vIN+ vDOC))

LDA
Results
context
H
istory
I loved every choice in this ﬁx!! Great job!
Great Stylist Perfect

LDA
Results
context
H
istory
Body Fit
My measurements are 36-28-32. If that helps.
I like wearing some clothing that is fitted.
Very hard for me to find pants that fit right.

LDA
Results
context
H
istory
Sizing
Really enjoyed the experience and the
pieces, sizing for tops was too big.
Looking forward to my next box!
Excited for next

LDA
Results
context
H
istory
Almost Bought
It was a great ﬁx. Loved the two items I
kept and the three I sent back were close!
Perfect

All of the following ideas will change what
‘words’ and ‘context’ represent.

paragraph
vector
What about summarizing documents?
On the day he took office, President Obama reached out to America’s enemies,
offering in his first inaugural address to extend a hand if you are willing to unclench
your fist. More than six years later, he has arrived at a moment of truth in testing that

The framework nuclear agreement he reached with Iran on Thursday did not provide
the deﬁnitive answer to whether Mr. Obama’s audacious gamble will pay off. The ﬁst
Iran has shaken at the so-called Great Satan since 1979 has not completely relaxed.
paragraph
vector
Normal skipgram extends C words before, and C words after.
IN
OUT OUT

The framework nuclear agreement he reached with Iran on Thursday did not provide
the deﬁnitive answer to whether Mr. Obama’s audacious gamble will pay off. The ﬁst
Iran has shaken at the so-called Great Satan since 1979 has not completely relaxed.
paragraph
vector
A document vector simply extends the context to the whole document.
IN
OUT OUT
OUT OUTdoc_1347

from gensim.models import Doc2Vec
fn = “item_document_vectors”
model = Doc2Vec.load(fn)
model.most_similar('pregnant')
matches = list(filter(lambda x: 'SENT_' in x[0], matches))
# ['...I am currently 23 weeks pregnant...',
# '...I'm now 10 weeks pregnant...',
# '...not showing too much yet...',
# '...15 weeks now. Baby bump...',
# '...6 weeks post partum!...',
# '...12 weeks postpartum and am nursing...',
# '...I have my baby shower that...',
# '...am still breastfeeding...',
# '...I would love an outfit for a baby shower...']
sentence
search

lda2vec Text by the Bay 2016

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