Other Sequence Models · 2019. 11. 18. · Slides courtesy Rebecca Knowles. Preprocessing Whereas...

Latent Models:Sequence Models Beyond HMMs and

Machine Translation Alignment

CMSC 473/673

Outline

Review: EM for HMMs

Limited Sequence ModelsMaximum Entropy Markov ModelsConditional Random Fields

Recurrent Neural NetworksBasic DefinitionsExample in PyTorch

Why Do We Need Both the Forward and Backward Algorithms? Compute posteriors

α(i, s) * p(s’ | s) * p(obs at i+1 | s’) * β(i+1, s’) =total probability of paths through the s→s’ arc (at time i)

α(i, s) * β(i, s) = total probability of paths through state s at step i

𝑝 𝑧𝑖 = 𝑠 𝑤1, ⋯ , 𝑤𝑁) =𝛼 𝑖, 𝑠 ∗ 𝛽(𝑖, 𝑠)

𝛼(𝑁 + 1, END)

𝑝 𝑧𝑖 = 𝑠, 𝑧𝑖+1 = 𝑠′ 𝑤1, ⋯ , 𝑤𝑁) =𝛼 𝑖, 𝑠 ∗ 𝑝 𝑠′ 𝑠 ∗ 𝑝 obs𝑖+1 𝑠′ ∗ 𝛽(𝑖 + 1, 𝑠′)

𝛼(𝑁 + 1, END)

EM for HMMs0. Assume some value for your parameters

Two step, iterative algorithm

1. E-step: count under uncertainty, assuming these parameters

2. M-step: maximize log-likelihood, assuming these uncertain counts

estimated counts

pobs(w | s)

ptrans(s’ | s)

𝑝∗ 𝑧𝑖 = 𝑠 𝑤1, ⋯ ,𝑤𝑁) =𝛼 𝑖, 𝑠 ∗ 𝛽(𝑖, 𝑠)

𝛼(𝑁 + 1, END)

𝑝∗ 𝑧𝑖 = 𝑠, 𝑧𝑖+1 = 𝑠′ 𝑤1, ⋯ ,𝑤𝑁) =𝛼 𝑖, 𝑠 ∗ 𝑝 𝑠′ 𝑠 ∗ 𝑝 obs𝑖+1 𝑠′ ∗ 𝛽(𝑖 + 1, 𝑠′)

𝛼(𝑁 + 1, END)

EM For HMMs (Baum-Welch

Algorithm)

α = computeForwards()

β = computeBackwards()

L = α[N+1][END]

for(i = N; i ≥ 0; --i) {

for(next = 0; next < K*; ++next) {

cobs(obsi+1 | next) += α[i+1][next]* β[i+1][next]/L

for(state = 0; state < K*; ++state) {

u = pobs(obsi+1 | next) * ptrans (next | state)

ctrans(next| state) +=

α[i][state] * u * β[i+1][next]/L

update pobs, ptrans using cobs, ctrans

Semi-Supervised Learning

? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?? ? ?

labeled data:• human annotated• relatively small/few

examples

unlabeled data:• raw; not annotated• plentiful

Outline

Review: EM for HMMs

Warren Weaver’s Note

When I look at an article in Russian, I say “This is really written in English, but it has been coded in some strange symbols. I will now proceed to decode.”

(Warren Weaver, 1947)http://www.mt-archive.info/Weaver-1949.pdf

Slides courtesy Rebecca Knowles

Noisy Channel Model

language

язы́к Decode

language

Rerank

language

written in (clean) English

observed Russian (noisy)

translation/decode model

(clean) language model

English

Noisy Channel Model

Decode Rerank

English

language

язы́к

language

Noisy Channel Model

Decode Rerank

English

language

язы́к

language

Translation

Translate French (observed) into English:

The cat is on the chair.

Le chat est sur la chaise.

Translation

Alignment

Parallel Texts

Whereas recognition of the inherent dignity and of the equal and inalienable rights of all members of the human family is the foundation of freedom, justice and peace in the world,

Whereas disregard and contempt for human rights have resulted in barbarous acts which have outraged the conscience of mankind, and the advent of a world in which human beings shall enjoy freedom of speech and belief and freedom from fear and want has been proclaimed as the highest aspiration of the common people,

Whereas it is essential, if man is not to be compelled to have recourse, as a last resort, to rebellion against tyranny and oppression, that human rights should be protected by the rule of law,

Whereas it is essential to promote the development of friendly relations between nations,…

http://www.un.org/en/universal-declaration-human-rights/

Yolki, pampa ni tlatepanitalotl, ni tlasenkauajkayotl iuan ni kuali nemilistli ipan ni tlalpan, yaya ni moneki moixmatis uan monemilis, ijkinoj nochi kuali tiitstosej ika touampoyouaj.

Pampa tlaj amo tikixmatij tlatepanitalistli uan tlen kuali nemilistli ipan ni tlalpan, yeka onkatok kualantli, onkatok tlateuilistli, onkatok majmajtli uan sekinok tlamantli teixpanolistli; yeka moneki ma kuali timouikakaj ika nochi touampoyouaj, ma amo onkaj majmajyotl uan teixpanolistli; moneki ma onkaj yejyektlalistli, ma titlajtlajtokaj uan ma tijneltokakaj tlen tojuantij tijnekij tijneltokasej uan amo tlen ma topanti, kenke, pampa tijnekij ma onkaj tlatepanitalistli.

Pampa ni tlatepanitalotl moneki ma tiyejyekokaj, ma tijchiuakaj uan ma tijmanauikaj; ma nojkia kiixmatikaj tekiuajtinij, uejueyij tekiuajtinij, ijkinoj amo onkas nopeka se akajya touampoj san tlen ueli kinekis techchiuilis, technauatis, kinekis technauatis ma tijchiuakaj se tlamantli tlen amo kuali; yeka ni tlatepanitalotl tlauel moneki ipan tonemilis ni tlalpan.

Pampa nojkia tlauel moneki ma kuali timouikakaj, ma tielikaj keuak tiiknimej, nochi tlen tlakamej uan siuamej tlen tiitstokej ni tlalpan.…

http://www.ohchr.org/EN/UDHR/Pages/Language.aspx?LangID=nhn

Preprocessing

Whereas recognition of the inherent dignity and of the equal and inalienable rights of all members of the human family is the foundation of freedom, justice and peace in the world,

Whereas disregard and contempt for human rights have resulted in barbarous acts which have outraged the conscience of mankind, and the advent of a world in which human beings shall enjoy freedom of speech and belief and freedom from fear and want has been proclaimed as the highest aspiration of the common people,

Whereas it is essential, if man is not to be compelled to have recourse, as a last resort, to rebellion against tyranny and oppression, that human rights should be protected by the rule of law,

Whereas it is essential to promote the development of friendly relations between nations,…

http://www.un.org/en/universal-declaration-human-rights/Yolki, pampa ni tlatepanitalotl, ni tlasenkauajkayotl iuan ni kuali nemilistli ipan ni tlalpan, yaya ni moneki moixmatis uan monemilis, ijkinoj nochi kuali tiitstosej ika touampoyouaj.

Pampa tlaj amo tikixmatij tlatepanitalistli uan tlen kuali nemilistli ipan ni tlalpan, yeka onkatok kualantli, onkatok tlateuilistli, onkatok majmajtli uan sekinok tlamantli teixpanolistli; yeka moneki ma kuali timouikakaj ika nochi touampoyouaj, ma amo onkaj majmajyotl uan teixpanolistli; moneki ma onkaj yejyektlalistli, ma titlajtlajtokaj uan ma tijneltokakaj tlen tojuantij tijnekij tijneltokasej uan amo tlen ma topanti, kenke, pampa tijnekij ma onkaj tlatepanitalistli.

Pampa ni tlatepanitalotl moneki ma tiyejyekokaj, ma tijchiuakaj uan ma tijmanauikaj; ma nojkia kiixmatikaj tekiuajtinij, uejueyij tekiuajtinij, ijkinoj amo onkas nopeka se akajya touampoj san tlen ueli kinekis techchiuilis, technauatis, kinekis technauatis ma tijchiuakaj se tlamantli tlen amo kuali; yeka ni tlatepanitalotl tlauel moneki ipan tonemilis ni tlalpan.

Pampa nojkia tlauel moneki ma kuali timouikakaj, ma tielikaj keuak tiiknimej, nochi tlen tlakamej uan siuamej tlen tiitstokej ni tlalpan.…

http://www.ohchr.org/EN/UDHR/Pages/Language.aspx?LangID=nhn

• Sentence align• Clean corpus• Tokenize• Handle case• Word segmentation

(morphological, BPE, etc.)• Language-specific

preprocessing (example: pre-reordering)

• ...

Alignments

If we had word-aligned text, we could easily estimate P(f|e).

But we don’t usually have word alignments, and they are expensive to produce by hand…

If we had P(f|e) we could produce alignments automatically.

IBM Model 1 (1993)

• Lexical Translation Model• Word Alignment Model• The simplest of the original IBM models• For all IBM models, see the original paper

(Brown et al, 1993): http://www.aclweb.org/anthology/J93-2003

Simplified IBM 1

• We’ll work through an example with a simplified version of IBM Model 1

• Figures and examples are drawn from A Statistical MT Tutorial Workbook, Section 27, (Knight, 1999)

• Simplifying assumption: each source word must translate to exactly one target word and vice versa

IBM Model 1 (1993)

f: vector of French words

(visualization of alignment)

e: vector of English words

a: vector of alignment indices

Le chat est sur la chaise verte

The cat is on the green chair

0 1 2 3 4 6 5

IBM Model 1 (1993)

f: vector of French words

(visualization of alignment)

e: vector of English words

a: vector of alignment indices

t(fj|ei) : translation probability of the word fj given the word ei

Le chat est sur la chaise verte

The cat is on the green chair

0 1 2 3 4 6 5

Model and Parameters

Want: P(f|e)But don’t know how to train this directly…

Solution: Use P(a, f|e), where a is an alignmentRemember:

Model and Parameters: Intuition

Translation prob.:

Example:

Interpretation:How probable is it that we see fj given ei

Alignment/translation prob.:

Example (visual representation of a):

P( | “the cat”) < P( | “the cat”)

Interpretation:How probable are the alignment a and the translation f (given e)

le chat

the cat

le chat

the cat

Alignment prob.:Example:

P( | “le chat”, “the cat”) < P( | “le chat”, “the cat”)

Interpretation:How probable is alignment a (given e and f)

Model and Parameters

How to compute:

Parameters

For IBM model 1, we can compute all parameters given translation parameters:

How many of these are there?

Parameters

For IBM model 1, we can compute all parameters given translation parameters:

How many of these are there?|French vocabulary| x |English vocabulary|

Two sentence pairs:

English French

b c x y

All Possible Alignments

(French: x, y)

(English: b, c)

Remember:simplifying assumption that each word must be aligned exactly once

Expectation Maximization (EM)0. Assume some value for and compute other parameter values

Two step, iterative algorithm

1. E-step: count alignments and translations under uncertainty, assuming these parameters

2. M-step: maximize log-likelihood (update parameters), using uncertain counts

estimated counts

P( | “the cat”)

P( | “the cat”)le chat

le chat

Review of IBM Model 1 & EM

Iteratively learned an alignment/translation model from sentence-aligned text (without “gold standard” alignments)

Model can now be used for alignment and/or word-level translation

We explored a simplified version of this; IBM Model 1 allows more types of alignments

Why is Model 1 insufficient?

Why won’t this produce great translations?Indifferent to order (language model may help?)Translates one word at a timeTranslates each word in isolation...

Uses for Alignments

Component of machine translation systems

Produce a translation lexicon automatically

Cross-lingual projection/extraction of information

Supervision for training other models (for example, neural MT systems)

Evaluating Machine Translation

Human evaluations:Test set (source, human reference translations, MT output)

Humans judge the quality of MT output (in one of several possible ways)

Koehn (2017), http://mt-class.org/jhu/slides/lecture-evaluation.pdf

Evaluating Machine Translation

Automatic evaluations:Test set (source, human reference translations, MT output)

Aim to mimic (correlate with) human evaluations

Many metrics:TER (Translation Error/Edit Rate)

HTER (Human-Targeted Translation Edit Rate)

BLEU (Bilingual Evaluation Understudy)

METEOR (Metric for Evaluation of Translation with Explicit Ordering)

Machine Translation Alignment Now

Explicitly with fancier IBM models

Implicitly/learned jointly with attention in recurrent neural networks (RNNs)

Outline

Review: EM for HMMs

Recall: N-gram to Maxent to Neural Language Models

predict the next word

given some context…

𝑝 𝑤𝑖 𝑤𝑖−3, 𝑤𝑖−2, 𝑤𝑖−1) ∝ 𝑐𝑜𝑢𝑛𝑡(𝑤𝑖−3, 𝑤𝑖−2, 𝑤𝑖−1, 𝑤𝑖)

wi-3 wi-2

compute beliefs about what is likely…

Recall: N-gram to Maxent to Neural Language Models

given some context…wi-3 wi-2

𝑝 𝑤𝑖 𝑤𝑖−3, 𝑤𝑖−2, 𝑤𝑖−1) = softmax(𝜃 ⋅ 𝑓(𝑤𝑖−3, 𝑤𝑖−2, 𝑤𝑖−1, 𝑤𝑖))

Hidden Markov Model Representation

𝑝 𝑧1, 𝑤1, 𝑧2, 𝑤2, … , 𝑧𝑁, 𝑤𝑁 = 𝑝 𝑧1| 𝑧0 𝑝 𝑤1|𝑧1 ⋯𝑝 𝑧𝑁| 𝑧𝑁−1 𝑝 𝑤𝑁|𝑧𝑁

𝑝 𝑤𝑖|𝑧𝑖 𝑝 𝑧𝑖| 𝑧𝑖−1emission

probabilities/parameterstransitionprobabilities/parameters

w2 w3 w4

z2 z3 z4

represent the probabilities and independence assumptions in a graph

A Different Model’s Representation

w2 w3 w4

z2 z3 z4

w2 w3 w4

z2 z3 z4

𝑝 𝑧1, 𝑧2, … , 𝑧𝑁|𝑤1, 𝑤2, … , 𝑤𝑁 = 𝑝 𝑧1| 𝑧0, 𝑤1 ⋯𝑝 𝑧𝑁| 𝑧𝑁−1, 𝑤𝑁

𝑝 𝑧𝑖| 𝑧𝑖−1, 𝑤𝑖

w2 w3 w4

z2 z3 z4

𝑝 𝑧𝑖 𝑧𝑖−1, 𝑤𝑖) ∝ exp( 𝜃𝑇𝑓 𝑤𝑖 , 𝑧𝑖−1, 𝑧𝑖 )

w2 w3 w4

z2 z3 z4

Maximum Entropy Markov Model (MEMM)

𝑝 𝑧𝑖 𝑧𝑖−1, 𝑤𝑖) ∝ exp( 𝜃𝑇𝑓 𝑤𝑖 , 𝑧𝑖−1, 𝑧𝑖 )

Discriminative: don’t care about generating observed sequence at all

Maxent: use features

Problem: Label-Bias problem

w2 w3 w4

z2 z3 z4

Label-Bias Problem

1incoming mass must

sum to 1

Label-Bias Problem

1 1incoming mass must

sum to 1outgoing mass must

sum to 1

Label-Bias Problem

1 1incoming mass must

sum to 1outgoing mass must

sum to 1

observe, but do not generate (explain) the

observation

Take-aways:• the model can learn to

ignore observations• the model can get itself

stuck on “bad” paths

Outline

Review: EM for HMMs

(Linear Chain) Conditional Random Fields

Discriminative: don’t care about generating observed sequence at all

Condition on the entire observed word sequence w1…wN

Maxent: use features

Solves the label-bias problem

z1 …

w1 w2 w3 w4 …

z2 z3 z4

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁)

∝ෑ

exp( 𝜃𝑇𝑓 𝑧𝑖−1, 𝑧𝑖 , 𝑤1, … , 𝑤𝑁 )

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁)

∝ෑ

exp( 𝜃𝑇𝑓 𝑧𝑖−1, 𝑧𝑖 , 𝒘𝟏, … ,𝒘𝑵 )

condition on entire sequence

CRFs are Very Popular for {POS, NER, other sequence tasks}

• POSf(𝑧𝑖−1, 𝑧𝑖 , 𝒘) =

(𝑧𝑖−1 == Noun & 𝑧𝑖 == Verb &(𝑤𝑖−2 in list of adjectives or determiners))

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁) ∝

• NERfpath p(𝑧𝑖−1, 𝑧𝑖 , 𝒘) =

(𝑧𝑖−1 == Per & 𝑧𝑖 == Per &(syntactic path p involving 𝑤𝑖 exists ))

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁) ∝

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁) ∝

Can’t easily do these with an HMM

Conditional modelscan allow richer

features

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁) ∝

features

We’ll cover syntactic paths next class

z1 …

w1 w2 w3 w4 …

z2 z3 z4

𝑝 𝑧1, … , 𝑧𝑁 𝑤1, … , 𝑤𝑁) ∝

features

CRFs can be used in neural networks too:https://www.tensorflow.org/versions/r1.15/api_docs/python

/tf/contrib/crf/CrfForwardRnnCellhttps://pytorch-crf.readthedocs.io/en/stable/

Conditional vs. Sequence

CRF Tutorial, Fig 1.2, Sutton & McCallum (2012)

We’ll cover these in 691: Graphical and Statistical

Models of Learning

Outline

Review: EM for HMMs

Recall: N-gram to Maxent to NeuralLanguage Models

given some context…wi-3 wi-2

𝑝 𝑤𝑖 𝑤𝑖−3, 𝑤𝑖−2, 𝑤𝑖−1) = softmax(𝜃𝑤𝑖⋅ 𝒇(𝑤𝑖−3, 𝑤𝑖−2, 𝑤𝑖−1))

create/use “distributed representations”… ei-3 ei-2 ei-1

combine these representations… C = f

matrix-vector product

A More Typical View of Recurrent Neural Language Modeling

wi-3 wi-2 wiwi-1

hi-3 hi-2 hi-1 hi

wi-2 wi-1 wi+1wi

wi-3 wi-2 wiwi-1

hi-3 hi-2 hi-1 hi

wi-2 wi-1 wi+1wi

observe these words one at a time

wi-3 wi-2 wiwi-1

hi-3 hi-2 hi-1 hi

wi-2 wi-1 wi+1wi

wi-3 wi-2 wiwi-1

hi-3 hi-2 hi-1 hi

wi-2 wi-1 wi+1wi

from these hidden states

wi-3 wi-2 wiwi-1

hi-3 hi-2 hi-1 hi

wi-2 wi-1 wi+1wi

from these hidden states

“cell”

wiwi-1

hi-1 hi

wi+1wi

A Recurrent Neural Network Cell

wiwi-1

hi-1 hi

wi+1wi

encoding

wiwi-1

hi-1 hi

wi+1wi

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

A Simple Recurrent Neural Network Cell

ℎ𝑖 = 𝜎(𝑊ℎ𝑖−1 + 𝑈𝑤𝑖)

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

ℎ𝑖 = 𝜎(𝑊ℎ𝑖−1 + 𝑈𝑤𝑖)𝜎 𝑥 =

1 + exp(−𝑥)

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

1 + exp(−𝑥)

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

1 + exp(−𝑥)

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

1 + exp(−𝑥)ෝ𝑤𝑖+1 = softmax(𝑆ℎ𝑖)

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

ෝ𝑤𝑖+1 = softmax(𝑆ℎ𝑖)

must learn matrices U, S, W

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

suggested solution: gradient descent on prediction ability

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

problem: they’re tied across inputs/timesteps

decoding

encoding

wiwi-1

hi-1 hi

wi+1wi

problem: they’re tied across inputs/timesteps

good news for you: many toolkits do this automatically

Why Is Training RNNs Hard?

Conceptually, it can get strange

But really getting the gradient just requires many applications of the chain rule for derivatives

Why Is Training RNNs Hard?

Conceptually, it can get strange

Vanishing gradients

Multiply the same matrices at eachtimestep➔multiply many matrices in the gradients

Why Is Training RNNs Hard?Conceptually, it can get strange

Vanishing gradients

Multiply the same matrices at eachtimestep➔multiply many matrices in the gradients

One solution: clip the gradients to a max value

Outline

Review: EM for HMMs

Natural Language Processing

from torch import *from keras import *

Pick Your Toolkit

PyTorch

Deeplearning4j

TensorFlow

Comparisons:https://en.wikipedia.org/wiki/Comparison_of_deep_learning_softwarehttps://deeplearning4j.org/compare-dl4j-tensorflow-pytorchhttps://github.com/zer0n/deepframeworks (older---2015)

Defining A Simple RNN in Python (Modified Very Slightly)

http://pytorch.org/tutorials/intermediate/char_rnn_classification_tutorial.html

hi-2 hi-1 hi

encode

hi-2 hi-1 hi

decode

hi-2 hi-1 hi

Training A Simple RNN in Python(Modified Very Slightly)

Negative log-likelihood

get predictions

hi-2 hi-1 hi

get predictions

eval predictions

get predictions

eval predictions

compute gradient

get predictions

eval predictions

compute gradient

perform SGD

Another Solution: LSTMs/GRUs

LSTM: Long Short-Term Memory (Hochreiter & Schmidhuber, 1997)

GRU: Gated Recurrent Unit (Cho et al., 2014)

Basic Ideas: learn to forgethttp://colah.github.io/posts/2015-08-Understanding-LSTMs/

forget line

representation line

Outline

Review: EM for HMMs

Other Sequence Models · 2019. 11. 18. · Slides courtesy Rebecca Knowles. Preprocessing Whereas...

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