程序代写代做代考 scheme information theory Hidden Markov Mode algorithm Bayesian chain AI Speech and Language Processing. Daniel Jurafsky & James H. Martin. Copyright c© 2018. All

Speech and Language Processing. Daniel Jurafsky & James H. Martin. Copyright c© 2018. All
rights reserved. Draft of September 23, 2018.

CHAPTER

8 Part-of-Speech Tagging
Dionysius Thrax of Alexandria (c. 100 B.C.), or perhaps someone else (it was a long
time ago), wrote a grammatical sketch of Greek (a “technē”) that summarized the
linguistic knowledge of his day. This work is the source of an astonishing proportion
of modern linguistic vocabulary, including words like syntax, diphthong, clitic, and
analogy. Also included are a description of eight parts-of-speech: noun, verb,parts-of-speech
pronoun, preposition, adverb, conjunction, participle, and article. Although earlier
scholars (including Aristotle as well as the Stoics) had their own lists of parts-of-
speech, it was Thrax’s set of eight that became the basis for practically all subsequent
part-of-speech descriptions of most European languages for the next 2000 years.

Schoolhouse Rock was a series of popular animated educational television clips
from the 1970s. Its Grammar Rock sequence included songs about exactly 8 parts-
of-speech, including the late great Bob Dorough’s Conjunction Junction:

Conjunction Junction, what’s your function?
Hooking up words and phrases and clauses…

Although the list of 8 was slightly modified from Thrax’s original, the astonishing
durability of the parts-of-speech through two millenia is an indicator of both the
importance and the transparency of their role in human language.1

Parts-of-speech (also known as POS, word classes, or syntactic categories) arePOS
useful because they reveal a lot about a word and its neighbors. Knowing whether a
word is a noun or a verb tells us about likely neighboring words (nouns are preceded
by determiners and adjectives, verbs by nouns) and syntactic structure word (nouns
are generally part of noun phrases), making part-of-speech tagging a key aspect
of parsing (Chapter 11). Parts of speech are useful features for labeling named
entities like people or organizations in information extraction (Chapter 17), or for
coreference resolution (Chapter 20). A word’s part-of-speech can even play a role
in speech recognition or synthesis, e.g., the word content is pronounced CONtent
when it is a noun and conTENT when it is an adjective.

This chapter introduces parts-of-speech, and then introduces two algorithms for
part-of-speech tagging, the task of assigning parts-of-speech to words. One is
generative— Hidden Markov Model (HMM)—and one is discriminative—the Max-
imum Entropy Markov Model (MEMM). Chapter 9 then introduces a third algorithm
based on the recurrent neural network (RNN). All three have roughly equal perfor-
mance but, as we’ll see, have different tradeoffs.

8.1 (Mostly) English Word Classes

Until now we have been using part-of-speech terms like noun and verb rather
freely. In this section we give a more complete definition of these and other classes.
While word classes do have semantic tendencies—adjectives, for example, often

1 Nonetheless, eight isn’t very many and, as we’ll see, recent tagsets have more.

2 CHAPTER 8 • PART-OF-SPEECH TAGGING

describe properties and nouns people— parts-of-speech are traditionally defined in-
stead based on syntactic and morphological function, grouping words that have sim-
ilar neighboring words (their distributional properties) or take similar affixes (their
morphological properties).

Parts-of-speech can be divided into two broad supercategories: closed classclosed class
types and open class types. Closed classes are those with relatively fixed member-open class
ship, such as prepositions—new prepositions are rarely coined. By contrast, nouns
and verbs are open classes—new nouns and verbs like iPhone or to fax are contin-
ually being created or borrowed. Any given speaker or corpus may have different
open class words, but all speakers of a language, and sufficiently large corpora,
likely share the set of closed class words. Closed class words are generally function
words like of, it, and, or you, which tend to be very short, occur frequently, andfunction word
often have structuring uses in grammar.

Four major open classes occur in the languages of the world: nouns, verbs,
adjectives, and adverbs. English has all four, although not every language does.
The syntactic class noun includes the words for most people, places, or things, butnoun
others as well. Nouns include concrete terms like ship and chair, abstractions like
bandwidth and relationship, and verb-like terms like pacing as in His pacing to and
fro became quite annoying. What defines a noun in English, then, are things like its
ability to occur with determiners (a goat, its bandwidth, Plato’s Republic), to take
possessives (IBM’s annual revenue), and for most but not all nouns to occur in the
plural form (goats, abaci).

Open class nouns fall into two classes. Proper nouns, like Regina, Colorado,proper noun
and IBM, are names of specific persons or entities. In English, they generally aren’t
preceded by articles (e.g., the book is upstairs, but Regina is upstairs). In written
English, proper nouns are usually capitalized. The other class, common nouns, arecommon noun
divided in many languages, including English, into count nouns and mass nouns.count noun

mass noun Count nouns allow grammatical enumeration, occurring in both the singular and plu-
ral (goat/goats, relationship/relationships) and they can be counted (one goat, two
goats). Mass nouns are used when something is conceptualized as a homogeneous
group. So words like snow, salt, and communism are not counted (i.e., *two snows
or *two communisms). Mass nouns can also appear without articles where singular
count nouns cannot (Snow is white but not *Goat is white).

Verbs refer to actions and processes, including main verbs like draw, provide,verb
and go. English verbs have inflections (non-third-person-sg (eat), third-person-sg
(eats), progressive (eating), past participle (eaten)). While many researchers believe
that all human languages have the categories of noun and verb, others have argued
that some languages, such as Riau Indonesian and Tongan, don’t even make this
distinction (Broschart 1997; Evans 2000; Gil 2000) .

The third open class English form is adjectives, a class that includes many termsadjective
for properties or qualities. Most languages have adjectives for the concepts of color
(white, black), age (old, young), and value (good, bad), but there are languages
without adjectives. In Korean, for example, the words corresponding to English
adjectives act as a subclass of verbs, so what is in English an adjective “beautiful”
acts in Korean like a verb meaning “to be beautiful”.

The final open class form, adverbs, is rather a hodge-podge in both form andadverb
meaning. In the following all the italicized words are adverbs:

Actually, I ran home extremely quickly yesterday

What coherence the class has semantically may be solely that each of these
words can be viewed as modifying something (often verbs, hence the name “ad-

8.1 • (MOSTLY) ENGLISH WORD CLASSES 3

verb”, but also other adverbs and entire verb phrases). Directional adverbs or loca-
tive adverbs (home, here, downhill) specify the direction or location of some action;locative
degree adverbs (extremely, very, somewhat) specify the extent of some action, pro-degree
cess, or property; manner adverbs (slowly, slinkily, delicately) describe the mannermanner
of some action or process; and temporal adverbs describe the time that some ac-temporal
tion or event took place (yesterday, Monday). Because of the heterogeneous nature
of this class, some adverbs (e.g., temporal adverbs like Monday) are tagged in some
tagging schemes as nouns.

The closed classes differ more from language to language than do the open
classes. Some of the important closed classes in English include:

prepositions: on, under, over, near, by, at, from, to, with
particles: up, down, on, off, in, out, at, by
determiners: a, an, the
conjunctions: and, but, or, as, if, when
pronouns: she, who, I, others
auxiliary verbs: can, may, should, are
numerals: one, two, three, first, second, third

Prepositions occur before noun phrases. Semantically they often indicate spatialpreposition
or temporal relations, whether literal (on it, before then, by the house) or metaphor-
ical (on time, with gusto, beside herself), but often indicate other relations as well,
like marking the agent in (Hamlet was written by Shakespeare, A particle resemblesparticle
a preposition or an adverb and is used in combination with a verb. Particles often
have extended meanings that aren’t quite the same as the prepositions they resemble,
as in the particle over in she turned the paper over.

A verb and a particle that act as a single syntactic and/or semantic unit are
called a phrasal verb. The meaning of phrasal verbs is often problematically non-phrasal verb
compositional—not predictable from the distinct meanings of the verb and the par-
ticle. Thus, turn down means something like ‘reject’, rule out ‘eliminate’, find out
‘discover’, and go on ‘continue’.

A closed class that occurs with nouns, often marking the beginning of a noun
phrase, is the determiner. One small subtype of determiners is the article: Englishdeterminer

article has three articles: a, an, and the. Other determiners include this and that (this chap-
ter, that page). A and an mark a noun phrase as indefinite, while the can mark it
as definite; definiteness is a discourse property (Chapter 21). Articles are quite fre-
quent in English; indeed, the is the most frequently occurring word in most corpora
of written English, and a and an are generally right behind.

Conjunctions join two phrases, clauses, or sentences. Coordinating conjunc-conjunctions
tions like and, or, and but join two elements of equal status. Subordinating conjunc-
tions are used when one of the elements has some embedded status. For example,
that in “I thought that you might like some milk” is a subordinating conjunction
that links the main clause I thought with the subordinate clause you might like some
milk. This clause is called subordinate because this entire clause is the “content” of
the main verb thought. Subordinating conjunctions like that which link a verb to its
argument in this way are also called complementizers.complementizer

Pronouns are forms that often act as a kind of shorthand for referring to somepronoun
noun phrase or entity or event. Personal pronouns refer to persons or entities (you,personal
she, I, it, me, etc.). Possessive pronouns are forms of personal pronouns that in-possessive
dicate either actual possession or more often just an abstract relation between the
person and some object (my, your, his, her, its, one’s, our, their). Wh-pronounswh
(what, who, whom, whoever) are used in certain question forms, or may also act as

4 CHAPTER 8 • PART-OF-SPEECH TAGGING

complementizers (Frida, who married Diego. . . ).
A closed class subtype of English verbs are the auxiliary verbs. Cross-linguist-auxiliary

ically, auxiliaries mark semantic features of a main verb: whether an action takes
place in the present, past, or future (tense), whether it is completed (aspect), whether
it is negated (polarity), and whether an action is necessary, possible, suggested, or
desired (mood). English auxiliaries include the copula verb be, the two verbs do andcopula
have, along with their inflected forms, as well as a class of modal verbs. Be is calledmodal
a copula because it connects subjects with certain kinds of predicate nominals and
adjectives (He is a duck). The verb have can mark the perfect tenses (I have gone, I
had gone), and be is used as part of the passive (We were robbed) or progressive (We
are leaving) constructions. Modals are used to mark the mood associated with the
event depicted by the main verb: can indicates ability or possibility, may permission
or possibility, must necessity. There is also a modal use of have (e.g., I have to go).

English also has many words of more or less unique function, including inter-
jections (oh, hey, alas, uh, um), negatives (no, not), politeness markers (please,interjection

negative thank you), greetings (hello, goodbye), and the existential there (there are two on
the table) among others. These classes may be distinguished or lumped together as
interjections or adverbs depending on the purpose of the labeling.

8.2 The Penn Treebank Part-of-Speech Tagset

An important tagset for English is the 45-tag Penn Treebank tagset (Marcus et al.,
1993), shown in Fig. 8.1, which has been used to label many corpora. In such
labelings, parts-of-speech are generally represented by placing the tag after each
word, delimited by a slash:

Tag Description Example Tag Description Example Tag Description Example
CC coordinating

conjunction
and, but, or PDT predeterminer all, both VBP verb non-3sg

present
eat

CD cardinal number one, two POS possessive ending ’s VBZ verb 3sg pres eats
DT determiner a, the PRP personal pronoun I, you, he WDT wh-determ. which, that
EX existential ‘there’ there PRP$ possess. pronoun your, one’s WP wh-pronoun what, who
FW foreign word mea culpa RB adverb quickly WP$ wh-possess. whose
IN preposition/

subordin-conj
of, in, by RBR comparative

adverb
faster WRB wh-adverb how, where

JJ adjective yellow RBS superlatv. adverb fastest $ dollar sign $
JJR comparative adj bigger RP particle up, off # pound sign #
JJS superlative adj wildest SYM symbol +,%, & “ left quote ‘ or “
LS list item marker 1, 2, One TO “to” to ” right quote ’ or ”
MD modal can, should UH interjection ah, oops ( left paren [, (, {, < NN sing or mass noun llama VB verb base form eat ) right paren ], ), }, >
NNS noun, plural llamas VBD verb past tense ate , comma ,
NNP proper noun, sing. IBM VBG verb gerund eating . sent-end punc . ! ?
NNPS proper noun, plu. Carolinas VBN verb past part. eaten : sent-mid punc : ; … – –

Figure 8.1 Penn Treebank part-of-speech tags (including punctuation).

(8.1) The/DT grand/JJ jury/NN commented/VBD on/IN a/DT number/NN of/IN
other/JJ topics/NNS ./.

(8.2) There/EX are/VBP 70/CD children/NNS there/RB

8.2 • THE PENN TREEBANK PART-OF-SPEECH TAGSET 5

(8.3) Preliminary/JJ findings/NNS were/VBD reported/VBN in/IN today/NN
’s/POS New/NNP England/NNP Journal/NNP of/IN Medicine/NNP ./.

Example (8.1) shows the determiners the and a, the adjectives grand and other,
the common nouns jury, number, and topics, and the past tense verb commented.
Example (8.2) shows the use of the EX tag to mark the existential there construction
in English, and, for comparison, another use of there which is tagged as an adverb
(RB). Example (8.3) shows the segmentation of the possessive morpheme ’s a pas-
sive construction, ‘were reported’, in which reported is marked as a past participle
(VBN). Note that since New England Journal of Medicine is a proper noun, the Tree-
bank tagging chooses to mark each noun in it separately as NNP, including journal
and medicine, which might otherwise be labeled as common nouns (NN).

Corpora labeled with parts-of-speech are crucial training (and testing) sets for
statistical tagging algorithms. Three main tagged corpora are consistently used for
training and testing part-of-speech taggers for English. The Brown corpus is a mil-Brown
lion words of samples from 500 written texts from different genres published in the
United States in 1961. The WSJ corpus contains a million words published in theWSJ
Wall Street Journal in 1989. The Switchboard corpus consists of 2 million wordsSwitchboard
of telephone conversations collected in 1990-1991. The corpora were created by
running an automatic part-of-speech tagger on the texts and then human annotators
hand-corrected each tag.

There are some minor differences in the tagsets used by the corpora. For example
in the WSJ and Brown corpora, the single Penn tag TO is used for both the infinitive
to (I like to race) and the preposition to (go to the store), while in Switchboard the
tag TO is reserved for the infinitive use of to and the preposition is tagged IN:

Well/UH ,/, I/PRP ,/, I/PRP want/VBP to/TO go/VB to/IN a/DT restaurant/NN

Finally, there are some idiosyncracies inherent in any tagset. For example, be-
cause the Penn 45 tags were collapsed from a larger 87-tag tagset, the original
Brown tagset, some potential useful distinctions were lost. The Penn tagset was
designed for a treebank in which sentences were parsed, and so it leaves off syntac-
tic information recoverable from the parse tree. Thus for example the Penn tag IN is
used for both subordinating conjunctions like if, when, unless, after:

after/IN spending/VBG a/DT day/NN at/IN the/DT beach/NN

and prepositions like in, on, after:

after/IN sunrise/NN

Words are generally tokenized before tagging. The Penn Treebank and the
British National Corpus split contractions and the ’s-genitive from their stems:2

would/MD n’t/RB
children/NNS ’s/POS

The Treebank tagset assumes that tokenization of multipart words like New
York is done at whitespace, thus tagging. a New York City firm as a/DT New/NNP
York/NNP City/NNP firm/NN.

Another commonly used tagset, the Universal POS tag set of the Universal De-
pendencies project (Nivre et al., 2016), is used when building systems that can tag
many languages. See Section 8.7.

2 Indeed, the Treebank tag POS is used only for ’s, which must be segmented in tokenization.

6 CHAPTER 8 • PART-OF-SPEECH TAGGING

8.3 Part-of-Speech Tagging

Part-of-speech tagging is the process of assigning a part-of-speech marker to eachpart-of-speechtagging
word in an input text.3 The input to a tagging algorithm is a sequence of (tokenized)
words and a tagset, and the output is a sequence of tags, one per token.

Tagging is a disambiguation task; words are ambiguous —have more than oneambiguous
possible part-of-speech—and the goal is to find the correct tag for the situation.
For example, book can be a verb (book that flight) or a noun (hand me that book).
That can be a determiner (Does that flight serve dinner) or a complementizer (I
thought that your flight was earlier). The goal of POS-tagging is to resolve theseambiguityresolution
ambiguities, choosing the proper tag for the context. How common is tag ambiguity?
Fig. 8.2 shows that most word types (80-86%) are unambiguous (Janet is always
NNP, funniest JJS, and hesitantly RB). But the ambiguous words, though accounting
for only 14-15% of the vocabulary, are very common words, and hence 55-67% of
word tokens in running text are ambiguous.4

Types: WSJ Brown
Unambiguous (1 tag) 44,432 (86%) 45,799 (85%)
Ambiguous (2+ tags) 7,025 (14%) 8,050 (15%)

Tokens:
Unambiguous (1 tag) 577,421 (45%) 384,349 (33%)
Ambiguous (2+ tags) 711,780 (55%) 786,646 (67%)

Figure 8.2 Tag ambiguity for word types in Brown and WSJ, using Treebank-3 (45-tag)
tagging. Punctuation were treated as words, and words were kept in their original case.

Some of the most ambiguous frequent words are that, back, down, put and set;
here are some examples of the 6 different parts-of-speech for the word back:

earnings growth took a back/JJ seat
a small building in the back/NN
a clear majority of senators back/VBP the bill
Dave began to back/VB toward the door
enable the country to buy back/RP about debt
I was twenty-one back/RB then

Nonetheless, many words are easy to disambiguate, because their different tags
aren’t equally likely. For example, a can be a determiner or the letter a, but the
determiner sense is much more likely. This idea suggests a simplistic baseline algo-
rithm for part-of-speech tagging: given an ambiguous word, choose the tag which is
most frequent in the training corpus. This is a key concept:

Most Frequent Class Baseline: Always compare a classifier against a baseline at
least as good as the most frequent class baseline (assigning each token to the class
it occurred in most often in the training set).

How good is this baseline? A standard way to measure the performance of part-
of-speech taggers is accuracy: the percentage of tags correctly labeled (matchingaccuracy

3 Tags are also applied to punctuation, so assumes tokenzing of commas, quotation marks, etc., and
disambiguating end-of-sentence periods from periods inside words (e.g., etc.).
4 Note the large differences across the two genres, especially in token frequency. Tags in the WSJ corpus
are less ambiguous; its focus on financial news leads to a more limited distribution of word usages than
the diverse genres of the Brown corpus.

8.4 • HMM PART-OF-SPEECH TAGGING 7

human labels on a test set). If we train on the WSJ training corpus and test on sec-
tions 22-24 of the same corpus the most-frequent-tag baseline achieves an accuracy
of 92.34%. By contrast, the state of the art in part-of-speech tagging on this dataset
is around 97% tag accuracy, a performance that is achievable by most algorithms
(HMMs, MEMMs, neural networks, rule-based algorithms). See Section 8.7 on
other languages and genres.

8.4 HMM Part-of-Speech Tagging

In this section we introduce the use of the Hidden Markov Model for part-of-speech
tagging. The HMM is a sequence model. A sequence model or sequence classi-sequence model
fier is a model whose job is to assign a label or class to each unit in a sequence,
thus mapping a sequence of observations to a sequence of labels. An HMM is a
probabilistic sequence model: given a sequence of units (words, letters, morphemes,
sentences, whatever), it computes a probability distribution over possible sequences
of labels and chooses the best label sequence.

8.4.1 Markov Chains
The HMM is based on augmenting the Markov chain. A Markov chain is a modelMarkov chain
that tells us something about the probabilities of sequences of random variables,
states, each of which can take on values from some set. These sets can be words, or
tags, or symbols representing anything, for example the weather. A Markov chain
makes a very strong assumption that if we want to predict the future in the sequence,
all that matters is the current state. All the states before the current state have no im-
pact on the future except via the current state. It’s as if to predict tomorrow’s weather
you could examine today’s weather but you weren’t allowed to look at yesterday’s
weather.

WARM3HOT1

COLD2

.1 .1

.1
.1

charminguniformly

are

.4 .5

.5
.5 .2

.6 .2

(a) (b)

Figure 8.3 A Markov chain for weather (a) and one for words (b), showing states and
transitions. A start distribution π is required; setting π = [0.1, 0.7, 0.2] for (a) would mean a
probability 0.7 of starting in state 2 (cold), probability 0.1 of starting in state 1 (hot), etc.

More formally, consider a sequence of state variables q1,q2, …,qi. A Markov
model embodies the Markov assumption on the probabilities of this sequence: thatMarkovassumption
when predicting the future, the past doesn’t matter, only the present.

Markov Assumption: P(qi = a|q1…qi−1) = P(qi = a|qi−1) (8.4)

Figure 8.3a shows a Markov chain for assigning a probability to a sequence of
weather events, for which the vocabulary consists of HOT, COLD, and WARM. The

8 CHAPTER 8 • PART-OF-SPEECH TAGGING

states are represented as nodes in the graph, and the transitions, with their probabil-
ities, as edges. The transitions are probabilities: the values of arcs leaving a given
state must sum to 1. Figure 8.3b shows a Markov chain for assigning a probability to
a sequence of words w1…wn. This Markov chain should be familiar; in fact, it repre-
sents a bigram language model, with each edge expressing the probability p(wi|w j)!
Given the two models in Fig. 8.3, we can assign a probability to any sequence from
our vocabulary.

Formally, a Markov chain is specified by the following components:

Q = q1q2 . . .qN a set of N states
A = a11a12 . . .an1 . . .ann a transition probability matrix A, each ai j represent-

ing the probability of moving from state i to state j, s.t.∑n
j=1 ai j = 1 ∀i

π = π1,π2, …,πN an initial probability distribution over states. πi is the
probability that the Markov chain will start in state i.
Some states j may have π j = 0, meaning that they cannot
be initial states. Also,

∑n
i=1 πi = 1

Before you go on, use the sample probabilities in Fig. 8.3a (with π = [.1, .7.,2])
to compute the probability of each of the following sequences:

(8.5) hot hot hot hot
(8.6) cold hot cold hot

What does the difference in these probabilities tell you about a real-world weather
fact encoded in Fig. 8.3a?

8.4.2 The Hidden Markov Model
A Markov chain is useful when we need to compute a probability for a sequence
of observable events. In many cases, however, the events we are interested in are
hidden: we don’t observe them directly. For example we don’t normally observehidden
part-of-speech tags in a text. Rather, we see words, and must infer the tags from the
word sequence. We call the tags hidden because they are not observed.

A hidden Markov model (HMM) allows us to talk about both observed eventsHiddenMarkov model
(like words that we see in the input) and hidden events (like part-of-speech tags) that
we think of as causal factors in our probabilistic model. An HMM is specified by
the following components:

Q = q1q2 . . .qN a set of N states
A = a11 . . .ai j . . .aNN a transition probability matrix A, each ai j representing the probability

of moving from state i to state j, s.t.
∑N

j=1 ai j = 1 ∀i
O = o1o2 . . .oT a sequence of T observations, each one drawn from a vocabulary V =

v1,v2, …,vV
B = bi(ot) a sequence of observation likelihoods, also called emission probabili-

ties, each expressing the probability of an observation ot being generated
from a state i

π = π1,π2, …,πN an initial probability distribution over states. πi is the probability that
the Markov chain will start in state i. Some states j may have π j = 0,
meaning that they cannot be initial states. Also,

∑n
i=1 πi = 1

8.4 • HMM PART-OF-SPEECH TAGGING 9

A first-order hidden Markov model instantiates two simplifying assumptions.
First, as with a first-order Markov chain, the probability of a particular state depends
only on the previous state:

Markov Assumption: P(qi|q1…qi−1) = P(qi|qi−1) (8.7)

Second, the probability of an output observation oi depends only on the state that
produced the observation qi and not on any other states or any other observations:

Output Independence: P(oi|q1 . . .qi, . . . ,qT ,o1, . . . ,oi, . . . ,oT ) = P(oi|qi) (8.8)

8.4.3 The components of an HMM tagger
Let’s start by looking at the pieces of an HMM tagger, and then we’ll see how to use
it to tag. An HMM has two components, the A and B probabilities.

The A matrix contains the tag transition probabilities P(ti|ti−1) which represent
the probability of a tag occurring given the previous tag. For example, modal verbs
like will are very likely to be followed by a verb in the base form, a VB, like race, so
we expect this probability to be high. We compute the maximum likelihood estimate
of this transition probability by counting, out of the times we see the first tag in a
labeled corpus, how often the first tag is followed by the second:

P(ti|ti−1) =
C(ti−1, ti)
C(ti−1)

(8.9)

In the WSJ corpus, for example, MD occurs 13124 times of which it is followed
by VB 10471, for an MLE estimate of

P(V B|MD) =
C(MD,V B)

C(MD)
=

10471
13124

= .80 (8.10)

Let’s walk through an example, seeing how these probabilities are estimated and
used in a sample tagging task, before we return to the algorithm for decoding.

In HMM tagging, the probabilities are estimated by counting on a tagged training
corpus. For this example we’ll use the tagged WSJ corpus.

The B emission probabilities, P(wi|ti), represent the probability, given a tag (say
MD), that it will be associated with a given word (say will). The MLE of the emis-
sion probability is

P(wi|ti) =
C(ti,wi)

C(ti)
(8.11)

Of the 13124 occurrences of MD in the WSJ corpus, it is associated with will 4046
times:

P(will|MD) =
C(MD,will)

C(MD)
=

4046
13124

= .31 (8.12)

We saw this kind of Bayesian modeling in Chapter 4; recall that this likelihood
term is not asking “which is the most likely tag for the word will?” That would be
the posterior P(MD|will). Instead, P(will|MD) answers the slightly counterintuitive
question “If we were going to generate a MD, how likely is it that this modal would
be will?”

The A transition probabilities, and B observation likelihoods of the HMM are
illustrated in Fig. 8.4 for three states in an HMM part-of-speech tagger; the full
tagger would have one state for each tag.

10 CHAPTER 8 • PART-OF-SPEECH TAGGING

NN3VB1

MD2

a22

a11

a12
a21

a13

a33

a32

a23

a31

Figure 8.4 An illustration of the two parts of an HMM representation: the A transition
probabilities used to compute the prior probability, and the B observation likelihoods that are
associated with each state, one likelihood for each possible observation word.

8.4.4 HMM tagging as decoding
For any model, such as an HMM, that contains hidden variables, the task of deter-
mining the hidden variables sequence corresponding to the sequence of observations
is called decoding. More formally,decoding

Decoding: Given as input an HMM λ = (A,B) and a sequence of ob-
servations O = o1,o2, …,oT , find the most probable sequence of states
Q = q1q2q3 . . .qT .

For part of speech tagging, the goal of HMM decoding is to choose the tag
sequence tn1 that is most probable given the observation sequence of n words words
wn1:

t̂n1 = argmax
tn1

P(tn1 |w
n
1) (8.13)

The way we’ll do this in the HMM is to use Bayes’ rule to instead compute:

t̂n1 = argmax
tn1

P(wn1|t
n
1 )P(t

n
1 )

P(wn1)
(8.14)

Furthermore, we simplify Eq. 8.14 by dropping the denominator P(wn1):

t̂n1 = argmax
tn1

P(wn1|t
n
1 )P(t

n
1 ) (8.15)

HMM taggers make two further simplifying assumptions. The first is that the
probability of a word appearing depends only on its own tag and is independent of
neighboring words and tags:

P(wn1|t
n
1 ) ≈

n∏
i=1

P(wi|ti) (8.16)

The second assumption, the bigram assumption, is that the probability of a tag
is dependent only on the previous tag, rather than the entire tag sequence;

P(tn1 ) ≈
n∏

i=1

P(ti|ti−1) (8.17)

8.4 • HMM PART-OF-SPEECH TAGGING 11

Plugging the simplifying assumptions from Eq. 8.16 and Eq. 8.17 into Eq. 8.15
results in the following equation for the most probable tag sequence from a bigram
tagger:

t̂n1 = argmax
tn1

P(tn1 |w
n
1)≈ argmax

tn1

n∏
i=1

emission︷︸︸︷
P(wi|ti)

transition︷︸︸︷
P(ti|ti−1) (8.18)

The two parts of Eq. 8.18 correspond neatly to the B emission probability and
A transition probability that we just defined above!

8.4.5 The Viterbi Algorithm
The decoding algorithm for HMMs is the Viterbi algorithm shown in Fig. 8.5. AsViterbialgorithm
an instance of dynamic programming, Viterbi resembles the dynamic program-
ming minimum edit distance algorithm of Chapter 2.

function VITERBI(observations of len T,state-graph of len N) returns best-path, path-prob

create a path probability matrix viterbi[N,T]
for each state s from 1 to N do ; initialization step

viterbi[s,1]←πs ∗ bs(o1)
backpointer[s,1]←0

for each time step t from 2 to T do ; recursion step
for each state s from 1 to N do

viterbi[s,t]←
N

max
s′=1

viterbi[s′, t−1] ∗ as′,s ∗ bs(ot)

backpointer[s,t]←
N

argmax
s′=1

viterbi[s′, t−1] ∗ as′,s ∗ bs(ot)

bestpathprob←
N

max
s=1

viterbi[s,T ] ; termination step

bestpathpointer←
N

argmax
s=1

viterbi[s,T ] ; termination step

bestpath← the path starting at state bestpathpointer, that follows backpointer[] to states back in time
return bestpath, bestpathprob

Figure 8.5 Viterbi algorithm for finding the optimal sequence of tags. Given an observation sequence and an
HMM λ = (A,B), the algorithm returns the state path through the HMM that assigns maximum likelihood to
the observation sequence.

The Viterbi algorithm first sets up a probability matrix or lattice, with one col-
umn for each observation ot and one row for each state in the state graph. Each col-
umn thus has a cell for each state qi in the single combined automaton. Figure 8.6
shows an intuition of this lattice for the sentence Janet will back the bill.

Each cell of the trellis, vt( j), represents the probability that the HMM is in state
j after seeing the first t observations and passing through the most probable state
sequence q1, …,qt−1, given the HMM λ . The value of each cell vt( j) is computed
by recursively taking the most probable path that could lead us to this cell. Formally,
each cell expresses the probability

vt( j) = max
q1,…,qt−1

P(q1…qt−1,o1,o2 . . .ot ,qt = j|λ ) (8.19)

We represent the most probable path by taking the maximum over all possible
previous state sequences max

q1,…,qt−1
. Like other dynamic programming algorithms,

12 CHAPTER 8 • PART-OF-SPEECH TAGGING

NNP NNP NNP

MD MD MD MD

VB VB

JJ JJ JJ

NN NN

RB RBRBRB

DT DT DT DT

NNP

Janet will back the bill

NNP

Figure 8.6 A sketch of the lattice for Janet will back the bill, showing the possible tags (qi)
for each word and highlighting the path corresponding to the correct tag sequence through the
hidden states. States (parts-of-speech) which have a zero probability of generating a particular
word according to the B matrix (such as the probability that a determiner DT will be realized
as Janet) are greyed out.

Viterbi fills each cell recursively. Given that we had already computed the probabil-
ity of being in every state at time t−1, we compute the Viterbi probability by taking
the most probable of the extensions of the paths that lead to the current cell. For a
given state q j at time t, the value vt( j) is computed as

vt( j) =
N

max
i=1

vt−1(i) ai j b j(ot) (8.20)

The three factors that are multiplied in Eq. 8.20 for extending the previous paths to
compute the Viterbi probability at time t are

vt−1(i) the previous Viterbi path probability from the previous time step
ai j the transition probability from previous state qi to current state q j
b j(ot) the state observation likelihood of the observation symbol ot given

the current state j

8.4.6 Working through an example
Let’s tag the sentence Janet will back the bill; the goal is the correct series of tags
(see also Fig. 8.6):

(8.21) Janet/NNP will/MD back/VB the/DT bill/NN

Let the HMM be defined by the two tables in Fig. 8.7 and Fig. 8.8. Figure 8.7
lists the ai j probabilities for transitioning between the hidden states (part-of-speech
tags). Figure 8.8 expresses the bi(ot) probabilities, the observation likelihoods of
words given tags. This table is (slightly simplified) from counts in the WSJ corpus.
So the word Janet only appears as an NNP, back has 4 possible parts of speech, and
the word the can appear as a determiner or as an NNP (in titles like “Somewhere
Over the Rainbow” all words are tagged as NNP).

Figure 8.9 shows a fleshed-out version of the sketch we saw in Fig. 8.6, the
Viterbi trellis for computing the best hidden state sequence for the observation se-
quence Janet will back the bill.

8.4 • HMM PART-OF-SPEECH TAGGING 13

NNP MD VB JJ NN RB DT
0.2767 0.0006 0.0031 0.0453 0.0449 0.0510 0.2026
NNP 0.3777 0.0110 0.0009 0.0084 0.0584 0.0090 0.0025
MD 0.0008 0.0002 0.7968 0.0005 0.0008 0.1698 0.0041
VB 0.0322 0.0005 0.0050 0.0837 0.0615 0.0514 0.2231
JJ 0.0366 0.0004 0.0001 0.0733 0.4509 0.0036 0.0036
NN 0.0096 0.0176 0.0014 0.0086 0.1216 0.0177 0.0068
RB 0.0068 0.0102 0.1011 0.1012 0.0120 0.0728 0.0479
DT 0.1147 0.0021 0.0002 0.2157 0.4744 0.0102 0.0017

Figure 8.7 The A transition probabilities P(ti|ti−1) computed from the WSJ corpus without
smoothing. Rows are labeled with the conditioning event; thus P(V B|MD) is 0.7968.

Janet will back the bill
NNP 0.000032 0 0 0.000048 0
MD 0 0.308431 0 0 0
VB 0 0.000028 0.000672 0 0.000028
JJ 0 0 0.000340 0 0
NN 0 0.000200 0.000223 0 0.002337
RB 0 0 0.010446 0 0
DT 0 0 0 0.506099 0

Figure 8.8 Observation likelihoods B computed from the WSJ corpus without smoothing,
simplified slightly.

There are N = 5 state columns. We begin in column 1 (for the word Janet) by
setting the Viterbi value in each cell to the product of the π transition probability
(the start probability for that state i, which we get from the < s > entry of Fig. 8.7),
and the observation likelihood of the word Janet given the tag for that cell. Most of
the cells in the column are zero since the word Janet cannot be any of those tags.
The reader should find this in Fig. 8.9.

Next, each cell in the will column gets updated. For each state, we compute the
value viterbi[s, t] by taking the maximum over the extensions of all the paths from the
previous column that lead to the current cell according to Eq. 8.20. We have shown
the values for the MD, VB, and NN cells. Each cell gets the max of the 7 values
from the previous column, multiplied by the appropriate transition probability; as it
happens in this case, most of them are zero from the previous column. The remaining
value is multiplied by the relevant observation probability, and the (trivial) max is
taken. In this case the final value, .0000002772, comes from the NNP state at the
previous column. The reader should fill in the rest of the trellis in Fig. 8.9 and
backtrace to reconstruct the correct state sequence NNP MD VB DT NN.

8.4.7 Extending the HMM Algorithm to Trigrams

Practical HMM taggers have a number of extensions of this simple model. One
important missing feature is a wider tag context. In the tagger described above the
probability of a tag depends only on the previous tag:

P(tn1 ) ≈
n∏

i=1

P(ti|ti−1) (8.22)

In practice we use more of the history, letting the probability of a tag depend on

14 CHAPTER 8 • PART-OF-SPEECH TAGGING

π

P(NNP|st
art)

= .28

* P(MD|MD)
= 0

*
P(

M
D|

NN
P)

.0
00

00
9*

.0
1

=
.

00
00

00
9

v1(2)=
.0006 x 0 =

0

v1(1) =
.28* .000032

= .000009

t

MDq2

q1

o1

Janet billwill
o2 o3

back

VB

JJ

v1(3)=
.0031 x 0

= 0

v1(4)= .
045*0=0

o4

* P(MD|VB) = 0

* P(MD|JJ)

= 0

P(VB
|star

t)

= .00
31

P(JJ
|sta

rt) =

.045

backtrace

q3

q4

the

NNq5

RBq6

DTq7

v2(2) =
max * .308 =
.0000002772

v2(5)=
max * .0002
= .0000000001

v2(3)=
max * .000028

= 2.5e-11

v3(6)=
max * .0104

v3(5)=
max * .
000223

v3(4)=
max * .00034

v3(3)=
max * .00067

v1(5)

v1(6)

v1(7)

v2(1)

v2(4)

v2(6)

v2(7)

backtrace

* P
(R

B|
NN

)

* P(NN|NN)

start start start start start

o5

NNP

P(MD
|star

t)

= .00
06

Figure 8.9 The first few entries in the individual state columns for the Viterbi algorithm. Each cell keeps the
probability of the best path so far and a pointer to the previous cell along that path. We have only filled out
columns 1 and 2; to avoid clutter most cells with value 0 are left empty. The rest is left as an exercise for the
reader. After the cells are filled in, backtracing from the end state, we should be able to reconstruct the correct
state sequence NNP MD VB DT NN.

the two previous tags:

P(tn1 ) ≈
n∏

i=1

P(ti|ti−1, ti−2) (8.23)

Extending the algorithm from bigram to trigram taggers gives a small (perhaps a
half point) increase in performance, but conditioning on two previous tags instead of
one requires a significant change to the Viterbi algorithm. For each cell, instead of
taking a max over transitions from each cell in the previous column, we have to take
a max over paths through the cells in the previous two columns, thus considering N2

rather than N hidden states at every observation.
In addition to increasing the context window, HMM taggers have a number of

other advanced features. One is to let the tagger know the location of the end of the
sentence by adding dependence on an end-of-sequence marker for tn+1. This gives
the following equation for part-of-speech tagging:

t̂n1 = argmax
tn1

P(tn1 |w
n
1)≈ argmax

tn1

[
n∏

i=1

P(wi|ti)P(ti|ti−1, ti−2)

]
P(tn+1|tn) (8.24)

In tagging any sentence with Eq. 8.24, three of the tags used in the context will
fall off the edge of the sentence, and hence will not match regular words. These tags,

8.4 • HMM PART-OF-SPEECH TAGGING 15

t−1, t0, and tn+1, can all be set to be a single special ‘sentence boundary’ tag that is
added to the tagset, which assumes sentences boundaries have already been marked.

One problem with trigram taggers as instantiated in Eq. 8.24 is data sparsity.
Any particular sequence of tags ti−2, ti−1, ti that occurs in the test set may simply
never have occurred in the training set. That means we cannot compute the tag
trigram probability just by the maximum likelihood estimate from counts, following
Eq. 8.25:

P(ti|ti−1, ti−2) =
C(ti−2, ti−1, ti)
C(ti−2, ti−1)

(8.25)

Just as we saw with language modeling, many of these counts will be zero
in any training set, and we will incorrectly predict that a given tag sequence will
never occur! What we need is a way to estimate P(ti|ti−1, ti−2) even if the sequence
ti−2, ti−1, ti never occurs in the training data.

The standard approach to solving this problem is the same interpolation idea
we saw in language modeling: estimate the probability by combining more robust,
but weaker estimators. For example, if we’ve never seen the tag sequence PRP VB
TO, and so can’t compute P(TO|PRP,VB) from this frequency, we still could rely
on the bigram probability P(TO|VB), or even the unigram probability P(TO). The
maximum likelihood estimation of each of these probabilities can be computed from
a corpus with the following counts:

Trigrams P̂(ti|ti−1, ti−2) =
C(ti−2, ti−1, ti)
C(ti−2, ti−1)

(8.26)

Bigrams P̂(ti|ti−1) =
C(ti−1, ti)
C(ti−1)

(8.27)

Unigrams P̂(ti) =
C(ti)

N
(8.28)

The standard way to combine these three estimators to estimate the trigram probabil-
ity P(ti|ti−1, ti−2) is via linear interpolation. We estimate the probability P(ti|ti−1ti−2)
by a weighted sum of the unigram, bigram, and trigram probabilities:

P(ti|ti−1ti−2) = λ3P̂(ti|ti−1ti−2)+λ2P̂(ti|ti−1)+λ1P̂(ti) (8.29)

We require λ1 + λ2 + λ3 = 1, ensuring that the resulting P is a probability distri-
bution. The λ s are set by deleted interpolation (Jelinek and Mercer, 1980): wedeletedinterpolation
successively delete each trigram from the training corpus and choose the λ s so as to
maximize the likelihood of the rest of the corpus. The deletion helps to set the λ s
in such a way as to generalize to unseen data and not overfit. Figure 8.10 gives a
deleted interpolation algorithm for tag trigrams.

8.4.8 Beam Search
When the number of states grows very large, the vanilla Viterbi algorithm be slow.
The complexity of the algorithm is O(N2T ); N (the number of states) can be large
for trigram taggers, which have to consider every previous pair of the 45 tags, re-
sulting in 453 = 91,125 computations per column. N can be even larger for other
applications of Viterbi, for example to decoding in neural networks, as we will see
in future chapters.

One common solution to the complexity problem is the use of beam searchbeam search
decoding. In beam search, instead of keeping the entire column of states at each

16 CHAPTER 8 • PART-OF-SPEECH TAGGING

function DELETED-INTERPOLATION(corpus) returns λ1,λ2,λ3

λ1, λ2, λ3←0
foreach trigram t1, t2, t3 with C(t1, t2, t3)> 0

depending on the maximum of the following three values
case C(t1,t2,t3)−1C(t1,t2)−1 : increment λ3 by C(t1, t2, t3)

case C(t2,t3)−1C(t2)−1 : increment λ2 by C(t1, t2, t3)

case C(t3)−1N−1 : increment λ1 by C(t1, t2, t3)
end

end
normalize λ1,λ2,λ3
return λ1,λ2,λ3

Figure 8.10 The deleted interpolation algorithm for setting the weights for combining un-
igram, bigram, and trigram tag probabilities. If the denominator is 0 for any case, we define
the result of that case to be 0. N is the number of tokens in the corpus. After Brants (2000).

time point t, we just keep the best few hypothesis at that point. At time t this requires
computing the Viterbi score for each of the N cells, sorting the scores, and keeping
only the best-scoring states. The rest are pruned out and not continued forward to
time t +1.

One way to implement beam search is to keep a fixed number of states instead of
all N current states. Here the beam width β is a fixed number of states. Alternativelybeam width
β can be modeled as a fixed percentage of the N states, or as a probability threshold.
Figure 8.11 shows the search lattice using a beam width of 2 states.

JJ

NNP NNP NNP

MD MD MD MD

VB VB

JJ JJ JJ

NN NN

RB RBRBRB

DT DT DT DT

NNP

Janet will back the bill

NN

VB

MD

NN

VB

JJ

RB

NNP

DT

NN

VB

Figure 8.11 A beam search version of Fig. 8.6, showing a beam width of 2. At each time
t, all (non-zero) states are computed, but then they are sorted and only the best 2 states are
propagated forward and the rest are pruned, shown in orange.

8.5 • MAXIMUM ENTROPY MARKOV MODELS 17

8.4.9 Unknown Words
words people
never use —
could be
only I
know them Ishikawa Takuboku 1885–1912

To achieve high accuracy with part-of-speech taggers, it is also important to have
a good model for dealing with unknown words. Proper names and acronyms areunknownwords
created very often, and even new common nouns and verbs enter the language at a
surprising rate. One useful feature for distinguishing parts of speech is word shape:
words starting with capital letters are likely to be proper nouns (NNP).

But the strongest source of information for guessing the part-of-speech of un-
known words is morphology. Words that end in -s are likely to be plural nouns
(NNS), words ending with -ed tend to be past participles (VBN), words ending with
-able adjectives (JJ), and so on. We store for each final letter sequence (for sim-
plicity referred to as word suffixes) of up to 10 letters the statistics of the tag it was
associated with in training. We are thus computing for each suffix of length i the
probability of the tag ti given the suffix letters (Samuelsson 1993, Brants 2000):

P(ti|ln−i+1 . . . ln) (8.30)

Back-off is used to smooth these probabilities with successively shorter suffixes.
Because unknown words are unlikely to be closed-class words like prepositions,
suffix probabilities can be computed only for words whose training set frequency is
≤ 10, or only for open-class words. Separate suffix tries are kept for capitalized and
uncapitalized words.

Finally, because Eq. 8.30 gives a posterior estimate p(ti|wi), we can compute
the likelihood p(wi|ti) that HMMs require by using Bayesian inversion (i.e., using
Bayes rule and computation of the two priors P(ti) and P(ti|ln−i+1 . . . ln)).

In addition to using capitalization information for unknown words, Brants (2000)
also uses capitalization for known words by adding a capitalization feature to each
tag. Thus, instead of computing P(ti|ti−1, ti−2) as in Eq. 8.26, the algorithm com-
putes the probability P(ti,ci|ti−1,ci−1, ti−2,ci−2). This is equivalent to having a cap-
italized and uncapitalized version of each tag, doubling the size of the tagset.

Combining all these features, a trigram HMM like that of Brants (2000) has a
tagging accuracy of 96.7% on the Penn Treebank, perhaps just slightly below the
performance of the best MEMM and neural taggers.

8.5 Maximum Entropy Markov Models

While an HMM can achieve very high accuracy, we saw that it requires a number of
architectural innovations to deal with unknown words, backoff, suffixes, and so on.
It would be so much easier if we could add arbitrary features directly into the model
in a clean way, but that’s hard for generative models like HMMs. Luckily, we’ve
already seen a model for doing this: the logistic regression model of Chapter 5! But
logistic regression isn’t a sequence model; it assigns a class to a single observation.
However, we could turn logistic regression into a discriminative sequence model
simply by running it on successive words, using the class assigned to the prior word

18 CHAPTER 8 • PART-OF-SPEECH TAGGING

as a feature in the classification of the next word. When we apply logistic regression
in this way, it’s called the maximum entropy Markov model or MEMM5MEMM

Let the sequence of words be W = wn1 and the sequence of tags T = t
n
1 . In an

HMM to compute the best tag sequence that maximizes P(T |W ) we rely on Bayes’
rule and the likelihood P(W |T ):

T̂ = argmax
T

P(T |W )

= argmax
T

P(W |T )P(T )

= argmax
T

∏
i

P(wordi|tagi)
∏

i

P(tagi|tagi−1) (8.31)

In an MEMM, by contrast, we compute the posterior P(T |W ) directly, training it to
discriminate among the possible tag sequences:

T̂ = argmax
T

P(T |W )

= argmax
T

∏
i

P(ti|wi, ti−1) (8.32)

Consider tagging just one word. A multinomial logistic regression classifier could
compute the single probability P(ti|wi, ti−1) in a different way that an HMM. Fig. 8.12
shows the intuition of the difference via the direction of the arrows; HMMs compute
likelihood (observation word conditioned on tags) but MEMMs compute posterior
(tags conditioned on observation words).

will

MD VB DT NN

Janet back the bill

NNP

will

MD VB DT NN

Janet back the bill

NNP

Figure 8.12 A schematic view of the HMM (top) and MEMM (bottom) representation of
the probability computation for the correct sequence of tags for the back sentence. The HMM
computes the likelihood of the observation given the hidden state, while the MEMM computes
the posterior of each state, conditioned on the previous state and current observation.

8.5.1 Features in a MEMM
Of course we don’t build MEMMs that condition just on wi and ti−1. The reason to
use a discriminative sequence model is that it’s easier to incorporate a lots of fea-
tures.6 Figure 8.13 shows a graphical intuition of some of these additional features.

5 ‘Maximum entropy model’ is an outdated name for logistic regression; see the history section.
6 Because in HMMs all computation is based on the two probabilities P(tag|tag) and P(word|tag), if
we want to include some source of knowledge into the tagging process, we must find a way to encode
the knowledge into one of these two probabilities. Each time we add a feature we have to do a lot of
complicated conditioning which gets harder and harder as we have more and more such features.

8.5 • MAXIMUM ENTROPY MARKOV MODELS 19

will

MD VB

Janet back the bill

NNP

wi wi+1wi-1

ti-1ti-2

wi-1

Figure 8.13 An MEMM for part-of-speech tagging showing the ability to condition on
more features.

A basic MEMM part-of-speech tagger conditions on the observation word it-
self, neighboring words, and previous tags, and various combinations, using feature
templates like the following:templates

〈ti,wi−2〉,〈ti,wi−1〉,〈ti,wi〉,〈ti,wi+1〉,〈ti,wi+2〉
〈ti, ti−1〉,〈ti, ti−2, ti−1〉,

〈ti, ti−1,wi〉,〈ti,wi−1,wi〉〈ti,wi,wi+1〉, (8.33)

Recall from Chapter 5 that feature templates are used to automatically populate the
set of features from every instance in the training and test set. Thus our example
Janet/NNP will/MD back/VB the/DT bill/NN, when wi is the word back, would gen-
erate the following features:

ti = VB and wi−2 = Janet
ti = VB and wi−1 = will
ti = VB and wi = back
ti = VB and wi+1 = the
ti = VB and wi+2 = bill
ti = VB and ti−1 = MD
ti = VB and ti−1 = MD and ti−2 = NNP
ti = VB and wi = back and wi+1 = the

Also necessary are features to deal with unknown words, expressing properties of
the word’s spelling or shape:

wi contains a particular prefix (from all prefixes of length ≤ 4)
wi contains a particular suffix (from all suffixes of length ≤ 4)
wi contains a number
wi contains an upper-case letter
wi contains a hyphen
wi is all upper case
wi’s word shape
wi’s short word shape
wi is upper case and has a digit and a dash (like CFC-12)
wi is upper case and followed within 3 words by Co., Inc., etc.

Word shape features are used to represent the abstract letter pattern of the wordword shape
by mapping lower-case letters to ‘x’, upper-case to ‘X’, numbers to ’d’, and retaining
punctuation. Thus for example I.M.F would map to X.X.X. and DC10-30 would
map to XXdd-dd. A second class of shorter word shape features is also used. In these
features consecutive character types are removed, so DC10-30 would be mapped to
Xd-d but I.M.F would still map to X.X.X. For example the word well-dressed would
generate the following non-zero valued feature values:

20 CHAPTER 8 • PART-OF-SPEECH TAGGING

prefix(wi) = w
prefix(wi) = we
prefix(wi) = wel
prefix(wi) = well
suffix(wi) = ssed
suffix(wi) = sed
suffix(wi) = ed
suffix(wi) = d
has-hyphen(wi)
word-shape(wi) = xxxx-xxxxxxx
short-word-shape(wi) = x-x

Features for known words, like the templates in Eq. 8.33, are computed for every
word seen in the training set. The unknown word features can also be computed for
all words in training, or only on training words whose frequency is below some
threshold. The result of the known-word templates and word-signature features is a
very large set of features. Generally a feature cutoff is used in which features are
thrown out if they have count < 5 in the training set. 8.5.2 Decoding and Training MEMMs The most likely sequence of tags is then computed by combining these features of the input word wi, its neighbors within l words w i+l i−l , and the previous k tags t i−1 i−k as follows (using θ to refer to feature weights instead of w to avoid the confusion with w meaning words): T̂ = argmax T P(T |W ) = argmax T ∏ i P(ti|wi+li−l , t i−1 i−k ) = argmax T ∏ i exp  ∑ j θ j f j(ti,w i+l i−l , t i−1 i−k )   ∑ t ′∈tagset exp  ∑ j θ j f j(t ′,wi+li−l , t i−1 i−k )   (8.34) How should we decode to find this optimal tag sequence T̂ ? The simplest way to turn logistic regression into a sequence model is to build a local classifier that classifies each word left to right, making a hard classification of the first word in the sentence, then a hard decision on the second word, and so on. This is called a greedy decoding algorithm, because we greedily choose the best tag for each word,greedy as shown in Fig. 8.14. function GREEDY SEQUENCE DECODING(words W, model P) returns tag sequence T for i = 1 to length(W) t̂i = argmax t ′∈ T P(t ′ | wi+li−l , t i−1 i−k ) Figure 8.14 In greedy decoding we simply run the classifier on each token, left to right, each time making a hard decision of which is the best tag. 8.6 • BIDIRECTIONALITY 21 The problem with the greedy algorithm is that by making a hard decision on each word before moving on to the next word, the classifier can’t use evidence from future decisions. Although the greedy algorithm is very fast, and occasionally has sufficient accuracy to be useful, in general the hard decision causes too much a drop in performance, and we don’t use it. Instead we decode an MEMM with the Viterbi algorithm just as with the HMM,Viterbi finding the sequence of part-of-speech tags that is optimal for the whole sentence. For example, assume that our MEMM is only conditioning on the previous tag ti−1 and observed word wi. Concretely, this involves filling an N × T array with the appropriate values for P(ti|ti−1,wi), maintaining backpointers as we proceed. As with HMM Viterbi, when the table is filled, we simply follow pointers back from the maximum value in the final column to retrieve the desired set of labels. The requisite changes from the HMM-style application of Viterbi have to do only with how we fill each cell. Recall from Eq. 8.20 that the recursive step of the Viterbi equation computes the Viterbi value of time t for state j as vt( j) = N max i=1 vt−1(i)ai j b j(ot); 1≤ j ≤ N,1 < t ≤ T (8.35) which is the HMM implementation of vt( j) = N max i=1 vt−1(i) P(s j|si) P(ot |s j) 1≤ j ≤ N,1 < t ≤ T (8.36) The MEMM requires only a slight change to this latter formula, replacing the a and b prior and likelihood probabilities with the direct posterior: vt( j) = N max i=1 vt−1(i) P(s j|si,ot) 1≤ j ≤ N,1 < t ≤ T (8.37) Learning in MEMMs relies on the same supervised learning algorithms we presented for logistic regression. Given a sequence of observations, feature functions, and cor- responding hidden states, we use gradient descent to train the weights to maximize the log-likelihood of the training corpus. 8.6 Bidirectionality The one problem with the MEMM and HMM models as presented is that they are exclusively run left-to-right. While the Viterbi algorithm still allows present deci- sions to be influenced indirectly by future decisions, it would help even more if a decision about word wi could directly use information about future tags ti+1 and ti+2. Adding bidirectionality has another useful advantage. MEMMs have a theoret- ical weakness, referred to alternatively as the label bias or observation bias prob-label bias observation bias lem (Lafferty et al. 2001, Toutanova et al. 2003). These are names for situations when one source of information is ignored because it is explained away by another source. Consider an example from Toutanova et al. (2003), the sequence will/NN to/TO fight/VB. The tag TO is often preceded by NN but rarely by modals (MD), and so that tendency should help predict the correct NN tag for will. But the previ- ous transition P(twill |〈s〉) prefers the modal, and because P(TO|to, twill) is so close to 1 regardless of twill the model cannot make use of the transition probability and incorrectly chooses MD. The strong information that to must have the tag TO has ex- plained away the presence of TO and so the model doesn’t learn the importance of 22 CHAPTER 8 • PART-OF-SPEECH TAGGING the previous NN tag for predicting TO. Bidirectionality helps the model by making the link between TO available when tagging the NN. One way to implement bidirectionality is to switch to a more powerful model called a conditional random field or CRF. The CRF is an undirected graphicalCRF model, which means that it’s not computing a probability for each tag at each time step. Instead, at each time step the CRF computes log-linear functions over a clique, a set of relevant features. Unlike for an MEMM, these might include output features of words in future time steps. The probability of the best sequence is similarly computed by the Viterbi algorithm. Because a CRF normalizes probabilities over all tag sequences, rather than over all the tags at an individual time t, training requires computing the sum over all possible labelings, which makes CRF training quite slow. Simpler methods can also be used; the Stanford tagger uses a bidirectionalStanford tagger version of the MEMM called a cyclic dependency network (Toutanova et al., 2003). Alternatively, any sequence model can be turned into a bidirectional model by using multiple passes. For example, the first pass would use only part-of-speech features from already-disambiguated words on the left. In the second pass, tags for all words, including those on the right, can be used. Alternately, the tagger can be run twice, once left-to-right and once right-to-left. In greedy decoding, for each word the classifier chooses the highest-scoring of the tag assigned by the left-to-right and right-to-left classifier. In Viterbi decoding, the classifier chooses the higher scoring of the two sequences (left-to-right or right-to-left). These bidirectional models lead directly into the bi-LSTM models that we will introduce in Chapter 9 as a standard neural sequence model. 8.7 Part-of-Speech Tagging for Other Languages Augmentations to tagging algorithms become necessary when dealing with lan- guages with rich morphology like Czech, Hungarian and Turkish. These productive word-formation processes result in a large vocabulary for these languages: a 250,000 word token corpus of Hungarian has more than twice as many word types as a similarly sized corpus of English (Oravecz and Dienes, 2002), while a 10 million word token corpus of Turkish contains four times as many word types as a similarly sized English corpus (Hakkani-Tür et al., 2002). Large vocabular- ies mean many unknown words, and these unknown words cause significant per- formance degradations in a wide variety of languages (including Czech, Slovene, Estonian, and Romanian) (Hajič, 2000). Highly inflectional languages also have much more information than English coded in word morphology, like case (nominative, accusative, genitive) or gender (masculine, feminine). Because this information is important for tasks like pars- ing and coreference resolution, part-of-speech taggers for morphologically rich lan- guages need to label words with case and gender information. Tagsets for morpho- logically rich languages are therefore sequences of morphological tags rather than a single primitive tag. Here’s a Turkish example, in which the word izin has three pos- sible morphological/part-of-speech tags and meanings (Hakkani-Tür et al., 2002): 1. Yerdeki izin temizlenmesi gerek. iz + Noun+A3sg+Pnon+Gen The trace on the floor should be cleaned. 2. Üzerinde parmak izin kalmiş iz + Noun+A3sg+P2sg+Nom Your finger print is left on (it). 8.8 • SUMMARY 23 3. Içeri girmek için izin alman gerekiyor. izin + Noun+A3sg+Pnon+Nom You need a permission to enter. Using a morphological parse sequence like Noun+A3sg+Pnon+Gen as the part- of-speech tag greatly increases the number of parts-of-speech, and so tagsets can be 4 to 10 times larger than the 50–100 tags we have seen for English. With such large tagsets, each word needs to be morphologically analyzed to generate the list of possible morphological tag sequences (part-of-speech tags) for the word. The role of the tagger is then to disambiguate among these tags. This method also helps with unknown words since morphological parsers can accept unknown stems and still segment the affixes properly. For non-word-space languages like Chinese, word segmentation (Chapter 2) is either applied before tagging or done jointly. Although Chinese words are on aver- age very short (around 2.4 characters per unknown word compared with 7.7 for En- glish) the problem of unknown words is still large. While English unknown words tend to be proper nouns in Chinese the majority of unknown words are common nouns and verbs because of extensive compounding. Tagging models for Chinese use similar unknown word features to English, including character prefix and suf- fix features, as well as novel features like the radicals of each character in a word. (Tseng et al., 2005). A stanford for multilingual tagging is the Universal POS tag set of the Universal Dependencies project, which contains 16 tags plus a wide variety of features that can be added to them to create a large tagset for any language (Nivre et al., 2016). 8.8 Summary This chapter introduced parts-of-speech and part-of-speech tagging: • Languages generally have a small set of closed class words that are highly frequent, ambiguous, and act as function words, and open-class words like nouns, verbs, adjectives. Various part-of-speech tagsets exist, of between 40 and 200 tags. • Part-of-speech tagging is the process of assigning a part-of-speech label to each of a sequence of words. • Two common approaches to sequence modeling are a generative approach, HMM tagging, and a discriminative approach, MEMM tagging. We will see a third, discriminative neural approach in Chapter 9. • The probabilities in HMM taggers are estimated by maximum likelihood es- timation on tag-labeled training corpora. The Viterbi algorithm is used for decoding, finding the most likely tag sequence • Beam search is a variant of Viterbi decoding that maintains only a fraction of high scoring states rather than all states during decoding. • Maximum entropy Markov model or MEMM taggers train logistic regres- sion models to pick the best tag given an observation word and its context and the previous tags, and then use Viterbi to choose the best sequence of tags. • Modern taggers are generally run bidirectionally. 24 CHAPTER 8 • PART-OF-SPEECH TAGGING Bibliographical and Historical Notes What is probably the earliest part-of-speech tagger was part of the parser in Zellig Harris’s Transformations and Discourse Analysis Project (TDAP), implemented be- tween June 1958 and July 1959 at the University of Pennsylvania (Harris, 1962), although earlier systems had used part-of-speech dictionaries. TDAP used 14 hand- written rules for part-of-speech disambiguation; the use of part-of-speech tag se- quences and the relative frequency of tags for a word prefigures all modern algo- rithms. The parser was implemented essentially as a cascade of finite-state trans- ducers; see Joshi and Hopely (1999) and Karttunen (1999) for a reimplementation. The Computational Grammar Coder (CGC) of Klein and Simmons (1963) had three components: a lexicon, a morphological analyzer, and a context disambiguator. The small 1500-word lexicon listed only function words and other irregular words. The morphological analyzer used inflectional and derivational suffixes to assign part- of-speech classes. These were run over words to produce candidate parts-of-speech which were then disambiguated by a set of 500 context rules by relying on sur- rounding islands of unambiguous words. For example, one rule said that between an ARTICLE and a VERB, the only allowable sequences were ADJ-NOUN, NOUN- ADVERB, or NOUN-NOUN. The TAGGIT tagger (Greene and Rubin, 1971) used the same architecture as Klein and Simmons (1963), with a bigger dictionary and more tags (87). TAGGIT was applied to the Brown corpus and, according to Francis and Kučera (1982, p. 9), accurately tagged 77% of the corpus; the remainder of the Brown corpus was then tagged by hand. All these early algorithms were based on a two-stage architecture in which a dictionary was first used to assign each word a set of potential parts-of-speech, and then lists of hand-written disambiguation rules winnowed the set down to a single part-of-speech per word. Soon afterwards probabilistic architectures began to be developed. Probabili- ties were used in tagging by Stolz et al. (1965) and a complete probabilistic tagger with Viterbi decoding was sketched by Bahl and Mercer (1976). The Lancaster- Oslo/Bergen (LOB) corpus, a British English equivalent of the Brown corpus, was tagged in the early 1980’s with the CLAWS tagger (Marshall 1983; Marshall 1987; Garside 1987), a probabilistic algorithm that approximated a simplified HMM tag- ger. The algorithm used tag bigram probabilities, but instead of storing the word likelihood of each tag, the algorithm marked tags either as rare (P(tag|word)< .01) infrequent (P(tag|word)< .10) or normally frequent (P(tag|word)> .10).

DeRose (1988) developed a quasi-HMM algorithm, including the use of dy-
namic programming, although computing P(t|w)P(w) instead of P(w|t)P(w). The
same year, the probabilistic PARTS tagger of Church (1988), (1989) was probably
the first implemented HMM tagger, described correctly in Church (1989), although
Church (1988) also described the computation incorrectly as P(t|w)P(w) instead
of P(w|t)P(w). Church (p.c.) explained that he had simplified for pedagogical pur-
poses because using the probability P(t|w) made the idea seem more understandable
as “storing a lexicon in an almost standard form”.

Later taggers explicitly introduced the use of the hidden Markov model (Ku-
piec 1992; Weischedel et al. 1993; Schütze and Singer 1994). Merialdo (1994)
showed that fully unsupervised EM didn’t work well for the tagging task and that
reliance on hand-labeled data was important. Charniak et al. (1993) showed the im-
portance of the most frequent tag baseline; the 92.3% number we give above was
from Abney et al. (1999). See Brants (2000) for many implementation details of an
HMM tagger whose performance is still roughly close to state of the art taggers.

EXERCISES 25

Ratnaparkhi (1996) introduced the MEMM tagger, called MXPOST, and the
modern formulation is very much based on his work.

The idea of using letter suffixes for unknown words is quite old; the early Klein
and Simmons (1963) system checked all final letter suffixes of lengths 1-5. The
probabilistic formulation we described for HMMs comes from Samuelsson (1993).
The unknown word features described on page 19 come mainly from (Ratnaparkhi,
1996), with augmentations from Toutanova et al. (2003) and Manning (2011).

State of the art taggers use neural algorithms or (bidirectional) log-linear models
Toutanova et al. (2003). HMM (Brants 2000; Thede and Harper 1999) and MEMM
tagger accuracies are likely just a tad lower.

An alternative modern formalism, the English Constraint Grammar systems (Karls-
son et al. 1995; Voutilainen 1995; Voutilainen 1999), uses a two-stage formalism
much like the early taggers from the 1950s and 1960s. A morphological analyzer
with tens of thousands of English word stem entries returns all parts-of-speech for a
word, using a large feature-based tagset. So the word occurred is tagged with the op-
tions 〈V PCP2 SV〉 and 〈V PAST VFIN SV〉, meaning it can be a participle (PCP2)
for an intransitive (SV) verb, or a past (PAST) finite (VFIN) form of an intransitive
(SV) verb. A set of 3,744 constraints are then applied to the input sentence to rule
out parts-of-speech inconsistent with the context. For example here’s a rule for the
ambiguous word that that eliminates all tags except the ADV (adverbial intensifier)
sense (this is the sense in the sentence it isn’t that odd):

ADVERBIAL-THAT RULE Given input: “that”
if (+1 A/ADV/QUANT); /* if next word is adj, adverb, or quantifier */

(+2 SENT-LIM); /* and following which is a sentence boundary, */
(NOT -1 SVOC/A); /* and the previous word is not a verb like */

/* ‘consider’ which allows adjs as object complements */
then eliminate non-ADV tags else eliminate ADV tag

Manning (2011) investigates the remaining 2.7% of errors in a state-of-the-art
tagger, the bidirectional MEMM-style model described above (Toutanova et al.,
2003). He suggests that a third or half of these remaining errors are due to errors or
inconsistencies in the training data, a third might be solvable with richer linguistic
models, and for the remainder the task is underspecified or unclear.

Supervised tagging relies heavily on in-domain training data hand-labeled by
experts. Ways to relax this assumption include unsupervised algorithms for cluster-
ing words into part-of-speech-like classes, summarized in Christodoulopoulos et al.
(2010), and ways to combine labeled and unlabeled data, for example by co-training
(Clark et al. 2003; Søgaard 2010).

See Householder (1995) for historical notes on parts-of-speech, and Sampson
(1987) and Garside et al. (1997) on the provenance of the Brown and other tagsets.

Exercises
8.1 Find one tagging error in each of the following sentences that are tagged with

the Penn Treebank tagset:

1. I/PRP need/VBP a/DT flight/NN from/IN Atlanta/NN
2. Does/VBZ this/DT flight/NN serve/VB dinner/NNS
3. I/PRP have/VB a/DT friend/NN living/VBG in/IN Denver/NNP
4. Can/VBP you/PRP list/VB the/DT nonstop/JJ afternoon/NN flights/NNS

26 CHAPTER 8 • PART-OF-SPEECH TAGGING

8.2 Use the Penn Treebank tagset to tag each word in the following sentences
from Damon Runyon’s short stories. You may ignore punctuation. Some of
these are quite difficult; do your best.

1. It is a nice night.
2. This crap game is over a garage in Fifty-second Street. . .
3. . . . Nobody ever takes the newspapers she sells . . .
4. He is a tall, skinny guy with a long, sad, mean-looking kisser, and a

mournful voice.
5. . . . I am sitting in Mindy’s restaurant putting on the gefillte fish, which is

a dish I am very fond of, . . .
6. When a guy and a doll get to taking peeks back and forth at each other,

why there you are indeed.

8.3 Now compare your tags from the previous exercise with one or two friend’s
answers. On which words did you disagree the most? Why?

8.4 Implement the “most likely tag” baseline. Find a POS-tagged training set,
and use it to compute for each word the tag that maximizes p(t|w). You will
need to implement a simple tokenizer to deal with sentence boundaries. Start
by assuming that all unknown words are NN and compute your error rate on
known and unknown words. Now write at least five rules to do a better job of
tagging unknown words, and show the difference in error rates.

8.5 Build a bigram HMM tagger. You will need a part-of-speech-tagged corpus.
First split the corpus into a training set and test set. From the labeled training
set, train the transition and observation probabilities of the HMM tagger di-
rectly on the hand-tagged data. Then implement the Viterbi algorithm so that
you can label an arbitrary test sentence. Now run your algorithm on the test
set. Report its error rate and compare its performance to the most frequent tag
baseline.

8.6 Do an error analysis of your tagger. Build a confusion matrix and investigate
the most frequent errors. Propose some features for improving the perfor-
mance of your tagger on these errors.

Exercises 27

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28 Chapter 8 • Part-of-Speech Tagging

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Part-of-Speech Tagging
(Mostly) English Word Classes
The Penn Treebank Part-of-Speech Tagset
Part-of-Speech Tagging
HMM Part-of-Speech Tagging
Markov Chains
The Hidden Markov Model
The components of an HMM tagger
HMM tagging as decoding
The Viterbi Algorithm
Working through an example
Extending the HMM Algorithm to Trigrams
Beam Search
Unknown Words

Maximum Entropy Markov Models
Features in a MEMM
Decoding and Training MEMMs

Bidirectionality
Part-of-Speech Tagging for Other Languages
Summary
Bibliographical and Historical Notes
Exercises

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