Machine Learning for Modeling Poetic Meter

LatinNatural Language ProcessingMachine Learning

08/02/2017:

Grammatical edits.

My interest in language was sparked by Latin classes I took in high-school. Latin is an interesting language for a number of reasons — the aspect of it that always fascinated me is the structure of Roman epic poetry. In this project I begin by developing a Bayesian classifier for predicting poetic meter in Virgil’s Aeneid. Following that, I highlight the problems inherent in using a Naive Bayes approach and solve those problems by extending the classifier with a Hidden Markov Model.

The Aeneid, a 12-book long poem that tells the story of the founding of Rome, uses a rhythmic scheme called dactylic hexameter. Dactylic hexameter¹ is a meter that consists of lines made from six bars or “feet”. Each foot can be either a dactyl, which contains a long syllable followed by two short syllables (“dum-ditty”), and is marked with the notation

‒ ∪ ∪

or a spondee, which contains a long syllable followed by another long syllable (“dum, dum”) and is marked as:

‒ ‒

The only exception to this rule is in the sixth foot where the last syllable in the line is an anceps syllable. Anceps can function as either long or short and are either marked with a

✕

or left blank. The metrical pattern of a line of dactylic hexameter looks something like:

‒ ∪ ∪ | ‒ ∪ ∪ | ‒ ‒ | ‒ ‒ | ‒ ∪ ∪ | ‒ ✕

Here’s an example from the Aeneid in which Virgil uses a series of dactyls (“dum-ditty”) to capture the speed of a running horse:

qūadrŭpĕ | dāntĕ pŭ | trēm sŏnĭ | tū qŭatĭt | ūngŭlă | cāmpum

“a hoof shakes the crumbling field with a galloping sound”

And another in which he does the opposite — using a series of spondees to mimic the pounding sound of blacksmiths at work (via Wikipedia):

īll(i) īn | tēr sē | sē mūl | tā vī | brācchĭă | tōllunt

“take up their arms with great strength one to another”

This line illustrates something that makes all of this even more complicated — a phenomenon called elision. If a word-terminal syllable ends in a vowel and the next word in the line begins with a vowel, the syllable can be completely omitted from the meter and the two words blend together when pronounced. In the line above, ‘īll(i) īntēr’ would be pronounced as ‘īllīntēr’. This is marked by wrapping the omitted vowel in ( ).

Latin poetry does not come with syllable lengths and metrical annotations. Presumably, native Latin speakers naturally knew how to determine syllable length. It is harder for a non-native speaker to do and there aren’t a set of rules that determine if a syllable is long or short. There are rough guidelines but authors often intentionally break them for poetic effect.² Metrical scansion is far from deterministic so the author has more freedom for creative expression. In my project, I write a computer program that uses a statistical model to scan lines of Latin poetry. I first create a naive Bayesian model to estimate the emission probability distribution of a Hidden Markov Model (HMM). I then find the Viterbi path on the HMM to predict the most likely sequence of syllable lengths for the line of poetry.

Building a Corpus

I obtained two corpora — a normal copy of Virgil’s Aeneid (in Latin, via the Project Gutenberg website) and a copy of the first 33 lines of the first book of the Aeneid with metrical scansion (in Latin, via Daniel Rodde’s website). I will refer to them as the non-scanned corpus and the scanned corpus, respectively. As an example, here is the first line from the non-scanned corpus:

Arma virumque cano, Trojae qui primus ab oris.

And from the scanned corpus

Ārmă vĭr | ūmqŭe că | nō, Trōj | āe qūi | prīmŭs ăb | ōris

In order to train the naive Bayes classifier, I needed to build a labeled corpus that contained a list of (syllable, length) tuples and preserved the word and line structures from the original text so that I could easily answer questions like “is this syllable the last one in the line?” when generating feature-sets for the syllables.

The author of the scanned corpus, Daniel Rodde, marked the metrical scansion with accented characters. I was able to extract the syllable lengths from the scanned corpus by iterating over the Unicode decomposition of every character in the text — any decomposition that contained U+0304 (macron, e.g. ā) denoted a long syllable and any decomposition that contained U+0306 (breve, e.g. ă) denoted a short one. Elisions were marked at every “(“³ and in-determinate syllables were marked at the end of every line.

One of the most difficult parts of this project was writing a regular expression to correctly syllabify Latin words. I eventually settled on the regular expression:

import re

syllable_pattern = re.compile(
	r"""(?ix)
	(.*?(ty|y|ae|au(?!m)|ei|oe|qui|oi|gui|\biu|iur|iac|[aeioy]|(?<!q)u)
	(?:[^aeioutdpbkgq](?=[^aeioyu]|\b)|
	[tdpbkg](?![lraeiou])|
	q(?!u)|\b
	)*)
	"""
)

re.findall(syllable_pattern, word), returns a list of all the syllables in word.⁴ I used this to break the non-scanned corpus into syllables, and then combined this list of syllables with the list of syllable lengths from the scanned corpus to create a (syllable, length) training set.

Extracting Features

My next task was building a feature set for all of the syllables in my labeled corpus. In Latin dactylic hexameter, there are four categories of traits that influence syllable length. They are ordered here roughly by the strength with which they contribute to the determination of the length of a syllable. Joseph Farrell’s Hexametrica webpage and (Boyd, 2009) were in-disposable in choosing these features.

1. ‘Ultima’

   • The first syllable on a line is always long.

   • The second to last syllable on a line is always long vowel.

   • The last syllable on a line always has an in-determinant length.

2. Length by Nature

   • Word-terminal syllables (i.e. the last syllable in a word) that end in -o, -i, -u are usually long.

   • Word-terminal syllables that end in -as, -es, -us are usually long.

   • Word-terminal syllables that end in -a, -is are often short.

   • Word-terminal syllables that end in -e are usually short.

   • Word-terminal syllables that end in -us are usually short.

   • Word-terminal syllables that end in -am, -em, -um are usually short.

3. Length by Position

   • Vowels that are followed by two consonants are usually long.

   • Vowels that are followed by stop-liquids (e.g. tr) are sometimes long.

   • Diphthongs (e.g. ae) are usually long.

4. Ability to Elide

   • Word-terminal syllables that end in a vowel or -m and are followed by a word that begins with a vowel or an h- can, but don’t have to, elide.

The ways that these features influence the length of a syllable are qualified with words that are frustratingly ambiguous — words like ’often’, ’usually’ and ’sometimes’. One of the nice side-effects of building a statistical model to classify the lengths of syllables is that it can estimate the distributions that underlie those fuzzy qualifiers. Another nice side-effect is that training the classifier on a single author’s work will produce a sort of fingerprint that captures that author’s tendencies to break, bend and ignore rules.

Training

My labeled corpus comprises 33 lines (506 syllables) of poetry. I trained the built-in NLTK naive Bayesian classifier on 75% of the data and withheld the remaining 25% for testing.

Evaluation

After the classifier was trained, it classified syllables in the test fold with an accuracy of 81.8% — baseline performance is 54.0%⁵. The tendencies of the classifier can be seen in the confusion matrix in the following table (rows = reference):

Below is the output from the classifier on the entire testing set. Green lines are correctly labeled. Red lines are incorrect and illegal dactylic hexameter.

Extending the Model

The naive Bayesian classifier assumes independence between syllables — the model doesn’t consider the lengths of the other syllables in a line when predicting the length of a particular syllable. Even though the classifier is more than 80% accurate at a syllable level, all but one of the output lines are illegal dactylic hexameter! The problem can be better modeled by the Hidden Markov Model (HMM) described by this state transition diagram:

Any path from the long syllable on the left side of the diagram (the first syllable in the line) to the indeterminate (✕) syllable on the right side (the last syllable in the line) constitutes a sequence that is a legal line of dactylic hexameter. I assume that the transition probability distribution from any state is uniform over the set of possible next states and the emission probability for each state is given by the naive Bayesian model trained earlier.

Computing the most likely sequence of syllable lengths for a line of poetry is fairly easy — each foot, except for the last, can have one of four scansions:

‒ ‒

‒ ‒ (w/ elision to next syllable)

∪ ∪

‒ ∪ ∪ (w/ elision to next syllable)

and the last foot is guaranteed as:

‒ ✕

so the space of possible paths is (surprisingly) relatively small (4⁵ = 1024). For any given line. The space can be further restricted by only considering paths that have a length equal to the number of syllables in the line. A line with 15 syllables, for example, only has 120 different possible metrical sequences. This is a small enough search space that it is not very expensive to compute the log-likelihood of every possible path. The path with the smallest negative log-likelihood corresponds to the most likely sequence of syllable lengths. Classifying a line of poetry by calculating the most likely sequence of hidden states in the HMM improves syllable classification accuracy to 85.3% and (more importantly) ensure that every line of labeled poetry that comes out of the classifier is legal. Below is the output from the new classifier on the entire test set. Green lines are correctly labeled. Non-highlighted lines are incorrect but legal dactylic hexameter.

Line-level accuracy has increased by a factor of four and every line is legal dactylic hexameter.

Source Code

The source code and the labeled and unlabeled datasets from this project are available on my GitHub.

Future Work

There are a few things that could improve the classifier I’ve built, and a few things that I think would be fun to do with it.

1. I would like to construct a larger corpus to train the model on. The current corpus has 506 labeled syllables in it but only 33 lines of poetry. Given the influence that the structure of a line has on the lengths of the syllables in it, 33 is too small of a number to train an accurate model. An additional benefit of having more lines is that it would allow the construction of a prior distribution that could capture a belief in how likely the scansion pattern of a line is (Virgil hardly ever writes lines with only long vowels, for example, so that sequence should have a lower prior probability than others).

2. The Viterbi algorithm is a dynamic programming approach that reduces the computational complexity of calculating the most likely sequence of states in the HMM from exponential to linear time (Bishop, 2006). While it isn’t necessary for the classifier currently, I would like to implement it because it would make it computationally feasible to extend the model to capture dependency between lines, which could be an interesting area of exploration.

3. I would like to develop a metric for measuring the character of a line of dactylic hexameter (e.g. lines with a lot of long syllables feel slower than lines with a lot of short syllables) so that the way the character of a poem changes over the course of a chapter, section, or book could be visualized.

4. A foot of dactylic hexameter can be thought of as a four-bar musical phrase where long syllables correspond to half notes and short syllables correspond to quarter notes. I think it would be interesting to run an entire book of the Aeneid through the classifier, write the metrical scansion to a MIDI file, and then use it in a musical composition as a rhythm track.

5. I’m curious to investigate how difficult it would be to extend this model to be able to scan other poetic meters.

References

Virgil. The Aeneid. Project Gutenberg.

Daniel Rodde. Aeneid Book 1 ll. 1-33 Scanned & Translated.

Dactylic Hexameter, Wikipedia.

Joseph Farrell. Hexametrica, 1999.

Barbara Boyd. Vergil’s Aeneid: Selections from Books 1, 2, 4, 6, 10 & 12. Bolchazy-Carducci Publishers, Inc, 2009.

Christopher M CM Christopher M. Bishop. Pattern Recognition and Machine Learning, volume 4 of Information science and statistics. Springer, 2006.

Footnotes