For my forthcoming book, which includes a chapter on the uses of topic modeling in literary studies, I wrote the following vignette. It is my imperfect attempt at making the mathematical magic of LDA palatable to the average humanist. Imperfect, but hopefully more fun than plate notation. . .
. . . imagine a quaint town, somewhere in New England perhaps. The town is a writer’s retreat, a place they come in the summer months to seek inspiration. Melville is there, Hemingway, Joyce, and Jane Austen just fresh from across the pond. In this mythical town there is spot popular among the inhabitants; it is a little place called the “LDA Buffet.” Sooner or later all the writers go there to find themes for their novels. . .
One afternoon Herman Melville bumps into Jane Austen at the bocce ball court, and they get to talking.
“You know,” says Austen, “I have not written a thing in weeks.”
“Arrrrgh,” Melville replies, “me neither.”
So hand in hand they stroll down Gibbs Lane to the LDA Buffet. Now, down at the LDA Buffet no one gets fat. The buffet only serves light (leit?) motifs, themes, topics, and tropes (seasonal). Melville hands a plate to Austen, grabs another for himself, and they begin walking down the buffet line. Austen is finicky; she spoons a dainty helping of words out of the bucket marked “dancing.” A slightly larger spoonful of words, she takes from the “gossip” bucket and then a good ladle’s worth of “courtship.”
Melville makes a bee line for the “whaling” trough, and after piling on an Ahab-sized handful of whaling words, he takes a smaller spoonful of “seafaring” and then just a smidgen of “cetological jargon.”
The two companions find a table where they sit and begin putting all the words from their plates into sentences, paragraphs, and chapters.
At one point, Austen interrupts this business: “Oh Herman, you must try a bit of this courtship.”
He takes a couple of words but is not really fond of the topic. Then Austen, to her credit, asks permission before reaching across the table and sticking her fork in Melville’s pile of seafaring words, “just a taste,” she says. This work goes on for a little while; they order a few drinks and after a few hours, voila! Moby Dick and Persuasion are written . . .
[Now, dear reader, our story thus far provides an approximation of the first assumption made in LDA. We assume that documents are constructed out of some finite set of available topics. It is in the next part that things become a little complicated, but fear not, for you shall sample themes both grand and beautiful.]
. . . Filled with a sense of deep satisfaction, the two begin walking back to the lodging house. Along the way, they bump into a blurry-eyed Hemingway, who is just then stumbling out of the Rising Sun Saloon.
Having taken on a bit too much cargo, Hemingway stops on the sidewalk in front of the two literati. Holding out a shaky pointer finger, and then feigning an English accent, Hemingway says: “Stand and Deliver!”
To this, Austen replies, “Oh come now, Mr. Hemingway, must we do this every season?”
More gentlemanly then, Hemingway replies, “My dear Jane, isn’t it pretty to think so. Now if you could please be so kind as to tell me what’s in the offing down at the LDA Buffet.”
Austen turns to Melville and the two writers frown at each other. Hemingway was recently banned from the LDA Buffet. Then Austen turns toward Hemingway and holds up six fingers, the sixth in front of her now pursed lips.
“Six topics!” Hemingway says with surprise, “but what are today’s themes?”
“Now wouldn’t you like to know that you old sot.” Says Melville.
The thousand injuries of Melville, Hemingway had borne as best he could, but when Melville ventured upon insult he vowed revenge. Grabbing their recently completed manuscripts, Hemingway turned and ran toward the South. Just before disappearing down an alleyway, he calls back to the dumbfounded writers: “All my life I’ve looked at words as though I were seeing them for the first time. . . tonight I will do so again! . . . ”
[Hemingway has thus overcome the first challenge of topic modeling. He has a corpus and a set number of topics to extract from it. In reality determining the number of topics to extract from a corpus is a bit trickier. If only we could ask the authors, as Hemingway has done here, things would be so much easier.]
. . . Armed with the manuscripts and the knowledge that there were six topics on the buffet, Hemingway goes to work.
After making backup copies of the manuscripts, he then pours all the words from the originals into a giant Italian-leather attache. He shakes the bag vigorously and then begins dividing its contents into six smaller ceramic bowls, one for each topic. When each of the six bowls is full, Hemingway gets a first glimpse of the topics that the authors might have found at the LDA Buffet. Regrettably, these topics are not very good at all; in fact, they are terrible, a jumble of random unrelated words . . .
[And now for the magic that is Gibbs Sampling.]
. . . Hemingway knows that the two manuscripts were written based on some mixture of topics available at the LDA Buffet. So to improve on this random assignment of words to topic bowls, he goes through the copied manuscripts that he kept as back ups. One at a time, he picks a manuscript and pulls out a word. He examines the word in the context of the other words that are distributed throughout each of the six bowls and in the context of the manuscript from which it was taken. The first word he selects is “heaven,” and at this word he pauses, and asks himself two questions:
- “How much of ‘Topic A,’ as it is presently represented in bowl A, is present in the current document?”
- “Which topic, of all of the topics, has the most ‘heaven’ in it?” . . .
[Here again dear reader, you must take with me a small leap of faith and engage in a bit of further make believe. There are some occult statistics here accessible only to the initiated. Nevertheless, the assumptions of Hemingway and of the topic model are not so far-fetched or hard to understand. A writer goes to his or her imaginary buffet of themes and pulls them out in different proportions. The writer then blends these themes together into a work of art. That we might now be able to discover the original themes by reading the book is not at all amazing. In fact we do it all the time--every time we say that such and such a book is about "whaling" or "courtship." The manner in which the computer (or dear Hemingway) does this is perhaps less elegant and involves a good degree of mathematical magic. Like all magic tricks, however, the explanation for the surprise at the end is actually quite simple: in this case our magician simply repeats the process 10 billion times! NOTE: The real magician behind this LDA story is David Mimno. I sent David a draft, and along with other constructive feedback, he supplied this beautiful line about computational magic.]
. . . As Hemingway examines each word in its turn, he decides based on the calculated probabilities whether that word would be more appropriately moved into one of the other topic bowls. So, if he were examining the word “whale” at a particular moment, he would assume that all of the words in the six bowls except for “whale” were correctly distributed. He’d now consider the words in each of those bowls and in the original manuscripts, and he would choose to move a certain number of occurrences of “whale” to one bowl or another.
Fortunately, Hemingway has by now bumped into James Joyce who arrives bearing a cup of coffee on which a spoon and napkin lay crossed. Joyce, no stranger to bags-of-words, asks with compassion: “Is this going to be a long night.”
“Yes,” Hemingway said, “yes it will, yes.”
Hemingway must now run through this whole process over and over again many times. Ultimately, his topic bowls reach a steady state where words are no longer needing to be being reassigned to other bowls; the words have found their proper context.
After pausing for a well-deserved smoke, Hemingway dumps out the contents of the first bowl and finds that it contains the following words:
“whale sea men ship whales penfon air side life bounty night oil natives shark seas beard sailors hands harpoon mast top feet arms teeth length voyage eye heart leviathan islanders flask soul ships fishery sailor sharks company. . . “
He peers into another bowl that looks more like this:
“marriage happiness daughter union fortune heart wife consent affection wishes life attachment lover family promise choice proposal hopes duty alliance affections feelings engagement conduct sacrifice passion parents bride misery reason fate letter mind resolution rank suit event object time wealth ceremony opposition age refusal result determination proposals. . .”
After consulting the contents of each bowl, Hemingway immediately knows what topics were on the menu at the LDA Buffet. And, not only this, Hemingway knows exactly what Melville and Austen selected from the Buffet and in what quantities. He discovers that Moby Dick is composed of 40% whaling, 18% seafaring and 2% gossip (from that little taste he got from Jane) and so on . . .
[Thus ends the fable.]
For the rest of the (LDA) story, see David Mimno’s Topic Modeling Bibliography