Empirical Measure of Reliability: Part Four

This fourth installment on Twitter predictions for the NBA Finals will wrap up, for now, my pilot study on measuring reliability as a function of qualities that are detectable in the writings of the individuals who make the predictions. I've made some observations in the three preceding posts, and here I will make a few more and summing up the overall results.

First, the lay of the land: I collected predictions that individuals made on Twitter regarding the 2011 NBA Finals. The predictions were of which team would win and how many games the best-of-seven series would last. This gave eight possible outcomes, which ranged from one team winning in a four-game sweep to the other winning in a four-game sweep. Besides the individuals making predictions, there were other ways to quantify the soundness of each possible outcome, and the odds posted by Las Vegas sports books offer a possible "rationalist" position. At least, if there is a systematic error in the sports books, then there is a way for someone who knows more to get rich.

The sports books predicted a fairly close series, with Miami favored, but only slightly, with Miami-in-seven as the most likely outcome. As such, the least-favored outcomes were blowouts -- Miami-in-four or Dallas-in-four. Even before the Finals began, those seemed to be the brashest/wrongest predictions. And that proved to be true very soon, as each team won one of the first two games, making both of those predictions already wrong. Note that in some other year, where one team was dramatically superior to the other, predicting a four-game series might have been the smart bet -- but that was not true this year.

The heart of this study is to analyze the text that these 165 Twitter users have offered in other tweets (not the specific single prediction itself) and see if there is a fingerprint for reliability in the text that people generate.

Here are the observations that I have previously noted:

1) The people who made the rashest and most-incorrect predictions, a four-game series, differed from the crowd in being less prone to punctuate their tweets. (Note: There were only six such individuals, so this finding may not be significant.) They did not stand out in other obvious ways, such as the use of capitalization.

2) The people who made more extreme predictions (four or five-game series; including the "5s" raised the sample size to 32) were more likely to use the modal verb "must" than the modal verb "might." This is suggestive that some people carry a black-and-white worldview around versus those who see things in shades of gray; the "must" people predicted a lopsided outcome despite the judgment of Las Vegas (and the actual outcome of the series) that was less extreme.

3) While the frequency of the eight possible predictions roughly matched the Las Vegas probabilities (Pearson correlation r=0.56), the crowd deviated from this primarily in over-predicting Dallas-in-six. Interestingly, this ended up being the actual outcome of the series! Is there a significant minority out there (about 25% of the individuals) who know better than Vegas?!

Now, two observations that I have not reported previously:

4) Do those Dallas-in-six predictors show some sign of brilliance in their vocabulary? The words most apt for those people to use more often than the other 75% of individuals were: {awesome, follow, through, morning, maybe}. The words they used less often than the others were: {watching, fun, free}. If there's anything plausible about a worldview here (as with the "must" vs. "might" observation) I don't see it.

5) We can rate the full set of predictions according to correctness (Dallas-in-six being exactly right, but every other prediction being a certain number of games away from this, ranging from one game off to five games off). And then we can correlate correctness with the gross properties of the individuals' tweets and we see that correctness correlated positively with:

A) People who type longer tweets were more accurate than those who type shorter tweets. Pearson correlation, r=0.48.

B) People who use more mixed capitalization (capitalizing the first letters of words, vs. leaving the whole word lowercase or all-uppercase) were more accurate: Pearson correlation, r=0.46.

C) An overall measure of "fluency", using the correct English function words like "and" and "be" correlated only slightly with correctness: r=0.08.

I stress again that this study was not painstakingly scientific, but I would like to use it as a pathfinder towards more informative studies in the coming months. An ambitious-enough goal would be to assess which individuals write in such a way as to seem to be systematically deluded, showing the world that they dispense with facts and wisdom and draw their own conclusions anyway. A yet-more ambitious goal would be to distinguish those individuals of exceptional reliability from those of average reliability, and perhaps to use the crowd as a predictor of the future that is better than anyone has yet systematically recognized (imagine if this led to predictions that were smarter than Las Vegas tends to posit).

While it will be fun and informative to continue this work with other sports events (a ready source of quantitative predictions that can be graded objectively), it would be even more rewarding to evaluate the soundness of predictions regarding politics, policy, technology, and science. It would of course be useful to analyze qualities that are deeper and more meaningful than punctuation. And I will confess to an ultimate goal of collecting empirical statistics on the soundness of various kinds of higher reasoning. Can we do the same as I've done here with arguments that intelligent astronomers made in the Twenties through Fifties, grading those predictions with the correct answers that we now in many cases have? Can we have a sort of truth-o-meter based on this sort of empirical work? Or, at least, can we show people that if they write badly they will seem less reliable? Watch this space in the months to come.

Empirical Measure of Reliability: Part Three

The NBA Finals ended last weekend with the Dallas Mavericks beating the Miami Heat in six games. This is an outcome that a significant minority of the Twitter users predicted -- specifically, it was the second-most common prediction (out of eight logical possibilities) with 24.8% of users choosing it.

What's interesting is to see how the predictions of the crowd selectively followed the probabilities implied by the odds posted by Las Vegas sports books. In the graph (click t0 enlarge), we see the possible outcomes along the bottom, with those most favorable to Miami on the right and those most favorable to Dallas on the left. The house (red line) gave Miami a modest edge in the series, and the probabilities hint at a Gaussian with a peak centered on "Miami winning in seven games." If we ignore the "Dallas in six" position, it looks like the crowd largely went with the gambling odds, choosing a peak that was nearby (Miami in six instead of seven) and then following a course somewhere between Response Matching and a Winner Takes All preference for the favored outcome.

However, the crowd deviated from that in one big way by giving far more credence to the "Dallas in six" outcome (and slightly more to "Miami in six" and slightly less to "Miami in seven"). It is specious to read too much into this single instance, but it looks like the crowd -- a significant minority of them -- got smart in a way that Las Vegas underestimated. Do those Dallas-in-six people have some special talent, or did they just get lucky? I'll take a look next time at how the Dallas-in-six predictors differed -- or didn't -- from the other predictors. Is there a smart gene somewhere in their writing?

Empirical Measure of Reliability: Part Two

My pilot study on the use of text analytics to determine reliability is underway. The idea was to log a lot of predictions regarding the NBA Finals before the event begins, then to analyze the text generated by the predictors and look for correlations between a person's language and their accuracy in predicting the future event.

This is not a proper experiment -- there's a lot of hackery on my part. My hope is to learn from this pilot study to gear up for a proper experiment in the coming months. As of this writing, two games in the best-of-seven series have been completed, with the Miami Heat and the Dallas Mavericks each having one win. At this point, I'll give a quick overview of things I've seen in the data, which I collected right up to the last hour before the series began.

First, the predictions themselves: I collected 245 predictions from users on Twitter. I chose only predictions in which the user specified the outcome in terms of the series winner and the total number of games. (A best-of-seven series ends whenever one team has four wins. This could happen in as few as four or as many as seven games.) The object of interest to me is to look at the text these users produce in posts besides the prediction post itself, so I cut the study to those 165 posters for whom I was able to collect at least 10 other Twitter posts (excluding those which are retweets, containing the posts of other users).

The users tended (59%) to prefer Miami and the single most common prediction was Miami to win in six games. This is not far from the predicted outcome implied by the Las Vegas odds, which favored Miami in seven games, with Miami in six as a close second. However, the overall profile of the Twitter predictors in some ways deviated quite a bit from the Las Vegas view.

The Twitter predictors have a strange overestimate of the likelihood of Dallas (the underdog) winning the series in six games. This is strange in that the odds predict that the most likely duration of the series is seven games (34% probability). However, 59% of Twitter users predict a six-game series (most favoring Miami, some Dallas). Why? Maybe the answer lies in history: Six games is historically the most likely duration of an NBA Finals (41.5% of the Finals since 1980). Maybe people begin by accepting the likely duration of the series, and impose upon that their selection of which team will be the beneficiary. If so, there is an illogical bias: If Dallas is to perform better than the odds predict, then it is more likely that Dallas will lose in seven games, or win in seven games. It seems that users who favor Dallas, however, "go big" in their favoritism, concluding that if Dallas is to do well, they will do really well, winning by the comparatively large margin of four games to two which the odds say is fairly unlikely (10.2% probability).

Looking at the gross breakdown of predictions, it is also interesting to consider those who predicted the series to end in just four games. At a glance, it looks like the predictors are conservative, with only 4% having predicted a four-game series while the odds give a 13% probability of that outcome and history telling us that 17% of Finals end in four games. However, seen another way, the predictors seem irrationally exuberant in predicting a four-game outcome. Given an objective determination of the probabilities, it is irrational for anyone to choose the least-likely outcome. Let's say that we had a six-sided die with one side marked A, two sides marked B, and three sides marked C. If we ask a million rational gamblers to bet on the outcome of a single roll, it's not that 1/6 should say "A"; rather, absolutely nobody should say "A" if they want to maximize their probability of being correct. That 4% of predictors predicted a four-game series sweep (four choosing Miami, two Dallas) indicates either that those predictors (and to a lesser extent, those choosing a five-game series or Dallas winning in six) are responding irrationally. Maybe for one of these reasons:

1) They incorrectly believe they know something that the rest of the world doesn't.

2) They actually do know something that the rest of the world doesn't.

3) The payoff for these predictors may favor winning and losing unequally. They may get great prestige or psychological reward from making a rare, perfect prediction, whereas they can simply ignore or walk away from their incorrect prediction should it not come true.

Interpretation (2), I should add, is not very persuasive. If a class of individuals had the ability to predict more accurately than the rest of the world, then some of those individuals would have the incentive to bet large sums of money on the event, which would shift the odds to the correct value. The odds should reflect the "smart money" quite closely unless someone has access to information that the world does not. (E.g., if the series is "fixed" by a point-shaving scheme.) It is unlikely, to say the least, that people posting on Twitter have rigged the series or are in on such a scheme and have decided to act on that information by posting a prediction to Twitter.

It is premature to call the study complete, but I will quickly note some characteristics of the data. First, I noted how much punctuation (particularly, periods, commas, or apostrophes/single quotes) per tweet each user produces. The average over all predictors is 2.34 punctuation marks (of those kinds) per tweet, with 60% of predictors using more than 2.0 punctuation marks per tweet. An interesting, if not significant observation: Of those users who predicted a series duration of five or more games, only 38% used fewer than 2.0 punctuation marks per tweet. Of those (only six) users who predicted a four-game series, 100% used fewer than 2.0 punctuation marks per tweet! Are the people who ignored their English teachers walking through life ignoring all sorts of wisdom, making basketball predictions as badly as they punctuate? There's no statistical significance in this result, but note that the four-game predictors are already wrong: Because each team has already won a game, the series will last at least five games.

Performing a similar analysis of how people capitalize has not shown any such effect, however. If people who punctuate poorly are ignoring reality, the same is not obviously happening with Twitter capitalization.

It is also going to be interesting to note the vocabulary biases in the various groups of predictors. Those who used the word "must" in their non-prediction posts had a 32% probability of predicting an extreme, and unlikely, outcome (four games or five). Only 12% of users who used the word "might" in non-prediction posts predicted such an outcome. Does this mean that there are people who see the world in black-and-white, who ignore the more likely median cases, the shades of gray? Perhaps! In future studies, it will be useful to collect more data to look at a wider range of terms that indicate a black-and-white worldview or a shades-of-gray outlook.

That's the mid-course report. I will provide more analysis as the results come in. And the tangible (if not statistically significant) determination of how accurate the predictions were will come courtesy of the Miami Heat and the Dallas Mavericks. Tonight: Game Three!

Empirical Measure of Reliability: Part One

Students writing essays. Contributors to Wikipedia. Economists, Wall Street traders, technologists, scientists, and political pundits predicting the future. A general enterprise for thinking persons is to understand the world, sometimes vying against the adversity of uncertainty. In various ways, those thinkers who venture an opinion are "graded" for the quality of their work, and those who do well are -- perhaps -- accorded more credibility in the future.

Separately, text analytics is a technology that is coming of age. Low-level properties of text are used to assess the meaning in interesting ways. I have worked to build business-to-business solutions in text analytics -- netnography at Netbase and I am currently building sentiment analysis classifiers in many languages for Meltwater News.

When one reads analysis (as when I graded research papers as a teacher at Western Reserve Academy), one inevitably feels that some writers show a high degree of insight while others analyze poorly and show this with writing of lower quality. If an analyst cannot construct a proper sentence, then doesn't that say something damning about the quality of the analysis? Is a tongue-tied politician inevitably a hack in determining policy? Can someone who confuses "there" and "their" have something worth saying?

Here, I announce a pilot study to examine if the low-level properties of text have a bearing on the quality of the analysis therein -- more specifically, the accuracy of predictions made by the analyst. Choosing an objective proposition that is close at hand, I will use the 2011 NBA Championship Series, which begins a few hours from now, featuring the Dallas Mavericks vs. the Miami Heat, as a test of the many people out there who are staking their reputation upon predictions of the outcome. In the era of social media, such predictions are not scarce. My experiment is to collect the identities of many Twitter users who are predicting the outcome of the series. Then we can analyze the low-level qualities of the text that these users produce and have an objective measure (albeit with very low N -- just one yes/no "grade") of the reliability of each user's predictions.

The provocative promise of this type of study is that we can find empirical evidence that people who express themselves in certain types of ways are better predictors than people who express themselves in other ways. Imagine the range of possible discoveries. Imagine the gleeful English teacher who can point to empirical fact to conclude once and for all, "People who do not capitalize and punctuate correctly think poorly and what they say is factually incorrect." Imagine the shock in academia if the reverse proves to be true!

To be clear, this pilot is far from a proper experiment. The "low N" problem (only one result) means that there cannot be much meaning in the result. Maybe the smart prediction will turn out to be wrong (say, if a player on the team that should have won suffers an unexpected injury). I am not carefully picking my variables in advance -- I will analyze them as the series takes place. And there is plenty of subjectivity even in the determination of what prediction is being made (the language of these tweets is very vague). Also, the independent variables will necessarily be low-level (like use of punctuation) and preclude the more interesting high-level variables like reasonableness-of-argument. I think a proper scientific analysis could find so many flaws in my methodology to disgrace me thoroughly.

But the topic, is for me, compelling, and can serve as a pilot for better studies in the future, addressing many of those shortcomings in future work. Call this observation instead of science.

I have been collecting prediction posts from Twitter over the last few days, and I continue to do so at the present moment. It seems that I will have roughly 200 users in my sample, with about 50 posts per user as the text that can be analyzed as a sample of their writing. I will separate the users into groups after the series begins this afternoon, and then we can see how the best-of-seven series speaks to the quality of the predictions.

I hope that this the beginning of future studies, extending the scope to other domains (e.g., election outcomes, public policy, the success of Internet startups), and more subtle qualities of the analysis (e.g., use of causality to explain one's points; proper use of logical reasoning). And maybe one day, we will be able to take much of what might be written and say, "That kind of thought is invalid." And maybe the world will raise the quality of its thought by a notch or two. Isn't it be pretty to think so?

My data collection continues. Predictors are typing away. And over the coming days, the Miami Heat and the Dallas Mavericks will help us determine what is right and what is not right.

Speech To Speech

When Google talks, people listen. Recently, Google has been saying that sometime in the near future, when you talk, people can listen in other languages, thanks to your phone and their software. Franz Och, the head of Google's translation services has said "We think speech-to-speech translation should be possible and work reasonably well in a few years' time." I'm not the only one who's skeptical.

In 2007, I evaluated a state-of-the-art StS MT system that was built for military applications (think of the Somali pirate crisis from 2009 or any scene from The Hurt Locker). I don't think it delivered. The issue is quality. StS MT can "work" if:

a) Both parties are extremely cooperative and are willing to put some work into the exchange. (Eg, training the system on their voices; repeating things, maybe more than once, if the result is unclear the first time; tolerating the inherent delays.) This could mean a life-or-death situation where the alternative -- no translation -- is worse than a bad translation. (Although the stakes could be higher, even deadly, if the translation is faulty.)

b) The comprehension of the content is held to a low standard. Eg, if two businesspeople or recreational chatters want to feel like they're getting to know each other; not trying to hammer out the fine details of a legal agreement.

c) There is no alternative. Because having the parties type content into an online text-based MT system immediately removes one source of error.

As long as the sources of error are as great as they are now, I have trouble thinking of many contexts where people would be willing to tolerate the flaws. Maybe chatters who are only looking for entertainment and have no bottom line regarding accuracy. In war / emergency contexts, perhaps. In business, I think the problems just about doom the effort, unless a cultural adjustment makes people value "meeting" someone in this way even when the comprehension is shaky.

I was, however, impressed by how well the speech recognition worked with my voice when I trained the system to recognize me. Perhaps if Google trains the system on enough people, just about anyone new to come along would sound close enough to one of those. The speech-to-text part of the problem just might be solvable for a large segment of people.

But that leaves the machine translation link in the chain, and that's something where there's little reason to suspect that a quantum leap is about to happen. I took Mr. Och's own quotation above and translated it to Spanish and then back to English using Google's text-to-text machine translation. It did a pretty good job, but it changed his use of the word "should" to "must". That's the sort of thing you don't want to have happen when a Somali pirate has his gun trained on you.

Inflection Predilection

Here's a lightweight, factoid-level look at a lot of different languages in a fun way.

We often hear that some languages are "heavily inflected". You can glance at tables of verb conjugations and noun declensions to see the brutal details: Russian surely does have a lot of declensions to memorize, just as Spanish does with verb conjugations. But that's all theory and not practice -- lots of those forms are hardly ever used. I lived in Italy and started making a mental note of how often I heard (or had to use) the second-person plural form of the future tense: Not often!

One way of quantifying how "heavily" inflected a language is can be seen from some statistical work I was doing for a more practical purpose. For each of sixteen languages, I processed corpora of news articles with total token counts for each language ranging from about 100,000 to 3 million. Based on this, I generated two ways of counting tokens: First, the absolute count of nonunique tokens (in other words, the total size of the corpus); Second, the sum of the unique token count of each article (in other words, counting each word just once for each article it occurs in).

If each word occurred at most once per article, these two counts would be identical. The ratio between the two counts thus expresses how much a language tends to repeat words. There are a number of factors that can determine the degree of repetition, but many of these should be more or less equally true of all languages across the news corpora. Inflectional morphology, however, varies greatly from one language to another. Where English would use the form "said" in the past tense regardless of the person and number of the verb, but would use "say" or "says" for, the present tense. Spanish could use "dijeron", "dijo", "dije", etc. for the past, and "dicen", "dice", "digo", etc. for the present. Meanwhile, Chinese would use the character "说" regardless of person, number, or tense. In this example, Spanish could have a relatively small discrepancy between the number of "SAY" tokens in an article and the number of "SAY" forms in the article. English would have a larger discrepancy, with only three forms likely to occur. Chinese, meanwhile, would have only one form regardless of any other factors, so the ratio of total "SAY" tokens and the count of one for that one form could be quite a bit larger. So "more inflected" languages should have lower ratios between the two forms of counts, while "uninflected" languages should have higher ratios.

Behold, we see the basic truths upheld. Finnish is the most inflected language in this sample, and Chinese the least. English is the least inflected European language. Among the branches of the Indo-European family in the sample, the Slavic branch is the most inflected, with Germanic (besides the mongrel English) next-most, and Romance least.

A bit of analysis: Finnish and Turkish are polysynthetic, allowing combinatorial addition of affixes and generating vast numbers of forms. Arabic manifests similar complexity in a slightly different way, with active derivational morphology combining with a respectable number of verb inflections.

Why do the Romance languages, with their vast verb conjugation tables look so uninflected? Almost certainly, the fact that this is a news corpus plays a big role. News preferentially favors the past tense and the third person, restricting verb conjugation more than, say, a corpus of spoken conversations would. The main complication of the Slavic languages, noun declension, is no more restricted in news than it would be in other contexts: nouns can still be subjects, objects, instruments, etc. Germanic languages, with their modest declension schemes, rank between that of Slavic and that of the undeclined Romance languages. English, which came out of the Norman conquest on a path to eliminate as much of the complexity of its Anglo-Saxon and Old French origins, ended up the least-inflected language in the region. Chinese is famously "uninflected", although I have to admit a procedural bias here: Tokenizing Chinese into single tokens guarantees that it occupies the extreme position; if I were tokenizing it into words (taking some side or another in the debate concerning what is a word in Chinese), the counts would be different, although its rank as the least-inflected language in the bunch would not.

One could have quite a bit of fun explaining all of the nuances in the ranking: Why are Danish and Norwegian so far apart? Because Norwegian has more zero-ending plurals? What about Spanish and Italian? Is it some nonmorphological reason?

Overall, the thing that was interesting here was to see the numeric basis to an observation that is made so readily about which languages are "heavily" inflected. Where qualitative truths exist, quantitative breakdowns can show them.

Parsing Twitter

The Internet has not re-invented language as such, but it has created many new registers that have to be parsed as such. Out-of-the-box NLP tools that were developed to parse the Wall Street Journal and other well-behaved text will fall down flat if they are used to process other niches around the Internet.

I have seen some of these phenomena going back a quarter of a century, in online chat. In a nutshell, people use Internet means of writing in ways more colloquial than formal writing tends (and tended) to be. But even without that broad sweep, there are many sub-niches of usage -- some determined by medium, and some determined by user population. (Besides the obvious segmentation into different national languages like English, German, and Chinese.)

Interest in parsing Twitter is suddenly getting hot, and while a lot of the linguistic behavior there resembles linguistic behavior in other online locales like chat rooms, email, and instant messaging, every niche ends up with its own rules (and lack thereof).

Here are some phenomena I've seen as I build a parser that is robust enough to handle Twitter:

1) Pro drop. Twitter in particular makes the first-person singular pronoun implicit. Many tweets look like English sentences that have the leading word "I" implied. In other cases, "I am" is implied.

2) Nonsentential statements. Sometimes a noun phrase stands alone, with an implied existential quantification out front. "Party tonight" means "There will be a party tonight."

3) A register that resembles Black English Vernacular has arisen. I would suggest that this new written form deliberately deviates from formal written standards. At the same time, it is economical, using shorter forms as rebuses for bulkier forms whenever the shorter form would be pronounced the same way. For example, rewriting "You know" as "u no" (4 characters instead of 8). One can feel William Safire quaking, but for those of us writing parsers, we must accept and embrace.

The first I noticed this was in the titles of songs written by Prince. The titles of songs on his first three albums never did this, but in albums released in 1981 and 1982, three of his songs had these elements in his titles (eg, "I would die 4 u"). You can see the deliberately contrary nature of his language by 1988, when he titled a song "Eye No", thus using a longer form instead of a standard shorter form. I don't know if Prince was significantly responsible for this phenomenon or not, but it has certainly caught on by now.

Incidentally, detecting a user's register is potentially quite valuable, since many business purposes for parsing Twitter would be involved with market analysis and market segmentation.

4) Acronyms and emoticons. These are so common in computer-mediated communication that it is impossible to be unaware of them. LOL.

5) Novel contractions, like "hella", "tryna", "weneva".

6) Repeating characters to establish emphasis. Eg, "welcomeeeeeeeeee". This is in some cases a challenge to parse (in principle, "good" is "god" with the "o" repeated). In other cases, it's easy to convert to standard usage, but it does defeat literal search mechanisms.

Notice that the aforementioned devices can occur in combination. For example, "lmaaooo" = "laughing my ass off" with the "a" and "o" repeated for emphasis.

7) Unique medium-specific entities like URLs and the Twitter features for directing a tweet to a user (eg, @FakeSteveJobs) or a topic (eg, #lost).

8) The substitution of characters that resemble other characters for one another. "3" can be used for "E", "0" for "o", "q" for "g".

9) Deliberate swapping of character order. For example, "teh" as a playful misspelling of "the". This can also combine with aforementioned devices. Eg, "pr0n" is a way to rewrite "porn".

Not every user partakes of these new linguistic devices, but a parser that is intended to wring meaning (and market intelligence) out of Twitter (or blogs or email or other electronic communication) ignores them at its peril. The more of these you miss, the more information you miss. And the people who have embraced these nonstandard devices represent a nontrivial amount of spending power.