1. Lecture 6: The Ultimate Authorship Problem: Verification for Short Docs Moshe Koppel and Yaron Winter

2. The Ultimate Problem Let’s skip right to the hardest problem: Given two anonymous short documents, determine if they were written by the same author. If we can solve this, we can solve pretty much any variation of the attribution problem.

3. Experimental Setup Construct pairs by choosing the first 500 words of blog i and the last 500 words of blog j. Create 1000 such pairs, half of which are same- author pairs (i=j). (In the real world, there are many more different-author pairs than same-author pairs, but let’s keep the bookkeeping simple for now.) Note: no individual author appears in more than one pair. The task is to label each pair as same-author or different-author.

4. A Simple Unsupervised Baseline Method 1.Vectorize B and E (e.g., as frequencies of character n-grams) 2.Compute the cosine similarity of B and E. 3.If/f it exceeds some (optimally chosen) threshold, assign the pair to same-author.

5. A Simple Unsupervised Baseline Method 1.Vectorize B and E (e.g., as frequencies of character n-grams) 2.Compute the cosine similarity of B and E. 3.If/f it exceeds some threshold, assign the pair to same-author. This method yields accuracy of 70.6% (using the optimal threshold).

6. A Simple Supervised Baseline Method Suppose that, in addition to the (test) corpus just described, we have a training corpus constructed the same way, but with each pair labeled. We can do the obvious thing: 1.Vectorize B and E (e.g., as frequencies of character n-grams) 2.Compute the difference vector (e.g., terms are |b i -e i |/(b i +e i ) ) 3.Learn on training corpus to find some suitable classifier

7. A Simple Supervised Baseline Method Suppose that, in addition to the (test) corpus just described, we have a training corpus constructed the same way, but with each pair labeled. We can do the obvious thing: 1.Vectorize B and E (e.g., as frequencies of character n-grams) 2.Compute the difference vector (e.g., terms are |b i -e i |/(b i +e i ) ) 3.Learn on training corpus to find some suitable classifier With a lot of effort, we get accuracy of 79.8%. But we suspect we can do better, even without using a labeled training corpus (too much).

8. Exploiting the Many-Authors Method 1.Given B and E, generate a list of impostors E 1,..,E n. 2.Use our algorithm for the many-candidate problem for anonymous text B and candidates {E, E 1,…,E n }. 3.If/f E is selected as the author with sufficiently high score, assign the pair to same-author. 4.(Optionally, add impostors to B and check if anonymous document E is assigned to author B.)

9. Design Choices There are some obvious questions we need to consider: How many impostors is optimal? (Fewer impostors means more false positives; more impostors means more false negatives.) Where should we get the impostors from? (If the impostors are not convincing enough, we’ll get too many false positives; if the impostors are too convincing – e.g. drawn from the genre of B that is not also the genre of E – we’ll get too many false negatives.)

10. How Many Impostors? We generated a random corpus of 25000 impostor documents (results of Google searches for medium-frequency words in our corpus). For each pair, we randomly selected N of these documents as impostors and applied our algorithm (using a fixed score threshold k=5%). Here are the accuracy results (y-axis) for different values of N:

11. Best result: 83.4% at 625 impostors Random Impostors

12. Best result: 83.4% at 625 impostors Random Impostors Fewer false negative

13. Which Impostors? Now, instead of using random impostors, for each pair, we choose the N impostors that have the most “lexical overlap” with B (or E). The idea is that more convincing impostors should prevent false positives.

14. Best result: 83.8% at 50 impostors Similar Impostors K=5%

15. Best accuracy result: 83.8% at 50 impostors Similar Impostors K=5% Only 2% false positive

16. Which Impostors? It turns out that (for a fixed score threshold k) using similar impostors doesn’t improve accuracy, but it allows us to use fewer impostors. We can also try to match impostors to the suspect’s genre. For example, suppose that we know that B and E are drawn from a blog corpus. We can limit impostors to blog posts.

17. Best result: 86.3% at 58 impostors Same-Genre Impostors K=5%

18. Impostors Protocol Optimizing on a development corpus, we settle on the following protocol: 1.From a large blog universe, choose as potential impostors the 250 blogs most similar to E. 2.Randomly choose 25 actual impostors from among the potential impostors. 3.Say that are same-author if score(B,E)≥k, where k is used to trade-off precision and accuracy.

19. Results

20. Optimizing thresholds on a development corpus, we obtain accuracies as follows:

21. Conclusions We can use (almost) unsupervised methods to determine if two short documents are by the same author. This actually works better than a supervised baseline method. The trick is to see how robustly the two can be tied together from among some set of impostors. The right number of impostors to use depends on the quality of the impostors and the relative cost of false-positives vs. false-negatives. We assumed throughout that the prior probability of same-author 0.5; we have obtained similar results for skewed corpora (just by changing the score threshold).

22. Open Questions What if x and y are in two different genres (e.g. blogs and facebook statuses)? What if a text was merely “influenced” by x but mostly written by y? Can we discern (or maybe quantify) this influence? Can we use these methods (or related ones) to identify outlier texts in a corpus (e.g. a play attributed to Shakespeare that wasn’t really written by Shakespeare)?