Grammatical Inference
25 Feb 2012 08:10
Meaing: inferring the rules of a formal language (its grammar) from examples, positive or negative. I'm mostly interested in the positive case, since I want to describe physical processes as though they were formal languages or (what is equivalent) automata.
— A result which has recently come to vex me is the fact that even finite automata are, in the computational learning theory sense, hard to learn. It's widely believed, but not proved, that common cryptographic systems are hard to crack, meaning that there are no efficient, polynomial-time algorithms for them (unless you have the key, of course...). It turns out that the ability to learn polynomially-sized deterministic finite automata in polynomial time would imply the ability to defeat RSA in polynomial time, which is a pretty good indication that it can't be done. (See Kearns and Vazirani for a very nice discussion.) Initial results were about uniform distributions over words, but it turns out further that this holds even when the distribution of words is generated by a stochastic automaton of the same form.
This is extremely annoying to me, because I want to learn stochastic automata from time series, and to do so in polynomial time (if not better). One possibility is that the time-complexity is just bad, in the worst case, and there is nothing to be done about this. (I fear this might be true.) This would not, however, address the scaling of prediction error and confidence with sample size, which is really what interests me. The other possibility is that I am interested in a rather different set-up than this, one where it's crucial that, as n grows, we see the continuation of a single sample path from a fixed automaton. (In the language, every allowed word is the prefix of infinitely many other allowed words.) Or: the experiment can go on forever. (In fact I'm often interested in the situation where the experiment could have been running forever, so every word is the suffix of infinitely many words.) I think, though I am not sure, that the ability to infer these languages quickly would not cause cryptographic horrors, because I think this restriction breaks the crypto-to-DFA mapping. Computational Learning Theory; Computational Mechanics; Linguistics; Machine Learning, Statistical Inference and Induction; Transducers
- Recommended (big picture):
- Remo Badii and Antonio Politi, Complexity: Hierarchical Structure and Scaling in Physics [Treating dynamical systems like formal languages. Review.]
- Eugene Charniak, Statistical Language Learning [Good stuff on learning grammars for the two lowest levels of the Chomsky hierarchy; explains the grammar ideas for the benefit of engineers.]
- Michael J. Kearns and Umesh V. Vazirani, An Introduction to Computational Learning Theory [Review: How to Build a Better Guesser]
- Christopher D. Manning and Hinrich Shutze, Foundations of Statistical Natural Language Processing
- Recommended (close-ups):
- P. Dupont, F. Denis and Y. Esposito, "Links between probabilistic automata and hidden Markov models: probability distributions, learning models and induction algorithms", Pattern Recognition 38 (2005): 1349--1371
- Jim Engle-Warnick, William J. McCausland and John H. Miller, "The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior" [i.e., inferring stochastic transducers from data; hence the inclusion here]
- Craig G. Nevill-Manning and Ian H. Witten, "Identifying Hierarchical Structure in Sequences: a Linear-Time Algorithm," cs.AI/9709102 [Scheme for inferring context-free grammars from sequential data streams; no consideration of probabilistic properties]
- Leonid Peshkin, "Structure induction by lossless graph compression", a href="http://arxiv.org/abs/cs.DS/0703132">cs.DS/0703132 [Adapting data-compression ideas, a la Nevill-Manning and Witten, to graphs]
- Patrick Suppes, Representation and Invariance of Scientific Structures [Provides a very counter-intuitive proof, originally presented in papers from the 1960s and 1970s, that certain stimulus-response learning models can, asymptotically, become isomorphic to arbitrary grammars.]
- Sebatiaan A. Terwijn, "On the Learnability of Hidden Markov Models", pp. 344--348 in P. Adriaans, H. Fornau and M. van Zaanen (eds.), Grammatical Inference: Algorithms and Applications, Lecture Notes in Computer Science 2484 (2002) [Straightforward, but it leans a lot on wanting to learn languages over words of fixed length, whereas for the cases of "physical", i.e., dynamical, interest, one is restricted to languages where every word has at least one one-letter extension in the language (and so, by induction, every finite word is the prefix of infinitely many words).]
- To read:
- Miguel Bugalho and Arlindo L. Oliveira, "Inference of regular languages using state merging algorithms with search", Pattern Recognition 38 (2005): 1457--1467
- Andreas Blume, "A Learning-Efficiency Explanation of Structure in Language", Theory and Decision 57 (2004): 265--285
- Francisco Casacuberta, Enrique Vidal and David Picó, "Inference of finite-state transducers from regular languages", Pattern Recognition 38 (2005): 1431--1443 ["Given a training corpus of input-output pairs of sentences, the proposed approach uses statistical alignment methods to produce a set of conventional strings from which a stochastic finite-state grammar is inferred. This grammar is finally transformed into a resulting finite-state transducer."]
- Alexander Clark, Christophe Costa Florencio and Chris Watkins, "Languages as hyperplanes: grammatical inference with string kernels", Machine Learning 82 (2011): 351--373
- Alexander Clark, Rémi Eyraud, Amaury Habrard, "Using Contextual Representations to Efficiently Learn Context-Free Languages", Journal of Machine Learning Research 11 (2010): 2707--2744
- Shay B. Cohen and Noah A. Smith, "Empirical Risk Minimization with Approximations of Probabilistic Grammars", NIPS 23 (2010) [PDF]
- P. Collet, A. Galves and A. Lopes, "Maximum Likelihood and Minimum Entropy Identfication of Grammars," Random and Computational Dynamics 3 (1995): 241--250
- Colin de la Higuera
- "A bibliographical study of grammatical
inference", Pattern
Recognition 38 (2005): 1332--1348
- Grammatical Inference: Learning Automata and Grammars [Blurb. I was one of the referees for the book proposal, and eagerly await reading the full thing.]
- C. de la Higuera and J. C. Janodet, "Inference of \omega-languages from prefixes", Theoretical Computer Science 313 (2004): 295--312 [abstract]
- Francois Denis, Aurelien Lemay and Alain Terlutte, "Learning regular languages using RFSAs", Theoretical Computer Science 313 (2004): 267--294 [abstract]
- Francois Denis, Yann Esposito and Amaury Habrard, "Learning rational stochastic languages", cs.LG/0602062
- Jeroen Geertzen, "String Alignment in Grammatical Inference: what suffix trees can do" [PDF]
- C. Lee Giles, Steve Lawrence and Ah Chung Tsoi, "Noisy Time Series Prediction Using Recurrent Neural Networks and Grammatical Inference," Machine Learning 44 (2001): 161--183
- James Henderson, Ivan Titov, "Incremental Sigmoid Belief Networks for Grammar Learning", Journal of Machine Learning Research 11 (2010): 3541--3570
- Mark Johnson, Thomas L. Griffiths and Sharon Goldwater, "Adaptor Grammars: A Framework for Specifying Composition Nonparametric Bayesian Models", NIPS 19 [But containing significant typos; see version at Johnson's website]
- Bill Keller and Rudi Lutz, "Evolutionary induction of stochastic context free grammars", Pattern Recognition 38 (2005): 1393--1406
- Dan Klein and Christopher D. Manning, "Natural language grammar induction with a generative constituent-context model", Pattern Recognition 38 (2005): 1407--1419 ["We present a generative probabilistic model for the unsupervised learning of hierarchical natural language syntactic structure. Unlike most previous work, we do not learn a context-free grammar, but rather induce a distributional model of constituents which explicitly relates constituent yields and their linear contexts.... [Gets the] best published unsupervised parsing results on the ATIS corpus...."]
- Leo Kontorovich, John Lafferty and David Blei, "Variational Inference and Learning for a Unified Model of Syntax, Semantics and Morphology" [Abstract, PDF]
- The Informational Complexity of Learning: Perspectives on Neural Networks and Generative Grammars [How many licks does it take to get to the core of a context-free grammar, Uncle Noam?]
- The Computational Nature of Language Learning and Evolution [Blurb]
- "Grammatical Inference in Bioinformatics", IEEE Transactions on Pattern Analysis and Machine Intelligence 27 (2005): 1051--1062
- "Learning context-free grammars using tabular representations", Pattern Recognition 38 (2005): 1272--1383 ["By employing this representation... the problem of learning context-free grammars from [positive and negative] examples can be reduced to the problem of partitioning the set of nonterminals. We use genetic algorithms for solving this partitioning problem."]
