Stochastic Gradient Descent Training for L1-regularizaed Log-linear Models with Cumulative Penalty

1. Stochastic Gradient Descent Training for L1-regularizaed Log-linear Models with Cumulative Penalty Yoshimasa Tsuruoka, Jun’ichi Tsujii, and Sophia Ananiadou University of Manchester

2. Log-linear models in NLP • Maximum entropy models • Text classification (Nigam et al., 1999) • History-based approaches (Ratnaparkhi, 1998) • Conditional random fields • Part-of-speech tagging (Lafferty et al., 2001), chunking (Sha and Pereira, 2003), etc. • Structured prediction • Parsing (Clark and Curan, 2004), Semantic Role Labeling (Toutanova et al, 2005), etc.

3. Log-linear models • Log-linear (a.k.a. maximum entropy) model • Training • Maximize the conditional likelihood of the training data Weight Feature function Partition function:

4. Regularization • To avoid overfitting to the training data • Penalize the weights of the features • L1 regularization • Most of the weights become zero • Produces sparse (compact) models • Saves memory and storage

5. Training log-linear models • Numerical optimization methods • Gradient descent (steepest descent or hill-climbing) • Quasi-Newton methods (e.g. BFGS, OWL-QN) • Stochastic Gradient Descent (SGD) • etc. • Training can take several hours (or even days), depending on the complexity of the model, the size of training data, etc.

6. Gradient Descent (Hill Climbing) objective

7. Stochastic Gradient Descent (SGD) objective Compute an approximate gradient using one training sample

8. Stochastic Gradient Descent (SGD) • Weight update procedure • very simple (similar to the Perceptron algorithm) Not differentiable : learning rate

9. Using subgradients • Weight update procedure

10. Using subgradients • Problems • L1 penalty needs to be applied to all features (including the ones that are not used in the current sample). • Few weights become zero as a result of training.

11. Clipping-at-zero approach • Carpenter (2008) • Special case of the FOLOS algorithm (Duchi and Singer, 2008) and the truncated gradient method (Langford et al., 2009) • Enables lazy update w

12. Clipping-at-zero approach

13. Text chunking • Named entity recognition • Part-of-speech tagging

14. Why it does not produce sparse models • In SGD, weights are not updated smoothly Fails to become zero! L1 penalty is wasted away

15. Cumulative L1 penalty • The absolute value of the total L1 penalty which should have been applied to each weight • The total L1 penalty which has actually been applied to each weight

16. Applying L1 with cumulative penalty • Penalize each weight according to the difference between and

17. Implementation 10 lines of code!

18. Experiments • Model: Conditional Random Fields (CRFs) • Baseline: OWL-QN (Andrew and Gao, 2007) • Tasks • Text chunking (shallow parsing) • CoNLL 2000 shared task data • Recognize base syntactic phrases (e.g. NP, VP, PP) • Named entity recognition • NLPBA 2004 shared task data • Recognize names of genes, proteins, etc. • Part-of-speech (POS) tagging • WSJ corpus (sections 0-18 for training)

19. CoNLL 2000 chunking task: objective

20. CoNLL 2000 chunking: non-zero features

21. CoNLL 2000 chunking • Performance of the produced model • Training is 4 times faster than OWL-QN • The model is 4 times smaller than the clipping-at-zero approach • The objective is also slightly better

22. NLPBA 2004 named entity recognition Part-of-speech tagging on WSJ

23. Discussions • Convergence • Demonstrated empirically • Penalties applied are not i.i.d. • Learning rate • The need for tuning can be annoying • Rule of thumb: • Exponential decay (passes = 30, alpha = 0.85)

24. Conclusions • Stochastic gradient descent training for L1-regularized log-linear models • Force each weight to receive the total L1 penalty that would have been applied if the true (noiseless) gradient were available • 3 to 4 times faster than OWL-QN • Extremely easy to implement