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

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

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

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

Yoshimasa Tsuruoka, Jun’ichi Tsujii, and Sophia Ananiadou

University of Manchester

- 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.

- Log-linear (a.k.a. maximum entropy) model
- Training
- Maximize the conditional likelihood of the training data

Weight

Feature function

Partition function:

- 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

- 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.

objective

objective

Compute an approximate

gradient using one

training sample

- Weight update procedure
- very simple (similar to the Perceptron algorithm)

Not differentiable

: learning rate

- Weight update procedure

- 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.

- 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

- Text chunking
- Named entity recognition
- Part-of-speech tagging

- In SGD, weights are not updated smoothly

Fails to become

zero!

L1 penalty is wasted away

- 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

- Penalize each weight according to the difference between and

10 lines of code!

- 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)

- Text chunking (shallow parsing)

- 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

NLPBA 2004 named entity recognition

Part-of-speech tagging on WSJ

- 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)

- 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