11/24/2006 CLSP, The Johns Hopkins University Random Forests for Language Modeling Peng Xu and Frederick Jelinek IPAM: January 24, 2006

1/24/2006 CLSP, The Johns Hopkins University What Is a Language Model? A probability distribution over word sequences Based on conditional probability distributions: probability of a word given its history (past words)

1/24/2006 CLSP, The Johns Hopkins University What Is a Language Model for? Speech recognition AW* AW Source-channel model

1/24/2006 CLSP, The Johns Hopkins University n-gram Language Models A simple yet powerful solution to LM (n-1) items in history: n-gram model Maximum Likelihood (ML) estimate: Sparseness Problem: training and test mismatch, most n-grams are never seen; need for smoothing

1/24/2006 CLSP, The Johns Hopkins University Sparseness Problem Example: Upenn Treebank portion of WSJ, 1 million words training data, 82 thousand words test data, 10-thousand-word open vocabulary n-gram3456 % unseen Sparseness makes language modeling a difficult regression problem: an n-gram model needs at least |V| n words to cover all n-grams

1/24/2006 CLSP, The Johns Hopkins University More Data More data  solution to data sparseness The web has “everything”: web data is noisy. The web does NOT have everything: language models using web data still have data sparseness problem.  [Zhu & Rosenfeld, 2001] In 24 random web news sentences, 46 out of 453 trigrams were not covered by Altavista. In domain training data is not always easy to get.

1/24/2006 CLSP, The Johns Hopkins University Dealing With Sparseness in n-gram Smoothing: take out some probability mass from seen n-grams and distribute among unseen n-grams Interpolated Kneser-Ney: consistently the best performance [Chen & Goodman, 1998]

1/24/2006 CLSP, The Johns Hopkins University Our Approach Extend the appealing idea of history to clustering via decision trees. Overcome problems in decision tree construction … by using Random Forests!

1/24/2006 CLSP, The Johns Hopkins University Decision Tree Language Models Decision trees: equivalence classification of histories Each leaf is specified by the answers to a series of questions (posed to “history”) which lead to the leaf from the root. Each leaf corresponds to a subset of the histories. Thus histories are partitioned (i.e.,classified).

1/24/2006 CLSP, The Johns Hopkins University Decision Tree Language Models: An Example Training data: aba, aca, bcb, bbb, ada {ab,ac,bc,bb,ad} a:3 b:2 {ab,ac,ad} a:3 b:0 {bc,bb} a:0 b:2 Is the first word in {a}?Is the first word in {b}? New event ‘bdb’ in testNew event ‘adb’ in test New event ‘cba’ in test: Stuck!

1/24/2006 CLSP, The Johns Hopkins University Decision Tree Language Models: An Example Example: trigrams ( w - 2, w - 1, w 0 ) Questions about positions: “Is w - i 2S ?” and “Is w - i 2S c ?” There are two history positions for trigram. Each pair, S and S c, defines a possible split of a node, and therefore, training data.  S and S c are complements with respect to training data A node gets less data than its ancestors. ( S, S c ) are obtained by an exchange algorithm.

1/24/2006 CLSP, The Johns Hopkins University Construction of Decision Trees Data Driven: decision trees are constructed on the basis of training data The construction requires: 1. The set of possible questions 2. A criterion evaluating the desirability of questions 3. A construction stopping rule or post-pruning rule

1/24/2006 CLSP, The Johns Hopkins University Construction of Decision Trees: Our Approach Grow a decision tree until maximum depth using training data Use training data likelihood to evaluate questions Perform no smoothing during growing Prune fully grown decision tree to maximize heldout data likelihood Incorporate KN smoothing during pruning

1/24/2006 CLSP, The Johns Hopkins University Smoothing Decision Trees Using similar ideas as interpolated Kneser- Ney smoothing: Note: All histories in one node are not smoothed in the same way. Only leaves are used as equivalence classes.

1/24/2006 CLSP, The Johns Hopkins University Problems with Decision Trees Training data fragmentation: As tree is developed, the questions are selected on the basis of less and less data. Lack of optimality:  The exchange algorithm is a greedy algorithm.  So is the tree growing algorithm Overtraining and undertraining: Deep trees: fit the training data well, will not generalize well to new test data. Shallow trees: not sufficiently refined.

1/24/2006 CLSP, The Johns Hopkins University Amelioration: Random Forests Breiman applied the idea of random forests to relatively small problems. [Breiman 2001]  Using different random samples of data and randomly chosen subsets of questions, construct K decision trees.  Apply test datum x to all the different decision trees. Produce classes y 1, y 2,…, y K.  Accept plurality decision:

1/24/2006 CLSP, The Johns Hopkins University Example of a Random Forest           T1T1 T2T2 T3T3 An example x will be classified as  according to this random forest.

1/24/2006 CLSP, The Johns Hopkins University Random Forests for Language Modeling Two kinds of randomness: Selection of positions to ask about  Alternatives: position 1 or 2 or the better of the two. Random initialization of the exchange algorithm 100 decision trees: i th tree estimates P DT ( i ) ( w 0 | w - 2, w - 1 ) The final estimate is the average of all trees

1/24/2006 CLSP, The Johns Hopkins University Experiments Perplexity (PPL): UPenn Treebank part of WSJ: about 1 million words for training and heldout (90%/10%), 82 thousand words for test

1/24/2006 CLSP, The Johns Hopkins University Experiments: trigram Baseline: KN-trigram No randomization: DT-trigram 100 random DTs: RF-trigram ModelheldoutTest PPLGainPPLGain % KN-trigram DT-trigram % % RF-trigram % %

1/24/2006 CLSP, The Johns Hopkins University Experiments: Aggregating Considerable improvement already with 10 trees!

1/24/2006 CLSP, The Johns Hopkins University Experiments: Analysis seen event :  KN-trigram: in training data  DT-trigram: in training data Analyze test data events by number of times seen in 100 DTs

1/24/2006 CLSP, The Johns Hopkins University Experiments: Stability PPL results of different realizations varies, but differences are small.

1/24/2006 CLSP, The Johns Hopkins University Experiments: Aggregation v.s. Interpolation  Aggregation:  Weighted average: Estimate weights so as to maximize heldout data log-likelihood

1/24/2006 CLSP, The Johns Hopkins University Experiments: Aggregation v.s. Interpolation Optimal interpolation gains almost nothing!

1/24/2006 CLSP, The Johns Hopkins University Experiments: High Order n-grams Models Baseline: KN n-gram 100 random DTs: RF n-gram n-gram3456 KN RF

1/24/2006 CLSP, The Johns Hopkins University Using Random Forests to Other Models: SLM Structured Language Model (SLM): [Chelba & Jelinek, 2000] Approximation: use tree triples SLM KN137.9 RF122.8

1/24/2006 CLSP, The Johns Hopkins University Speech Recognition Experiments (I) Word Error Rate (WER) by N-best Rescoring: WSJ text: 20 or 40 million words training WSJ DARPA’93 HUB1 test data: 213 utterances, 3446 words N-best rescoring: baseline WER is 13.7%  N-best lists were generated by a trigram baseline using Katz backoff smoothing.  The baseline trigram used 40 million words for training.  Oracle error rate is around 6%.

1/24/2006 CLSP, The Johns Hopkins University Speech Recognition Experiments (I) Baseline: KN smoothing 100 random DTs for RF 3-gram 100 random DTs for the PREDICTOR in SLM Approximation in SLM 3-gram (20M) 3-gram (40M) SLM (20M) KN14.0%13.0%12.8% RF12.9%12.4%11.9% p-value<0.001<0.05<0.001

1/24/2006 CLSP, The Johns Hopkins University Speech Recognition Experiments (II) Word Error Rate by Lattice Rescoring IBM 2004 Conversational Telephony System for Rich Transcription: 1 st place in RT-04 evaluation  Fisher data: 22 million words  WEB data: 525 million words, using frequent Fisher n- grams as queries  Other data: Switchboard, Broadcast News, etc. Lattice language model: 4-gram with interpolated Kneser-Ney smoothing, pruned to have 3.2 million unique n-grams, WER is 14.4% Test set: DEV04, 37,834 words

1/24/2006 CLSP, The Johns Hopkins University Speech Recognition Experiments (II) Baseline: KN 4-gram 110 random DTs for EB-RF 4-gram Sampling data without replacement Fisher and WEB models are interpolated Fisher 4-gram WEB 4-gram Fisher+WEB 4-gram KN14.1%15.2%13.7% RF13.5%15.0%13.1% p-value<0.001-

1/24/2006 CLSP, The Johns Hopkins University Practical Limitations of the RF Approach Memory: Decision tree construction uses much more memory. Little performance gain when training data is really large. Because we have 100 trees, the final model becomes too large to fit into memory. Effective language model compression or pruning remains an open question.

1/24/2006 CLSP, The Johns Hopkins University Conclusions: Random Forests New RF language modeling approach More general LM: RF  DT  n-gram Randomized history clustering Good generalization: better n-gram coverage, less biased to training data Extension of Brieman’s random forests for data sparseness problem

1/24/2006 CLSP, The Johns Hopkins University Conclusions: Random Forests Improvements in perplexity and/or word error rate over interpolated Kneser-Ney smoothing for different models: n-gram (up to n=6) Class-based trigram Structured Language Model Significant improvements in the best performing large vocabulary conversational telephony speech recognition system