Similarity-Based Models of Word Cooccurrence Probabilities

In many applications of natural language processing (NLP) it is necessary to determine the likelihood of a given word combination. For example, a speech recognizer may need to determine which of the two word combinations ``eat a peach'' and ``eat a beach'' is more likely. Statistical NLP methods determine the likelihood of a word combination from its frequency in a training corpus. However, the nature of language is such that many word combinations are infrequent and do not occur in any given corpus. In this work we propose a method for estimating the probability of such previously unseen word combinations using available information on ``most similar'' words. We describe probabilistic word association models based on distributional word similarity, and apply them to two tasks, language modeling and pseudo-word disambiguation. In the language modeling task, a similarity-based model is used to improve probability estimates for unseen bigrams in a back-off language model. The similarity-based method yields a 20% perplexity improvement in the prediction of unseen bigrams and statistically significant reductions in speech-recognition error. We also compare four similarity-based estimation methods against back-off and maximum-likelihood estimation methods on a pseudo-word sense disambiguation task in which we controlled for both unigram and bigram frequency to avoid giving too much weight to easy-to-disambiguate high-frequency configurations. The similarity-based methods perform up to 40% better on this particular task.Comment: 26 pages, 5 figure

Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires $k \to \infty$ as the sample size $n \to \infty$) into the functional of interest, the estimators we consider fix k and perform a bias correction. This is more efficient computationally, and, as we show in certain cases, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.Comment: 16 pages, 0 figure

Towards efficient music genre classification using FastMap

Automatic genre classification aims to correctly categorize an unknown recording with a music genre. Recent studies use the Kullback-Leibler (KL) divergence to estimate music similarity then perform classification using k-nearest neighbours (k-NN). However, this approach is not practical for large databases. We propose an efficient genre classifier that addresses the scalability problem. It uses a combination of modified FastMap algorithm and KL divergence to return the nearest neighbours then use 1- NN for classification. Our experiments showed that high accuracies are obtained while performing classification in less than 1/20 second per track

Optimal Kullback-Leibler Aggregation via Information Bottleneck

In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost; The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a sub-optimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.Comment: 13 pages, 4 figure