Dynamic Conditional Random Fields for Jointly Labeling Multiple Sequences

NIPS workshop on Syntax, Semantics, and Statistics, Vancouver, Canada, December 2003
Dynamic Conditional Random Fields for Jointly Labeling Multiple Sequences
Andrew McCallum, Khashayar Rohanimanesh, Charles Sutton, Andrew McCallum, Khashayar Rohanimanesh, Charles Sutton
Abstract

Conditional random fields (CRFs) for sequence modeling have several advantages over joint models such as HMMs, including the ability to relax strong independence assumptions made in those models, and the ability to incorporate arbitrary overlapping features. Previous work has focused on linear-chain CRFs, which correspond to finite-statemachines, and have efficient exact inference algorithms.

Often, however, we wish to label sequence data in multiple interacting ways—for example, performing part-of-speech tagging and noun phrase segmentation simultaneously, increasing joint accuracy by sharing information between them.

We present dynamic conditional randomfields (DCRFs), which are CRFs in which each time slice has a set of state variables and edges—a distributed state representation as in dynamic Bayesian networks—and parameters are tied across slices. (They could also be called conditionallytrained Dynamic Markov Networks.) Since exact inference can be intractable in these models, we perform approximate inference using the tree-based reparameterization framework (TRP). We also present empirical results comparing DCRFs with linear-chain CRFs on natural language data.

Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.

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