Training Factor Graphs with Atomic Gradients

Proceedings of the International Conference on Machine Learning (ICML), 2011.
Training Factor Graphs with Atomic Gradients
Michael Wick, Khashayar Rohanimanesh, Kedar Bellare, Aron Culotta, Andrew McCallum

We present SampleRank, an alternative to contrastive divergence (CD) for estimating parameters in complex graphical models. SampleRank harnesses a user-provided loss function to distribute stochastic gradients across an MCMC chain.

As a result, parameter updates can be computed between arbitrary MCMC states. SampleRank is not only faster than CD, but also achieves better accuracy in practice (up to 23% error reduction on noun-phrase coreference).

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.