Training Factor Graphs with Reinforcement Learning for Efficient MAP Inference

Neural Information Processing Systems (NIPS), 2009
Training Factor Graphs with Reinforcement Learning for Efficient MAP Inference
Michael Wick, Khashayar Rohanimanesh, Sameer Singh, Andrew McCallum, Michael Wick, Khashayar Rohanimanesh, Sameer Singh, Andrew McCallum

Large, relational factor graphs with structure defined by first-order logic or other languages give rise to notoriously difficult inference problems. Because unrolling the structure necessary to represent distributions over all hypotheses has exponential blow-up, solutions are often derived from MCMC.

However, because of limitations in the design and parameterization of the jump function, these samplingbased methods suffer from local minima—the system must transition through lower-scoring configurations before arriving at a better MAP solution. This paper presents a new method of explicitly selecting fruitful downward jumps by leveraging reinforcement learning (RL).

Rather than setting parameters to maximize the likelihood of the training data, parameters of the factor graph are treated as a log-linear function approximator and learned with methods of temporal difference (TD); MAP inference is performed by executing the resulting policy on held out test data.

Our method allows efficient gradient updates since only factors in the neighborhood of variables affected by an action need to be computed—we bypass the need to compute marginals entirely. Our method yields dramatic empirical success, producing new state-of-the-art results on a complex joint model of ontology alignment, with a 48% reduction in error over state-of-the-art in that domain.

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.