CATMS: an ATMS which avoids label explosions

Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI-91), Los Angeles, CA, July 1991
CATMS: an ATMS which avoids label explosions
J. Collins, Dennis DeCoste

Assumption-based truth maintenance systems have developed into powerful and popular means for considering multiple contexts simultaneously during problem solving. Unfortunately, increasing problem complexity can lead to explosive growth of node labels.

In this paper, we present a new ATMS algorithm (CATMS) which avoids the problem of label explosions, while preserving most of the query time efficiencies resulting from label compilations. CATMS generalizes the standard ATMS subsumption relation, allowing it to compress an entire label into a single assumption.

This compression of labels is balanced by an expansion of environments to include any implied assumptions. The result is a new dimension of flexibility, allowing CATMS to trade-off the query-time efficiency of uncompressed labels against the costs of computing them. To demonstrate the significant computational gains of CATMS over de Kleer’s ATMS,we compare the performance of the ATMS-based QPE [9] problem-solver using each.

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.