Design Rationale Capture as Knowledge Acquisition Tradeoffs in the Design of Interactive Tools

Proceedings of the Machine Learning Workshop. 1991
Design Rationale Capture as Knowledge Acquisition Tradeoffs in the Design of Interactive Tools
Thomas Gruber, Catherine Baudin, John Boose, Jay Weber
Abstract

This paper introduces a panel to be held at the Knowledge Acquisition Track of the Machine Learning Workshop (ML91). This panel will focus on the problem of acquiring design rationale knowledge from humans for later reuse.

The design of tools for design rationale capture reveals several fundamental issues for knowledge acquisition, such as the relationships among formality and expressiveness of representations, and kinds of automated support for elicitation and analysis of knowledge.

This paper sets the background for discussion by identifying dimensions of a design space for design rationale tools, and then includes position statements from each panelist arguing for various positions in this space.

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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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