Classifying non-Gaussian and Mixed Data Sets in their Natural Parameter Space

Proceedings of the Nineteenth IEEE Int’l Workshop on Machine Learning for Signal Processing, Grenoble, France. September 2009
Classifying non-Gaussian and Mixed Data Sets in their Natural Parameter Space
Cécile Levasseur, Uwe Mayer, Ken Kreutz-Delgado
Abstract

We consider the problem of both supervised and unsupervised classification for multidimensional data that are nongaussian and of mixed types (continuous and/or discrete). An important subclass of graphical model techniques called Generalized Linear Statistics (GLS) is used to capture the underlying statistical structure of these complex data.

GLS exploits the properties of exponential family distributions, which are assumed to describe the data components, and constrains latent variables to a lower dimensional parameter subspace.

Based on the latent variable information, classification is performed in the natural parameter subspace with classical statistical techniques. The benefits of decision making in parameter space is illustrated with examples of categorical data text categorization and mixed-type data classification.

As a text document preprocessing tool, an extension from binary to categorical data of the conditional mutual information maximization based feature selection algorithm is presented.

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Reputation and feedback systems in online marketplaces are often biased, making it difficult to ascertain the quality of sellers. We use post-transaction, buyer-to-seller message traffic to detect signals of unsatisfactory transactions on eBay. We posit that a message sent after the item was paid for serves as a reliable indicator that the buyer may be unhappy with that purchase, particularly when the message included words associated with a negative experience. The fraction of a seller's message traffic that was negative predicts whether a buyer who transacts with this seller will stop purchasing on eBay, implying that platforms can use these messages as an additional signal of seller quality.

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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