Anh Tuan Bui

Anh Tuan Bui

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features in most applications. To solve this problem, this paper proposes a broad class of methods, which is referred to as conditional multidimensional scaling (MDS). An algorithm for optimizing the objective function of conditional MDS is also developed. The convergence of this algorithm is proven under mild assumptions. Conditional MDS is illustrated with kinship terms, facial expressions, textile fabrics, car-brand perception, and cylinder machining examples. These examples demonstrate the advantages of conditional MDS over conventional dimension reduction in improving the estimation quality of the reduced-dimension space and simplifying visualization and knowledge discovery tasks. Computer codes for this work are available in the open-source cml R package.

Anh Tuan Bui

Conditional multidimensional scaling seeks for a low-dimensional configuration from pairwise dissimilarities, in the presence of other known features. By taking advantage of available data of the known features, conditional multidimensional scaling improves the estimation quality of the low-dimensional configuration and simplifies knowledge discovery tasks. However, existing conditional multidimensional scaling methods require full data of the known features, which may not be always attainable due to time, cost, and other constraints. This paper proposes a conditional multidimensional scaling method that can learn the low-dimensional configuration when there are missing values in the known features. The method can also impute the missing values, which provides additional insights of the problem. Computer codes of this method are maintained in the cml R package on CRAN.

Kungang Zhang, Anh T. Bui, Daniel W. Apley

Supervised learning models are one of the most fundamental classes of models. Viewing supervised learning from a probabilistic perspective, the set of training data to which the model is fitted is usually assumed to follow a stationary distribution. However, this stationarity assumption is often violated in a phenomenon called concept drift, which refers to changes over time in the predictive relationship between covariates $\mathbf{X}$ and a response variable $Y$ and can render trained models suboptimal or obsolete. We develop a comprehensive and computationally efficient framework for detecting, monitoring, and diagnosing concept drift. Specifically, we monitor the Fisher score vector, defined as the gradient of the log-likelihood for the fitted model, using a form of multivariate exponentially weighted moving average, which monitors for general changes in the mean of a random vector. In spite of the substantial performance advantages that we demonstrate over popular error-based methods, a score-based approach has not been previously considered for concept drift monitoring. Advantages of the proposed score-based framework include applicability to any parametric model, more powerful detection of changes as shown in theory and experiments, and inherent diagnostic capabilities for helping to identify the nature of the changes.