In this work, we focus on models and analysis of multivariate time series data that are organized in hierarchies. Such time series are referred to as hierarchical time series (HTS) and they are very common in business, management, energy consumption, social networks, or web traffic modeling and analysis. We propose a new flexible hierarchical forecasting framework, that takes advantage of the hierarchical relational structure to predict individual time series. Our new forecasting framework is able to (1) handle HTS modeling and forecasting problems; (2) make accurate forecasting for HTS with seasonal patterns; (3) incorporate various individual forecasting models and combine heuristics based on the HTS datasets' own characterization. The proposed framework is evaluated on a real-world web traffic data set. The results demonstrate that our approach is superior when applied to hierarchical web traffic prediction problems, and it outperforms alternative time series prediction models in terms of accuracy

Hierarchical time series (HTS) is a special class of multivariate time series where many related time series are organized in a hierarchical tree structure and they are consistent across hierarchy levels. HTS modeling is crucial and serves as the basis for business planning and management in many areas such as manufacturing inventory, energy and traffic management. However, due to machine failures, network disturbances or human maloperation, HTS data suffer from missing values across different hierarchical levels. In this paper, we study the missing value estimation problem under hierarchical web traffic settings, where the user-visit traffic are organized in various hierarchical structures, such as geographical structure and website structure. We develop an efficient algorithm, HTSImpute, to accurately estimate the missing value in multivariate noisy web traffic time series with specific hierarchical consistency in HTS settings. Our HTSImpute is able to (1) utilize the temporal dependence information within each individual time series, (2) exploit the intra-relations between time series through hierarchy, (3) guarantee the satisfaction of hierarchical consistency constraints. Results on three synthetic HTS datasets and three real-world hierarchical web traffic datasets demonstrate that our approach is able to provide more accurate and hierarchically consistent estimations than other baselines.

Medical coding or classification is the process of transforming information contained in patient medical records into standard predefined medical codes. There are several worldwide accepted medical coding conventions associated with diagnoses and medical procedures; however, in the United States the Ninth Revision of ICD(ICD-9) provides the standard for coding clinical records. Accurate medical coding is important since it is used by hospitals for insurance billing purposes. Since after discharge a patient can be assigned or classified to several ICD-9 codes, the coding problem can be seen as a multi-label classification problem. In this paper, we introduce a multi-label large-margin classifier that automatically learns the underlying inter-code structure and allows the controlled incorporation of prior knowledge about medical code relationships. In addition to refining and learning the code relationships, our classifier can also utilize this shared information to improve its performance. Experiments on a publicly available dataset containing clinical free text and their associated medical codes showed that our proposed multi-label classifier outperforms related multi-label models in this problem.

A popular approach for dimensionality reduction and data analysis is principal component analysis (PCA). A limiting factor with PCA is that it does not inform us on which of the original features are important. There is a recent interest in sparse PCA (SPCA). By applying an L1 regularizer to PCA, a sparse transformation is achieved. However, true feature selection may not be achieved as non-sparse coefficients may be distributed over several features. Feature selection is an NP-hard combinatorial optimization problem. This paper relaxes and re-formulates the feature selection problem as a convex continuous optimization problem that minimizes a mean-squared-reconstruction error (a criterion optimized by PCA) and considers feature redundancy into account (an important property in PCA and feature selection). We call this new method Convex Principal Feature Selection (CPFS). Experiments show that CPFS performed better than SPCA in selecting features that maximize variance or minimize the mean-squared-reconstruction error.