Frequent directions (FDs), as a deterministic matrix sketching technique, have been proposed for tackling low-rank approximation problems. This method has a high degree of accuracy and practicality but experiences a lot of computational cost for large-scale data. Several recent works on the randomized version of FDs greatly improve the computational efficiency but unfortunately sacrifice some precision. To remedy such an issue, this article aims to find a more accurate projection subspace to further improve the efficiency and effectiveness of the existing FDs' techniques. Specifically, by utilizing the power of the block Krylov iteration and random projection technique, this article presents a fast and accurate FDs algorithm named r-BKIFD. The rigorous theoretical analysis shows that the proposed r-BKIFD has a comparable error bound with original FDs, and the approximation error can be arbitrarily small when the number of iterations is chosen appropriately. Extensive experimental results on both synthetic and real data further demonstrate the superiority of r-BKIFD over several popular FDs algorithms both in terms of computational efficiency and accuracy.

We propose a preference-learning algorithm for uncovering Decision Makers’ (DMs’) contingent evaluation strategies in the context of multiple criteria sorting. We assume the preference information in the form of holistic assignment examples derived from the analysis of alternatives’ performance vectors and textual descriptions. We characterize the decision policies using a mixture of threshold-based, value-driven preference models and associated latent topics. The latter serve as the stimuli underlying the contingency in decision behavior. Such a probabilistic model is constructed by using a flexible and nonparametric Bayesian framework. The proposed method adopts a hierarchical Dirichlet process as the prior so that a group of DMs can share a countably infinite number of contingent models and topics. For all DMs, it automatically identifies the components representing their evaluation strategies adequately. The posterior is summarized by using the Hamiltonian Monte Carlo sampling method. We demonstrate the method’s practical usefulness in a real-world recruitment problem considered by a Chinese IT company. We also compare the approach with counterparts that use a single preference model, implement the parametric framework, or consider each DM’s preferences individually. The results indicate that our approach performs favorably in both interpreting DMs’ contingent decision behavior and recommending decisions on new alternatives. Furthermore, the approach’s performance and robustness are investigated through a computational experiment involving real-world data sets. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: J. Liu received financial support from the National Natural Science Foundation of China [Grants 72071155 and 71701160]. M. Kadziński received financial support from the Polish National Science Center under the SONATA BIS project [Grant DEC-2019/34/E/HS4/00045]. X. Liao received financial support from the National Natural Science Foundation of China [Grant 71872144]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1292 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0328 ) at ( http://dx.doi.org/10.5281/zenodo.7608750 ).

Hyperspectral (HS) imaging has been widely used in various real application problems. However, due to the hardware limitations, the obtained HS images usually have low spatial resolution, which could obviously degrade their performance. Through fusing a low spatial resolution HS image with a high spatial resolution auxiliary image (e.g., multispectral, RGB or panchromatic image), the so-called HS image fusion has underpinned much of recent progress in enhancing the spatial resolution of HS image. Nonetheless, a corresponding well registered auxiliary image cannot always be available in some real situations. To remedy this issue, we propose in this paper a newly single HS image super-resolution method based on a novel knowledge-driven deep unrolling technique. Precisely, we first propose a maximum a posterior based energy model with implicit priors, which can be solved by alternating optimization to determine an elementary iteration mechanism. We then unroll such iteration mechanism with an ingenious Transformer embedded convolutional recurrent neural network in which two structural designs are integrated. That is, the vision Transformer and 3D convolution learn the implicit spatial-spectral priors, and the recurrent hidden connections over iterations model the recurrence of the iterative reconstruction stages. Thus, an effective knowledge-driven, end-to-end and data-dependent HS image super-resolution framework can be successfully attained. Extensive experiments on three HS image datasets demonstrate the superiority of the proposed method over several state-of-the-art HS image super-resolution methods.

Ordinal regression predicts the objects’ labels that exhibit a natural ordering, which is vital to decision-making problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the individual features and their interactions affect the decisions is as critical as model performance. Unfortunately, the existing ordinal regression models in the machine learning community aim at improving prediction accuracy rather than explore explainability. To achieve high accuracy while explaining the relationships between the features and the predictions, we propose a new method for ordinal regression problems, namely the Explainable Ordinal Factorization Model (XOFM). XOFM uses piecewise linear functions to approximate the shape functions of individual features, and renders the pairwise features interaction effects as heat-maps. The proposed XOFM captures the nonlinearity in the main effects and ensures the interaction effects’ same flexibility. Therefore, the underlying model yields comparable performance while remaining explainable by explicitly describing the main and interaction effects. To address the potential sparsity problem caused by discretizing the whole feature scale into several sub-intervals, XOFM integrates the Factorization Machines (FMs) to factorize the model parameters. Comprehensive experiments with benchmark real-world and synthetic datasets demonstrate that the proposed XOFM leads to state-of-the-art prediction performance while preserving an easy-to-understand explainability.

The learning of predictive models for data-driven decision support has been a prevalent topic in many fields. However, construction of models that would capture interactions among input variables is a challenging task. In this paper, we present a new preference learning approach for multiple criteria sorting with potentially interacting criteria. It employs an additive piecewise-linear value function as the basic preference model, which is augmented with components for handling the interactions. To construct such a model from a given set of assignment examples concerning reference alternatives, we develop a convex quadratic programming model. Because its complexity does not depend on the number of training samples, the proposed approach is capable for dealing with data-intensive tasks. To improve the generalization of the constructed model on new instances and to overcome the problem of overfitting, we employ the regularization techniques. We also propose a few novel methods for classifying nonreference alternatives in order to enhance the applicability of our approach to different data sets. The practical usefulness of the proposed approach is demonstrated on a problem of parametric evaluation of research units, whereas its predictive performance is studied on several monotone classification problems. The experimental results indicate that our approach compares favourably with the classical UTilités Additives DIScriminantes (UTADIS) method and the Choquet integral-based sorting model. Summary of Contribution. The paper tackles vital challenges at the intersections of multiple criteria decision analysis and machine learning, showing how computationally advanced techniques can be used for faithfully representing human preferences and dealing with complex decision problems. Specifically, we propose a novel preference learning method for multiple criteria sorting problems. The introduced approach incorporates convex quadratic programming to construct a value-based preference model based on large sets of preference statements. In this way, we extend the applicability of decision analysis methods to preferences derived from historical data or observation of users' behavior in addition to the preference judgments explicitly revealed by the decision-makers. The method's practical usefulness is illustrated on a variety of real-world datasets from fields such as higher education, medicine, human resources, and housing market. Its potential for supporting better decision-making is enhanced by both an interpretable form of the assumed model handling interactions between criteria as well as a high predictive performance demonstrated in the extensive computational experiments.

It is known that boosting can be interpreted as an optimization technique to minimize an underlying loss function. Specifically, the underlying loss being minimized by the traditional AdaBoost is the exponential loss, which proves to be very sensitive to random noise/outliers. Therefore, several boosting algorithms, e.g., LogitBoost and SavageBoost, have been proposed to improve the robustness of AdaBoost by replacing the exponential loss with some designed robust loss functions. In this article, we present a new way to robustify AdaBoost, that is, incorporating the robust learning idea of self-paced learning (SPL) into the boosting framework. Specifically, we design a new robust boosting algorithm based on the SPL regime, that is, SPLBoost, which can be easily implemented by slightly modifying off-the-shelf boosting packages. Extensive experiments and a theoretical characterization are also carried out to illustrate the merits of the proposed SPLBoost.

It is known that frequent directions (FD) is a popular deterministic matrix sketching technique for low rank approximation. However, FD and its randomized variants usually meet high computational cost or computational instability in dealing with large-scale datasets, which limits their use in practice. To remedy such issues, this paper aims at improving the efficiency and effectiveness of FD. Specifically, by utilizing the power of Block Krylov Iteration and count sketch techniques, we propose a fast and accurate FD algorithm dubbed as BKICS-FD. We derive the error bound of the proposed BKICS-FD and then carry out extensive numerical experiments to illustrate its superiority over several popular FD algorithms, both in terms of computational speed and accuracy.