Georgios C. Anagnostopoulos

Akshay Aravamudan, Zimeena Rasheed, Xi Zhang et al.

The frequency of extreme flood events is increasing throughout the world. Daily, high-resolution (30m) Flood Inundation Maps (FIM) observed from space play a key role in informing mitigation and preparedness efforts to counter these extreme events. However, the temporal frequency of publicly available high-resolution FIMs, e.g., from Landsat, is at the order of two weeks thus limiting the effective monitoring of flood inundation dynamics. Conversely, global, low-resolution (~300m) Water Fraction Maps (WFM) are publicly available from NOAA VIIRS daily. Motivated by the recent successes of deep learning methods for single image super-resolution, we explore the effectiveness and limitations of similar data-driven approaches to downscaling low-resolution WFMs to high-resolution FIMs. To overcome the scarcity of high-resolution FIMs, we train our models with high-quality synthetic data obtained through physics-based simulations. We evaluate our models on real-world data from flood events in the state of Iowa. The study indicates that data-driven approaches exhibit superior reconstruction accuracy over non-data-driven alternatives and that the use of synthetic data is a viable proxy for training purposes. Additionally, we show that our trained models can exhibit superior zero-shot performance when transferred to regions with hydroclimatological similarity to the U.S. Midwest.

Niloofar Yousefi, Michael Georgiopoulos, Georgios C. Anagnostopoulos

When faced with learning a set of inter-related tasks from a limited amount of usable data, learning each task independently may lead to poor generalization performance. Multi-Task Learning (MTL) exploits the latent relations between tasks and overcomes data scarcity limitations by co-learning all these tasks simultaneously to offer improved performance. We propose a novel Multi-Task Multiple Kernel Learning framework based on Support Vector Machines for binary classification tasks. By considering pair-wise task affinity in terms of similarity between a pair's respective feature spaces, the new framework, compared to other similar MTL approaches, offers a high degree of flexibility in determining how similar feature spaces should be, as well as which pairs of tasks should share a common feature space in order to benefit overall performance. The associated optimization problem is solved via a block coordinate descent, which employs a consensus-form Alternating Direction Method of Multipliers algorithm to optimize the Multiple Kernel Learning weights and, hence, to determine task affinities. Empirical evaluation on seven data sets exhibits a statistically significant improvement of our framework's results compared to the ones of several other Clustered Multi-Task Learning methods.

Cong Li, Michael Georgiopoulos, Georgios C. Anagnostopoulos

Traditionally, Multi-task Learning (MTL) models optimize the average of task-related objective functions, which is an intuitive approach and which we will be referring to as Average MTL. However, a more general framework, referred to as Conic MTL, can be formulated by considering conic combinations of the objective functions instead; in this framework, Average MTL arises as a special case, when all combination coefficients equal 1. Although the advantage of Conic MTL over Average MTL has been shown experimentally in previous works, no theoretical justification has been provided to date. In this paper, we derive a generalization bound for the Conic MTL method, and demonstrate that the tightest bound is not necessarily achieved, when all combination coefficients equal 1; hence, Average MTL may not always be the optimal choice, and it is important to consider Conic MTL. As a byproduct of the generalization bound, it also theoretically explains the good experimental results of previous relevant works. Finally, we propose a new Conic MTL model, whose conic combination coefficients minimize the generalization bound, instead of choosing them heuristically as has been done in previous methods. The rationale and advantage of our model is demonstrated and verified via a series of experiments by comparing with several other methods.

Cong Li, Michael Georgiopoulos, Georgios C. Anagnostopoulos

A traditional and intuitively appealing Multi-Task Multiple Kernel Learning (MT-MKL) method is to optimize the sum (thus, the average) of objective functions with (partially) shared kernel function, which allows information sharing amongst tasks. We point out that the obtained solution corresponds to a single point on the Pareto Front (PF) of a Multi-Objective Optimization (MOO) problem, which considers the concurrent optimization of all task objectives involved in the Multi-Task Learning (MTL) problem. Motivated by this last observation and arguing that the former approach is heuristic, we propose a novel Support Vector Machine (SVM) MT-MKL framework, that considers an implicitly-defined set of conic combinations of task objectives. We show that solving our framework produces solutions along a path on the aforementioned PF and that it subsumes the optimization of the average of objective functions as a special case. Using algorithms we derived, we demonstrate through a series of experimental results that the framework is capable of achieving better classification performance, when compared to other similar MTL approaches.

Cong Li, Michael Georgiopoulos, Georgios C. Anagnostopoulos

In this paper we present two related, kernel-based Distance Metric Learning (DML) methods. Their respective models non-linearly map data from their original space to an output space, and subsequent distance measurements are performed in the output space via a Mahalanobis metric. The dimensionality of the output space can be directly controlled to facilitate the learning of a low-rank metric. Both methods allow for simultaneous inference of the associated metric and the mapping to the output space, which can be used to visualize the data, when the output space is 2- or 3-dimensional. Experimental results for a collection of classification tasks illustrate the advantages of the proposed methods over other traditional and kernel-based DML approaches.