SVRG-MKL: A Fast and Scalable Multiple Kernel Learning Solution for Features Combination in Multi-Class Classification Problems

Multi-omics fusion with soft labeling for enhanced prediction of distant metastasis in nasopharyngeal carcinoma patients after radiotherapy

Omics fusion has emerged as a crucial preprocessing approach in medical image processing, significantly assisting several studies. One of the challenges encountered in integrating omics data is the unpredictability arising from disparities in data sources and medical imaging equipment. Due to these differences, the distribution of omics futures exhibits spatial heterogeneity, diminishing their capacity to enhance subsequent tasks. To overcome this challenge and facilitate the integration of their joint application to specific medical objectives, this study aims to develop a fusion methodology for nasopharyngeal carcinoma (NPC) distant metastasis prediction to mitigate the disparities inherent in omics data. The multi-kernel late-fusion method can reduce the impact of these differences by mapping the features using the most suiTable single-kernel function and then combining them in a high-dimensional space that can effectively represent the data. The proposed approach in this study employs a distinctive framework incorporating a label-softening technique alongside a multi-kernel-based Radial basis function (RBF) neural network to address these limitations. An efficient representation of the data may be achieved by utilizing the multi-kernel to map the inherent features and then merging them in a space with many dimensions. However, the inflexibility of label fitting poses a constraint on using multi-kernel late-fusion methods in complex NPC datasets, hence affecting the efficacy of general classifiers in dealing with high-dimensional characteristics. The label softening increases the disparity between the two cohorts, providing a more flexible structure for allocating labels. The proposed model is evaluated on multi-omics datasets, and the results demonstrate its strength and effectiveness in predicting distant metastasis of NPC patients.

A Deterministic Approximation to Neural SDEs

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been remained unexplored so far. We report the empirical finding that obtaining well-calibrated uncertainty estimations from NSDEs is computationally prohibitive. As a remedy, we develop a computationally affordable deterministic scheme which accurately approximates the transition kernel, when dynamics is governed by a NSDE. Our method introduces a bidimensional moment matching algorithm: vertical along the neural net layers and horizontal along the time direction, which benefits from an original combination of effective approximations. Our deterministic approximation of the transition kernel is applicable to both training and prediction. We observe in multiple experiments that the uncertainty calibration quality of our method can be matched by Monte Carlo sampling only after introducing high computational cost. Thanks to the numerical stability of deterministic training, our method also improves prediction accuracy.

Multi-Nyström Method Based on Multiple Kernel Learning for Large Scale Imbalanced Classification

Extensions of kernel methods for the class imbalance problems have been extensively studied. Although they work well in coping with nonlinear problems, the high computation and memory costs severely limit their application to real-world imbalanced tasks. The Nyström method is an effective technique to scale kernel methods. However, the standard Nyström method needs to sample a sufficiently large number of landmark points to ensure an accurate approximation, which seriously affects its efficiency. In this study, we propose a multi-Nyström method based on mixtures of Nyström approximations to avoid the explosion of subkernel matrix, whereas the optimization to mixture weights is embedded into the model training process by multiple kernel learning (MKL) algorithms to yield more accurate low-rank approximation. Moreover, we select subsets of landmark points according to the imbalance distribution to reduce the model's sensitivity to skewness. We also provide a kernel stability analysis of our method and show that the model solution error is bounded by weighted approximate errors, which can help us improve the learning process. Extensive experiments on several large scale datasets show that our method can achieve a higher classification accuracy and a dramatical speedup of MKL algorithms.

MKL-GRNI: A parallel multiple kernel learning approach for supervised inference of large-scale gene regulatory networks

High throughput multi-omics data generation coupled with heterogeneous genomic data fusion are defining new ways to build computational inference models. These models are scalable and can support very large genome sizes with the added advantage of exploiting additional biological knowledge from the integration framework. However, the limitation with such an arrangement is the huge computational cost involved when learning from very large datasets in a sequential execution environment. To overcome this issue, we present a multiple kernel learning (MKL) based gene regulatory network (GRN) inference approach wherein multiple heterogeneous datasets are fused using MKL paradigm. We formulate the GRN learning problem as a supervised classification problem, whereby genes regulated by a specific transcription factor are separated from other non-regulated genes. A parallel execution architecture is devised to learn a large scale GRN by decomposing the initial classification problem into a number of subproblems that run as multiple processes on a multi-processor machine. We evaluate the approach in terms of increased speedup and inference potential using genomic data from Escherichia coli, Saccharomyces cerevisiae and Homo sapiens. The results thus obtained demonstrate that the proposed method exhibits better classification accuracy and enhanced speedup compared to other state-of-the-art methods while learning large scale GRNs from multiple and heterogeneous datasets.