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 Support Vector Machines



BrainRotViT: Transformer-ResNet Hybrid for Explainable Modeling of Brain Aging from 3D sMRI

arXiv.org Artificial Intelligence

The human brain undergoes continuous transformations across the lifespan, representing a natural component of aging that does not inherently signal pathological conditions [1]. Neurodegenerative disorders such as dementia can compromise the brain structure and accelerate aging processes. Understanding and characterizing healthy brain aging patterns therefore becomes essential for distinguishing normal aging from pathological neurodegeneration, potentially enabling earlier detection of neurodegenerative diseases. The Brain Age-Gap (BAG), i.e. the discrepancy between predicted brain age and chronological age, has emerged as a robust biomarker that captures pathological brain processes and offers insights into the rate at which an individual's brain ages in comparison to others in the population [2, 3]. It is not only associated with various neurological disorders, such as Alzheimer's disease, cognitive impairment, and Autism Spectrum Disorder, but also serves as an indicator of all-cause mortality [4, 5, 6, 7, 8] Brain age estimation has been approached through both conventional and machine learning techniques, analyzing either the whole brain, specific regions, or localized patches [9, 10, 11]. One particular study presented a method using T1-weighted MRI to predict age through region-level and voxel-level metrics [12]. Regression-based machine learning has shown promise for the brain age prediction, with kernel regression applied to whole-brain MRI across diverse age ranges [13]. Various algorithms including Support Vector Regression and Binary Decision Trees have been compared for their brain age prediction capabilities [14]. Additional regression techniques such as Relevance Vector Regression, Twin Support Vector Regression, and Gaussian Process Regression have been explored across different imaging modalities for age estimation and mortality prediction [11, 15, 16, 17].


Distributionally Robust Graphical Models

Neural Information Processing Systems

In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin methods---have their own distinct strengths but also possess significant drawbacks. Conditional random fields (CRFs) are Fisher consistent, but they do not permit integration of customized loss metrics into their learning process. Large-margin models, such as structured support vector machines (SSVMs), have the flexibility to incorporate customized loss metrics, but lack Fisher consistency guarantees. We present adversarial graphical models (AGM), a distributionally robust approach for constructing a predictor that performs robustly for a class of data distributions defined using a graphical structure. Our approach enjoys both the flexibility of incorporating customized loss metrics into its design as well as the statistical guarantee of Fisher consistency. We present exact learning and prediction algorithms for AGM with time complexity similar to existing graphical models and show the practical benefits of our approach with experiments.


A Smoother Way to Train Structured Prediction Models

Neural Information Processing Systems

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for the use of fast primal gradient-based optimization algorithms. We illustrate the proposed framework by developing a novel primal incremental optimization algorithm for the structural support vector machine. The proposed algorithm blends an extrapolation scheme for acceleration and an adaptive smoothing scheme and builds upon the stochastic variance-reduced gradient algorithm. We establish its worst-case global complexity bound and study several practical variants. We present experimental results on two real-world problems, namely named entity recognition and visual object localization. The experimental results show that the proposed framework allows us to build upon efficient inference algorithms to develop large-scale optimization algorithms for structured prediction which can achieve competitive performance on the two real-world problems.


But How Does It Work in Theory? Linear SVM with Random Features

Neural Information Processing Systems

We prove that, under low noise assumptions, the support vector machine with $N\ll m$ random features (RFSVM) can achieve the learning rate faster than $O(1/\sqrt{m})$ on a training set with $m$ samples when an optimized feature map is used. Our work extends the previous fast rate analysis of random features method from least square loss to 0-1 loss. We also show that the reweighted feature selection method, which approximates the optimized feature map, helps improve the performance of RFSVM in experiments on a synthetic data set.




PAC-Bayes bounds for stable algorithms with instance-dependent priors

Neural Information Processing Systems

P AC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the P AC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The P AC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our paper is using priors defined in terms of the data-generating distribution. Our main result estimates the risk of the randomized algorithm in terms of the hypothesis stability coefficients. We also provide a new bound for the SVM classifier, which is compared to other known bounds experimentally. Ours appears to be the first uniform hypothesis stability-based bound that evaluates to non-trivial values.


Motor Imagery Classification Using Feature Fusion of Spatially Weighted Electroencephalography

arXiv.org Artificial Intelligence

A Brain Computer Interface (BCI) connects the human brain to the outside world, providing a direct communication channel. Electroencephalography (EEG) signals are commonly used in BCIs to reflect cognitive patterns related to motor function activities. However, due to the multichannel nature of EEG signals, explicit information processing is crucial to lessen computational complexity in BCI systems. This study proposes an innovative method based on brain region-specific channel selection and multi-domain feature fusion to improve classification accuracy. The novelty of the proposed approach lies in region-based channel selection, where EEG channels are grouped according to their functional relevance to distinct brain regions. By selecting channels based on specific regions involved in motor imagery (MI) tasks, this technique eliminates irrelevant channels, reducing data dimensionality and improving computational efficiency. This also ensures that the extracted features are more reflective of the brain actual activity related to motor tasks. Three distinct feature extraction methods Common Spatial Pattern (CSP), Fuzzy C-means clustering, and Tangent Space Mapping (TSM), are applied to each group of channels based on their brain region. Each method targets different characteristics of the EEG signal: CSP focuses on spatial patterns, Fuzzy C means identifies clusters within the data, and TSM captures non-linear patterns in the signal. The combined feature vector is used to classify motor imagery tasks (left hand, right hand, and right foot) using Support Vector Machine (SVM). The proposed method was validated on publicly available benchmark EEG datasets (IVA and I) from the BCI competition III and IV. The results show that the approach outperforms existing methods, achieving classification accuracies of 90.77% and 84.50% for datasets IVA and I, respectively.


A Review of Statistical and Machine Learning Approaches for Coral Bleaching Assessment

arXiv.org Machine Learning

Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal environmental factors, are considered the primary reasons behind coral bleaching. The statistical and machine learning communities have focused on multiple aspects of the environment in detail. However, the literature on various stochastic modeling approaches for assessing coral bleaching is extremely scarce. Data-driven strategies are crucial for effective reef management, and this review article provides an overview of existing statistical and machine learning methods for assessing coral bleaching. Statistical frameworks, including simple regression models, generalized linear models, generalized additive models, Bayesian regression models, spatiotemporal models, and resilience indicators, such as Fisher's Information and Variance Index, are commonly used to explore how different environmental stressors influence coral bleaching. On the other hand, machine learning methods, including random forests, decision trees, support vector machines, and spatial operators, are more popular for detecting nonlinear relationships, analyzing high-dimensional data, and allowing integration of heterogeneous data from diverse sources. In addition to summarizing these models, we also discuss potential data-driven future research directions, with a focus on constructing statistical and machine learning models in specific contexts related to coral bleaching.