In the era of data-driven science, machine learning has emerged as a transformative tool, offering unprecedented solutions to complex problems across a wide range of scientific and technological domains. Specifically, machine learning has found applications in diverse fields such as biology, medicine, material science, engineering, energy, manufacturing, and agriculture. Notable examples include rapid detection of SARS-CoV-2 Ikponmwoba et al. [2022], advances in drug discovery and development Talevi et al. [2020], quality control and defect detection Wang et al. [2022], climate modeling and prediction Krasnopolsky and Fox-Rabinovitz [2006], as well as crop yield forecasting and optimization Di et al. [2022]. Some of these applications involve classification, which involves learning based on categorical data. In this regard, machine learning techniques, such as Support Vector Machines, Naive Bayes, K-nearest neighbor, and Neural Networks, have been used to extract texture features from images for subsequent classification Chola et al. [2022a,b]. Additionally, machine learning has facilitated the identification of high-order closure terms from fully kinetic simulations, a critical aspect of multi-scale modelingLaperre et al. [2022]. On the other hand, function approximation or regression involves estimating a continuous target quantity as a function of a set of input variables. Methods such as Sparse Identification of Nonlinear Dynamics (SINDy) Brunton et al. [2016], the Least Absolute Shrinkage and Selection Operator (LASSO) Tibshirani [1996], Dynamic Mode Decomposition (DMD) Schmid [2010], Mezić [2005], Koopman operator Mezić [2013] and the Eigensystem Realization Algorithm (ERA) Juang and Pappa [1985] have contributed significantly to understanding complex systems by offering effective strategies for model selection, variable regularization, decomposition of high-dimensional systems, and extraction of state-space models from input-output data.

The prediction of spin magnitudes in binary black hole and neutron star mergers is crucial for understanding the astrophysical processes and gravitational wave (GW) signals emitted during these cataclysmic events. In this paper, we present a novel Neuro-Symbolic Architecture (NSA) that combines the power of neural networks and symbolic regression to accurately predict spin magnitudes of black hole and neutron star mergers. Our approach utilizes GW waveform data obtained from numerical relativity simulations in the SXS Waveform catalog. By combining these two approaches, we leverage the strengths of both paradigms, enabling a comprehensive and accurate prediction of spin magnitudes. Our experiments demonstrate that the proposed architecture achieves an impressive root-mean-squared-error (RMSE) of 0.05 and mean-squared-error (MSE) of 0.03 for the NSA model and an RMSE of 0.12 for the symbolic regression model alone. We train this model to handle higher-order multipole waveforms, with a specific focus on eccentric candidates, which are known to exhibit unique characteristics. Our results provide a robust and interpretable framework for predicting spin magnitudes in mergers. This has implications for understanding the astrophysical properties of black holes and deciphering the physics underlying the GW signals.

Uncertainty sampling is a prevalent active learning algorithm that queries sequentially the annotations of data samples which the current prediction model is uncertain about. However, the usage of uncertainty sampling has been largely heuristic: (i) There is no consensus on the proper definition of "uncertainty" for a specific task under a specific loss; (ii) There is no theoretical guarantee that prescribes a standard protocol to implement the algorithm, for example, how to handle the sequentially arrived annotated data under the framework of optimization algorithms such as stochastic gradient descent. In this work, we systematically examine uncertainty sampling algorithms under both stream-based and pool-based active learning. We propose a notion of equivalent loss which depends on the used uncertainty measure and the original loss function and establish that an uncertainty sampling algorithm essentially optimizes against such an equivalent loss. The perspective verifies the properness of existing uncertainty measures from two aspects: surrogate property and loss convexity. Furthermore, we propose a new notion for designing uncertainty measures called \textit{loss as uncertainty}. The idea is to use the conditional expected loss given the features as the uncertainty measure. Such an uncertainty measure has nice analytical properties and generality to cover both classification and regression problems, which enable us to provide the first generalization bound for uncertainty sampling algorithms under both stream-based and pool-based settings, in the full generality of the underlying model and problem. Lastly, we establish connections between certain variants of the uncertainty sampling algorithms with risk-sensitive objectives and distributional robustness, which can partly explain the advantage of uncertainty sampling algorithms when the sample size is small.

Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on vector-based formulations in existing SVM-based models poses limitations regarding flexibility and ease of incorporating additional terms to handle specific challenges. To overcome these limitations, our research paper focuses on introducing a matrix formulation for SVM that effectively addresses these constraints. By employing the Accelerated Gradient Descent method in the dual, we notably enhance the efficiency of solving the Matrix-SVM problem. Experimental evaluations on multilabel and multiclass datasets demonstrate that Matrix SVM achieves superior time efficacy while delivering similar results to Binary Relevance SVM. Moreover, our matrix formulation unveils crucial insights and advantages that may not be readily apparent in traditional vector-based notations. We emphasize that numerous multilabel models can be viewed as extensions of SVM, with customised modifications to meet specific requirements. The matrix formulation presented in this paper establishes a solid foundation for developing more sophisticated models capable of effectively addressing the distinctive challenges encountered in multilabel learning.

Clinical Practice Guidelines (CPGs) for cancer diseases evolve rapidly due to new evidence generated by active research. Currently, CPGs are primarily published in a document format that is ill-suited for managing this developing knowledge. A knowledge model of the guidelines document suitable for programmatic interaction is required. This work proposes an automated method for extraction of knowledge from National Comprehensive Cancer Network (NCCN) CPGs in Oncology and generating a structured model containing the retrieved knowledge. The proposed method was tested using two versions of NCCN Non-Small Cell Lung Cancer (NSCLC) CPG to demonstrate the effectiveness in faithful extraction and modeling of knowledge. Three enrichment strategies using Cancer staging information, Unified Medical Language System (UMLS) Metathesaurus & National Cancer Institute thesaurus (NCIt) concepts, and Node classification are also presented to enhance the model towards enabling programmatic traversal and querying of cancer care guidelines. The Node classification was performed using a Support Vector Machine (SVM) model, achieving a classification accuracy of 0.81 with 10-fold cross-validation.

Plant breeders and agricultural researchers can increase crop productivity by identifying desirable features, disease resistance, and nutritional content by analysing the Dry Bean dataset. This study analyses and compares different Support Vector Machine (SVM) classification algorithms, namely linear, polynomial, and radial basis function (RBF), along with other popular classification algorithms. The analysis is performed on the Dry Bean Dataset, with PCA (Principal Component Analysis) conducted as a preprocessing step for dimensionality reduction. The primary evaluation metric used is accuracy, and the RBF SVM kernel algorithm achieves the highest Accuracy of 93.34%, Precision of 92.61%, Recall of 92.35% and F1 Score as 91.40%. Along with adept visualization and empirical analysis, this study offers valuable guidance by emphasizing the importance of considering different SVM algorithms for complex and non-linear structured datasets.

Timeseries classification as stochastic (noise-like) or non-stochastic (structured), helps understand the underlying dynamics, in several domains. Here we propose a two-legged matrix decomposition-based algorithm utilizing two complementary techniques for classification. In Singular Value Decomposition (SVD) based analysis leg, we perform topological analysis (Betti numbers) on singular vectors containing temporal information, leading to SVD-label. Parallely, temporal-ordering agnostic Principal Component Analysis (PCA) is performed, and the proposed PCA-derived features are computed. These features, extracted from synthetic timeseries of the two labels, are observed to map the timeseries to a linearly separable feature space. Support Vector Machine (SVM) is used to produce PCA-label. The proposed methods have been applied to synthetic data, comprising 41 realisations of white-noise, pink-noise (stochastic), Logistic-map at growth-rate 4 and Lorentz-system (non-stochastic), as proof-of-concept. Proposed algorithm is applied on astronomical data: 12 temporal-classes of timeseries of black hole GRS 1915+105, obtained from RXTE satellite with average length 25000. For a given timeseries, if SVD-label and PCA-label concur, then the label is retained; else deemed "Uncertain". Comparison of obtained results with those in literature are presented. It's found that out of 12 temporal classes of GRS 1915+105, concurrence between SVD-label and PCA-label is obtained on 11 of them.

Students who take an online course, such as a MOOC, use the course's discussion forum to ask questions or reach out to instructors when encountering an issue. However, reading and responding to students' questions is difficult to scale because of the time needed to consider each message. As a result, critical issues may be left unresolved, and students may lose the motivation to continue in the course. To help address this problem, we build predictive models that automatically determine the urgency of each forum post, so that these posts can be brought to instructors' attention. This paper goes beyond previous work by predicting not just a binary decision cut-off but a post's level of urgency on a 7-point scale. First, we train and cross-validate several models on an original data set of 3,503 posts from MOOCs at University of Pennsylvania. Second, to determine the generalizability of our models, we test their performance on a separate, previously published data set of 29,604 posts from MOOCs at Stanford University. While the previous work on post urgency used only one data set, we evaluated the prediction across different data sets and courses. The best-performing model was a support vector regressor trained on the Universal Sentence Encoder embeddings of the posts, achieving an RMSE of 1.1 on the training set and 1.4 on the test set. Understanding the urgency of forum posts enables instructors to focus their time more effectively and, as a result, better support student learning.

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum-inspired algorithm for recommendation systems [STOC'19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily\'en, Su, Low, and Wiebe [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: $\ell^2$-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

While kernel methods have shown excellent performance and generalization capabilities, they tend to fall behind when We propose a unifying setting that combines existing it comes to large-scale problems due to their memory and restricted kernel machine methods into a single computational complexity. Additionally, it can be difficult primal-dual multi-view framework for kernel to change their architecture to allow for hierarchical principal component analysis in both supervised representation learning, which is one of the most powerful and unsupervised settings. We derive the primal capabilities of neural networks. Recently, Restricted and dual representations of the framework and Kernel Machines (RKM), were proposed which connect relate different training and inference algorithms least-squares support vector machines and kernel principal from a theoretical perspective. We show how to component analysis (kernel PCA) with Restricted Boltzmann achieve full equivalence in primal and dual formulations machines (Suykens, 2017). RKMs extend the primal by rescaling primal variables. Finally, and dual model representations present in least-squares support we experimentally validate the equivalence and vector machines, from shallow to deep architectures by provide insight into the relationships between different introducing the dual variables as hidden features through methods on a number of time series data conjugate feature duality. This provides a framework of sets by recursively forecasting unseen test data kernel methods represented by visible and hidden units as and visualizing the learned features.