Dimensional Space Research Articles

Exploration-Exploitation and Suicidal Behavior in Borderline Personality Disorder and Depression.

Clinical theory and behavioral studies suggest that people experiencing suicidal crisis are often unable to find constructive solutions or incorporate useful information into their decisions, resulting in premature convergence on suicide and neglect of better alternatives. However, prior studies of suicidal behavior have not formally examined how individuals resolve the tradeoffs between exploiting familiar options and exploring potentially superior alternatives. To investigate exploration and exploitation in suicidal behavior from the formal perspective of reinforcement learning. Two case-control behavioral studies of exploration-exploitation of a large 1-dimensional continuous space and a 21-day prospective ambulatory study of suicidal ideation were conducted between April 2016 and March 2022. Participants were recruited from inpatient psychiatric units, outpatient clinics, and the community in Pittsburgh, Pennsylvania, and underwent laboratory and ambulatory assessments. Adults diagnosed with borderline personality disorder (BPD) and midlife and late-life major depressive disorder (MDD) were included, with each sample including demographically equated groups with a history of high-lethality suicide attempts, low-lethality suicide attempts, individuals with BPD or MDD but no suicide attempts, and control individuals without psychiatric disorders. The MDD sample also included a subgroup with serious suicidal ideation. Behavioral (model-free and model-derived) indices of exploration and exploitation, suicide attempt lethality (Beck Lethality Scale), and prospectively assessed suicidal ideation. The BPD group included 171 adults (mean [SD] age, 30.55 [9.13] years; 135 [79%] female). The MDD group included 143 adults (mean [SD] age, 62.03 [6.82] years; 81 [57%] female). Across the BPD (χ23 = 50.68; P < .001) and MDD (χ24 = 36.34; P < .001) samples, individuals with high-lethality suicide attempts discovered fewer options than other groups as they were unable to shift away from unrewarded options. In contrast, those with low-lethality attempts were prone to excessive behavioral shifts after rewarded and unrewarded actions. No differences were seen in strategic early exploration or in exploitation. Among 84 participants with BPD in the ambulatory study, 56 reported suicidal ideation. Underexploration also predicted incident suicidal ideation (χ21 = 30.16; P < .001), validating the case-control results prospectively. The findings were robust to confounds, including medication exposure, affective state, and behavioral heterogeneity. The findings suggest that narrow exploration and inability to abandon inferior options are associated with serious suicidal behavior and chronic suicidal thoughts. By contrast, individuals in this study who engaged in low-lethality suicidal behavior displayed a low threshold for taking potentially disadvantageous actions.

Exponentially improved efficient machine learning for quantum many-body states with provable guarantees

Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an m-dimensional space of physical parameters, the ground state and its properties at an arbitrary parameter configuration can be predicted via a machine learning protocol up to a prescribed prediction error ɛ, provided that a sample set (of size N) of the states can be efficiently prepared and measured. In a recent work [Huang , ], a rigorous guarantee for such a generalization was proved. Unfortunately, an exponential scaling for the provable sample complexity, N=mO(1ɛ), was found to be universal for generic gapped Hamiltonians. This result applies to the situation where the dimension of the parameter space is large, while the scaling with the accuracy is not an urgent factor, not entering the realm of more precise learning and prediction. In this work, we consider an alternative relevant scenario, where the effective dimension m is a finite, not necessarily large constant, while the scaling with the prediction error becomes the central concern. By jointly preserving the fundamental properties of density matrices in the learning protocol and utilizing the continuity of quantum states in the parameter range of interest, we rigorously obtain a polynomial sample complexity for predicting quantum many-body states and their properties, with respect to the prediction error ɛ and the number of qubits, n, with N=poly(ɛ−1,n,ln1δ), where poly denotes a polynomial function, and (1−δ) is the probability of success. Moreover, if restricted to learning local quantum-state properties, the number of samples can be further reduced to N=poly(ɛ−1,lnnδ). Numerical demonstrations confirm our findings, and an alternative approach utilizing statistical learning theory with reproducing kernel Hilbert space achieves consistent results. The mere continuity assumption indicates that our results are not restricted to gapped Hamiltonian systems and properties within the same phase. Published by the American Physical Society 2024

Research on the Effective Sheltering Rates of Public Buildings in Villages in Western Sichuan, China—A Case Study of Ganbao Tibetan Village

The western region of Sichuan Province, located in the Hengduan Mountains, is one of China’s most seismically active zones. Due to limited land resources, many villages in western Sichuan Province are situated in mountainous and valley areas, facing harsh climatic conditions, lagging economic development, and insufficient infrastructure. After experiencing seismic disasters, these villages often encounter challenges, such as cut-off mountain roads, difficulties in delivering relief supplies, and sharply a significant drop in nighttime temperatures due to the high-altitude climate. Consequently, in the case of the economic underdevelopment and limited resources, how to repurpose existing buildings for disaster relief has become a crucial issue for disaster prevention and mitigation in these villages. This paper takes Ganbao Tibetan Village, located in the alpine gorge regions of western Sichuan Province, as a case study. It evaluates the interior space utilization status of different types of existing public buildings during disasters, calculates the effective utilization rate of interior space disaster reduction conversion based on the spatial layout model, and extracts the typical interior space dimensions that are conducive to disaster relief and conversion of public buildings based on the interior space utilization characteristics of disaster relief. This study provides a reference for the design of public service buildings considering the requirements of disaster resilience transformation.

Single-camera photogrammetry using a mobile phone for low-cost documentation of corpses.

Photogrammetry is a technique for studying and defining objects' shape, dimension, and position in a three-dimensional space using measurements obtained from two-dimensional photographs. It has gained popularity following the development of computer graphics technologies and has been applied to various branches of medicine. In this study, the authors present a method for low-cost photorealistic documentation of corpses during autopsy using single-camera photogrammetry with a mobile phone. Besides representing the body by demonstrating the injured and non-injured body parts as control, evidencing the body parts on a 3D reconstruction allows easy explanation to nonmedical experts such as lawyers.

The R-mAtrIx Net

We provide a novel neural network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions, iii) explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains which they belong to. The neural network training is done by minimizing loss functions encoding Yang–Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our neural network on the spin chains of difference form with two-dimensional local space. In particular, we reconstruct the R-matrices for all 14 classes. We also demonstrate its utility as an Explorer, scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains with higher dimensional local space and in more general settings where no analytical methods are available.

Multi-armed bandit algorithm for sequential experiments of molecular properties with dynamic feature selection.

Sequential optimization is one of the promising approaches in identifying the optimal candidate(s) (molecules, reactants, drugs, etc.) with desired properties (reaction yield, selectivity, efficacy, etc.) from a large set of potential candidates, while minimizing the number of experiments required. However, the high dimensionality of the feature space (e.g., molecular descriptors) makes it often difficult to utilize the relevant features during the process of updating the set of candidates to be examined. In this article, we developed a new sequential optimization algorithm for molecular problems based on reinforcement learning, multi-armed linear bandit framework, and online, dynamic feature selections in which relevant molecular descriptors are updated along with the experiments. We also designed a stopping condition aimed to guarantee the reliability of the chosen candidate from the dataset pool. The developed algorithm was examined by comparing with Bayesian optimization (BO), using two synthetic datasets and two real datasets in which one dataset includes hydration free energy of molecules and another one includes a free energy difference between enantiomer products in chemical reaction. We found that the dynamic feature selection in representing the desired properties along the experiments provides a better performance (e.g., time required to find the best candidate and stop the experiment) as the overall trend and that our multi-armed linear bandit approach with a dynamic feature selection scheme outperforms the standard BO with fixed feature variables. The comparison of our algorithm to BO with dynamic feature selection is also addressed.

Multidimensional Hyperbolic Equations with Nonlocal Potentials: Families of Global Solutions

In spaces of arbitrary dimensions, hyperbolic differential–difference equations with potentials undergoing translations along arbitrary spatial directions are investigated. The fundamental novelty of this study is that, unlike previous investigations, no restrictions are imposed on the symbol of the differential–difference operator contained in the equation. For the investigated equation, we succeed to explicitly construct a multiparametric family of classical global solutions.

Deal.t: an implementation of multivariate analysis suitable T-splines within the deal.ii framework

AbstractWe present a numerical framework for solving partial differential equations within an isogeometric context using T-splines in two and three space dimensions. Within this paper, we explain the data structures used for the implementation of ( with T-splines) and main differences when using in contrast to . The authors present numerical experiments with error-based refinement (2D) and a priori refinement (3D) for scalar-valued problems. A full tutorial is given in the appendix. Since the new framework is based on , T-splines may be applied to various different PDEs.

Physics-informed neural network simulation of thermal cavity flow

Physics-informed neural networks (PINNs) are an emerging technology that can be used both in place of and in conjunction with conventional simulation methods. In this paper, we used PINNs to perform a forward simulation without leveraging known data. Our simulation was of a 2D natural convection-driven cavity using the vorticity-stream function formulation of the Navier-Stokes equations. We used both 2D simulations across the x and z domains at constant Rayleigh (Ra) numbers and 3D simulations across the x, z and Ra domains. The 3D simulation was tested for a PINN’s ability to learn solutions in a higher-dimensional space than standard simulations. The results were validated against published solutions at Ra values of 103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{3}$$\\end{document}, 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{4}$$\\end{document}, 105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{5}$$\\end{document}, and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{6}$$\\end{document}. Both the 2D simulations and 3D simulations successfully matched the expected results. For the 2D cases, more training iterations were needed for the model to converge at higher Ra values (105\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^5$$\\end{document} and 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^6$$\\end{document}) than at lower Ra (103\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document} and 104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}) indicating increased nonlinear fluid-thermal coupling. The 3D case was also able to converge but, but it required more training than any of the 2D cases due to the curse of dimensionality. These results showed the validity of standard simulations via PINNs and the feasibility of higher-order parameter space solutions that are not possible using conventional methods. They also showcased the additional computational demand associated with increasing the dimensionality of the learned parameter space.

Valuation of a financial claim contingent on the outcome of a quantum measurement

We consider a rational agent who at time 0 enters into a financial contract for which the payout is determined by a quantum measurement at some time T > 0. The state of the quantum system is given in the Heisenberg representation by a known density matrix p^ . How much will the agent be willing to pay at time 0 to enter into such a contract? In the case of a finite dimensional Hilbert space H , each such claim is represented by an observable X^T where the eigenvalues of X^T determine the amount paid if the corresponding outcome is obtained in the measurement. We prove, under reasonable axioms, that there exists a pricing state q^ which is equivalent to the physical state p^ such that the pricing function Π0T takes the linear form Π0T(X^T)=P0Ttr(q^X^T) for any claim X^T , where P0T is the one-period discount factor. By ‘equivalent’ we mean that p^ and q^ share the same null space: that is, for any |ξ⟩∈H one has p^|ξ⟩=0 if and only if q^|ξ⟩=0 . We introduce a class of optimization problems and solve for the optimal contract payout structure for a claim based on a given measurement. Then we consider the implications of the Kochen–Specker theorem in this setting and we look at the problem of forming portfolios of such contracts. Finally, we consider multi-period contracts.

Social media and political contention - challenges and opportunities for comparative research

ABSTRACT In this special issue, the authors theoretically, methodologically, and empirically address challenges and opportunities associated with comparative social media analysis in political contention. Actors from civil society, media, and institutional politics use social media to coordinate, mobilise, and communicate, turning public online communication into an arena of conflict that offers researchers valuable windows of observation. In this introduction to the special issue, we systematise comparative perspectives on social media and political contention. We outline the traditional comparative dimensions of space, time, platform, and case; and suggest an approach for comparison within dimensions that are less dependent on the rapidly changing social media environment and more attuned to the interconnection between social media and political contention.

Deep Learning-Based Multi-Fidelity Surrogate Modeling for High Dimensional Reliability Prediction

Abstract Multi-fidelity surrogate modeling offers a cost-effective approach to reduce extensive evaluations of expensive physics-based simulations for reliability predictions. However, considering spatial uncertainties in multi-fidelity surrogate modeling remains extremely challenging due to the curse of dimensionality. To address this challenge, this paper introduces a deep learning-based multi-fidelity surrogate modeling approach that fuses multi-fidelity datasets for high-dimensional reliability analysis of complex structures. It first involves a heterogeneous dimension transformation approach to bridge the gap in terms of input format between the low-fidelity and high-fidelity domains. Then, an explainable deep convolutional dimension-reduction network is proposed to effectively reduce the dimensionality of the structural reliability problems. To obtain a meaningful low dimensional space, a new knowledge reasoning-based loss regularization mechanism is integrated with the covariance matrix adaptation evolution strategy to encourage an unbiased linear pattern in the latent space for reliability predictions. Then, the high-fidelity data can be utilized for bias modeling using Gaussian process regression. Finally, Monte Carlo simulation is employed for the propagation of high-dimensional spatial uncertainties. Two structural examples are utilized to validate the effectiveness of the proposed method.

Maximum principle preserving time implicit DGSEM for linear scalar hyperbolic conservation laws

The properties of the high-order discontinuous Galerkin spectral element method (DGSEM) with implicit backward Euler time stepping are investigated for the approximation of hyperbolic linear scalar conservation equation in multiple space dimensions. We first prove that the DGSEM scheme in one space dimension preserves a maximum principle for the cell-averaged solution when the time step is large enough. This property however no longer holds in multiple space dimensions and we propose to use the flux-corrected transport (FCT) limiting [5] based on a low-order approximation using graph viscosity to impose a maximum principle on the cell-averaged solution. These results allow us to use a linear scaling limiter [58] in order to impose a maximum principle at nodal values within elements, while limiting the cell average with the FCT limiter improves the accuracy of the limited solution. Then, we investigate the inversion of the linear systems resulting from the time implicit discretization at each time step. We prove that the diagonal blocks are invertible and provide efficient algorithms for their inversion. Numerical experiments in one and two space dimensions are presented to illustrate the conclusions of the present analyses.

Principal dimensions of voice production and their role in vocal expression.

How we produce and perceive voice is constrained by laryngeal physiology and biomechanics. Such constraints may present themselves as principal dimensions in the voice outcome space that are shared among speakers. This study attempts to identify such principal dimensions in the voice outcome space and the underlying laryngeal control mechanisms in a three-dimensional computational model of voice production. A large-scale voice simulation was performed with parametric variations in vocal fold geometry and stiffness, glottal gap, vocal tract shape, and subglottal pressure. Principal component analysis was applied to data combining both the physiological control parameters and voice outcome measures. The results showed three dominant dimensions accounting for at least 50% of the total variance. The first two dimensions describe respiratory-laryngeal coordination in controlling the energy balance between low- and high-frequency harmonics in the produced voice, and the third dimension describes control of the fundamental frequency. The dominance of these three dimensions suggests that voice changes along these principal dimensions are likely to be more consistently produced and perceived by most speakers than other voice changes, and thus are more likely to have emerged during evolution and be used to convey important personal information, such as emotion and larynx size.

Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean–Vlasov stochastic differential equations

In this paper we prove that rectified deep neural networks do not suffer from the curse of dimensionality when approximating McKean–Vlasov SDEs in the sense that the number of parameters in the deep neural networks only grows polynomially in the space dimension d of the SDE and the reciprocal of the accuracy ϵ.

Well-posedness and scattering for a 2D inhomogeneous NLS with Aharonov-Bohm magnetic potential

We consider the magnetic nonlinear inhomogeneous Schrödinger equationi∂tu−(−i∇+α|x|2(−x2,x1))2u=±|x|−ϱ|u|p−1u,(t,x)∈R×R2, where α∈R∖Z,ϱ>0,p>1. We establish a dichotomy between global existence and scattering versus finite-time blow-up for energy solutions below the ground state threshold in the inter-critical regime. The scattering result is obtained by employing the novel approach developed by Dodson and Murphy (A new proof of scattering below the ground state for the 3D radial focusing cubic NLS, Proc. Am. Math. Soc. (2017)). We employ Tao's scattering criteria and Morawetz estimates as the foundation of this method. The novelty of our approach lies in two aspects: firstly, we explore the case of nonzero ϱα, and secondly, we consider general energy initial data that need not be radially symmetric. The specific instance of α=0, known as INLS, has garnered significant attention in recent years. Additionally, X. Gao and C. Xu recently investigated the case of ϱ=0 in the homogeneous regime, establishing scattering theory for spherically symmetric data in their work (Scattering theory for NLS with inverse-square potential in 2D, J. Math. Anal. Appl. (2020)). In the radial framework, the aforementioned problem can be translated to the INLS with an inverse square potential, which has been extensively studied in higher-dimensional spaces. The Hardy inequality ‖|x|−1f‖L2(RN)≤2N−2‖∇f‖L2(RN), which establishes the norm equivalence ‖f‖H1≃‖f‖H1+‖|x|−1f‖L2, does not hold in two space dimensions. Consequently, it remains unclear how to handle the NLS with an inverse square potential in the H1 framework for two-dimensional space. This article stands out as the first one to address the NLS with Aharonov-Bohm magnetic potential within the inhomogeneous regime, specifically when ϱ≠0.

Dimensions of Arachnoid Bulk Ratio: A Superior Optic Nerve Sheath Index for Intracranial Pressure.

Background Discrepancies in the literature regarding optimal optic nerve sheath diameter (ONSD) cutoffs for intracranial pressure (ICP) necessitate alternative neuroimaging parameters to improve clinical management. Purpose To evaluate the diagnostic accuracy of the dimensions of the perineural subarachnoid space to the optic nerve sheath ratio, measured using US, in predicting increased ICP. Materials and Methods In a prospective cohort study from April 2022 to December 2023, patients with suspected increased ICP underwent optic nerve US to determine the dimensions of arachnoid bulk (DAB) ratio and ONSD before invasive ICP measurement. Correlation between the parameters and ICP, as well as diagnostic accuracy, was assessed using area under the receiver operating characteristic curve (AUC) analysis. Results A total of 30 participants were included (mean age, 39 years ± 14 [SD]; 24 female). The DAB ratio and ONSD were significantly larger in participants with increased ICP (38% [0.16 of 0.42] and 14% [0.82 of 6.04 mm], respectively; P < .001). The DAB ratio showed a stronger correlation with ICP than ONSD (rs = 0.87 [P < .001] vs rs = 0.61 [P < .001]). The DAB ratio and ONSD optimal cutoffs for increased ICP were 0.5 and 6.5 mm, respectively, and the ratio had higher sensitivity (100% vs 92%) and specificity (94% vs 83%) compared with ONSD. Moreover, the DAB ratio better predicted increased ICP than ONSD, with a higher AUC (0.98 [95% CI: 0.95, 1.00] vs 0.86 [95% CI: 0.71, 0.95], P = .047). Conclusion An imaging ratio was proposed to predict ICP based on the relative anatomy of the cerebrospinal fluid space, demonstrating more accurate diagnosis of increased ICP and a strong correlation with ICP values, suggesting its potential utility as a neuroimaging marker in clinical settings. © RSNA, 2024 Supplemental material is available for this article. See also the editorial by Shepherd in this issue.

Interpretable multi-graph convolution network integrating spatial-temporal attention and dynamic combination for wind power forecasting

Graph neural networks (GNN) can effectively improve wind power forecasting accuracy due to its ability to capture spatial correlations between wind farms. However, conventional GNN-based forecasting models constructing the graphs from only one specific perspective fail to characterize the spatial correlation patterns comprehensively and accurately. Furthermore, their black-box structure leads to deficient interpretability of the forecasting results, which hampers the quantification of forecasts uncertainty and reduces the credibility of applying these forecasting models in practice. To address the above problems, an interpretable ultra-short-term wind power forecasting method is proposed based on multi-graph convolution network integrating spatial–temporal attention and dynamic graph combination. Four undirected weight graphs are constructed to form a multi-graph scheme by considering various geographical and statistical aspects, and then graph convolution network (GCN) and temporal convolution network (TCN) are used to enhance the forecasting performance by leveraging information in both space and time dimensions. Meanwhile, it consists of temporal attention that deeply mines the temporal dependence information and spatial attention that interprets influence of wind farms on the forecasts. Additionally, to boost the adaptability and generalization capability of the proposed method, an improved reinforcement learning is elaborately designed to combine the results of different graphs by dynamically optimizing their weights to obtain the final forecasts. Experiment results suggest that the proposed method exhibits superior forecasting accuracy and reasonable interpretability compared with other benchmark methods.

Multi-dimensional niche differentiation of two sympatric breeding secondary cave-nesting birds in Northeast China using DNA metabarcoding.

Niche theory predicts that ecologically similar sympatric species should show differentiation in at least one of the main niche dimensions (time, space, and/or food). Here, we combined observations of breeding timing, nest site selection, and diet (the latter determined using DNA metabarcoding) to analyze the niche overlap and differentiation between two sympatric secondary cavity-nesting birds, the Japanese Tit Parus minor and the Yellow-rumped Flycatcher Ficedula zanthopygia. The results showed that (1) there were significant differences in the first egg laying date, length of the egg laying period, incubation date, and hatching date between tits and flycatchers, and the breeding time of flycatchers peaked later (about 30 days) than that of tits; (2) the two species had a large overlap in nest site selection, although the canopy coverage and shrub density of flycatchers were significantly higher than those of tits; and (3) the niche overlap in diet was minimal, with both species heavily relying on Lepidoptera (39.6% and 63.7% for tits and flycatchers, respectively), but with flycatchers consuming significantly higher percentages of Lepidoptera, Diptera, and Coleoptera than tits. The results indicate that these two sympatric secondary cavity-nesting species have significant niche differentiation in breeding time and diet, but little differentiation in nest site selection.

Distributionally robust chance-constrained kernel-based support vector machine

Support vector machine (SVM) is a powerful model for supervised learning. This article addresses the nonlinear binary classification problem using kernel-based SVM with uncertainty involved in the input data specified by the first- and second-order moments. To achieve a robust classifier with small probabilities of misclassification, we investigate a distributionally robust chance-constrained kernel-based SVM model. Since the moment information in the original problem becomes unclear/unavailable in the feature space via kernel transformation, we develop a data-driven approach utilizing empirical moments to provide a second-order cone programming (SOCP) reformulation for efficient computation. To speed up the required computations for solving large-size problems in higher dimensional space and/or with more sampling points involved in estimating empirical moments, we further design an alternating direction multipliers-based algorithm for fast computations. Extensive computational results support the effectiveness and efficiency of the proposed model and solution method. Results on public benchmark datasets without any moment information indicate that the proposed approach still works and, surprisingly, outperforms some commonly used state-of-the-art kernel-based SVM models.