Related papers: Statistical Mechanics of Support Vector Regression
The soft-margin support vector machine (SVM) is a ubiquitous tool for prediction of binary-response data. However, the SVM is characterized entirely via a numerical optimization problem, rather than a probability model, and thus does not…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
This paper proposes a frequent pattern data mining algorithm based on support vector machine (SVM), aiming to solve the performance bottleneck of traditional frequent pattern mining algorithms in high-dimensional and sparse data…
Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…
Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical…
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…
Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…
Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems…
Deep learning revolutionized data science, and recently its popularity has grown exponentially, as did the amount of papers employing deep networks. Vision tasks, such as human pose estimation, did not escape from this trend. There is a…
Stochastic Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural stochastic Volterra equations as a physics-inspired architecture,…
Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural…
Adversarial attacks by generating examples which are almost indistinguishable from natural examples, pose a serious threat to learning models. Defending against adversarial attacks is a critical element for a reliable learning system.…
A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale.…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate.…
Support vector machine (SVM) is one of the most popular classification algorithms in the machine learning literature. We demonstrate that SVM can be used to balance covariates and estimate average causal effects under the unconfoundedness…
Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an…
Neural networks are a promising technique for parameterizing sub-grid-scale physics (e.g. moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption.…
We propose an algorithm for exploring the entire regularization path of asymmetric-cost linear support vector machines. Empirical evidence suggests the predictive power of support vector machines depends on the regularization parameters of…
Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al.…
Response variability, as measured by fluctuating responses upon repeated performance of trials, is a major component of neural responses, and its characterization is key to interpret high dimensional population recordings. Response…