Related papers: Maximing the Margin in the Input Space
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
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…
Nonlinear regression methods, such as local optimization algorithms, are widely used in the extraction of nanostructure profile parameters in optical scatterometry. The success of local optimization algorithms heavily relies on the…
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…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of…
The development of modern technology has enabled data collection of unprecedented size, which poses new challenges to many statistical estimation and inference problems. This paper studies the maximum score estimator of a semi-parametric…
In this paper, we propose the Lipschitz margin ratio and a new metric learning framework for classification through maximizing the ratio. This framework enables the integration of both the inter-class margin and the intra-class dispersion,…
In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with…
Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and…
While several feature scoring methods are proposed to explain the output of complex machine learning models, most of them lack formal mathematical definitions. In this study, we propose a novel definition of the feature score using the…
We consider some supervised binary classification tasks and a regression task, whereas SVM and Deep Learning, at present, exhibit the best generalization performances. We extend the work [3] on a generalized quadratic loss for learning…
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…
Parameter estimation is a growing area of interest in statistical signal processing. Some parameters in real-life applications vary in space as opposed to those that are static. Most common methods in estimating parameters involve solving…
Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion…
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast…
This paper addresses the pattern classification problem arising when available target data include some uncertainty information. Target data considered here is either qualitative (a class label) or quantitative (an estimation of the…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…