Related papers: Towards A Deeper Geometric, Analytic and Algorithm…
We consider the problem of cost sensitive multiclass classification, where we would like to increase the sensitivity of an important class at the expense of a less important one. We adopt an {\em apportioned margin} framework to address…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard…
In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
A formal link between regression and classification has been tenuous. Even though the margin maximization term $\|w\|$ is used in support vector regression, it has at best been justified as a regularizer. We show that a regression problem…
We study classification problems using binary estimators where the decision boundary is described by horizon functions and where the data distribution satisfies a geometric margin condition. A key novelty of our work is the derivation of…
Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a…
In this note, we revisit the algorithm of Har-Peled et. al. [HRZ07] for computing a linear maximum margin classifier. Our presentation is self contained, and the algorithm itself is slightly simpler than the original algorithm. The…
We identify the classical Perceptron algorithm with margin as a member of a broader family of large margin classifiers which we collectively call the Margitron. The Margitron, (despite its) sharing the same update rule with the Perceptron,…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
Metric learning aims to learn a distance metric such that semantically similar instances are pulled together while dissimilar instances are pushed away. Many existing methods consider maximizing or at least constraining a distance margin in…
In this paper we present a simple partitioning based technique to refine the statistical analysis of classification algorithms. The core of our idea is to divide the input space into two parts such that the first part contains a suitable…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning…
Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…
In this paper, we propose a novel image set representation and classification method by maximizing the margin of image sets. The margin of an image set is defined as the difference of the distance to its nearest image set from different…
Many problems in computational science and engineering become one-to-many after coarse graining, partial observation, or inverse reconstruction: a resolved state may not determine a unique subgrid forcing, a structural descriptor may not…
We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a…
In the propositional setting, the marginal problem is to find a (maximum-entropy) distribution that has some given marginals. We study this problem in a relational setting and make the following contributions. First, we compare two…