相关论文: Coherence Functions with Applications in Large-Mar…

We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examine the Nystr\"om method where the subspaces are defined by a…

We prove an L2 recovery bound for a family of sparse estimators defined as minimizers of some empirical loss functions -- which include hinge loss and logistic loss. More precisely, we achieve an upper-bound for coefficients estimation…

The key task of machine learning is to minimize the loss function that measures the model fit to the training data. The numerical methods to do this efficiently depend on the properties of the loss function. The most decisive among these…

One of the main challenges for feature representation in deep learning-based classification is the design of appropriate loss functions that exhibit strong discriminative power. The classical softmax loss does not explicitly encourage…

We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of a log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a…

High-dimensional classification problems often rely on the Lasso-penalized linear Support Vector Machines (SVMs). However, the double non-smoothness induced by the hinge loss and Lasso penalty in this model makes statistical inference…

In machine learning, the loss functions optimized during training often differ from the target loss that defines task performance due to computational intractability or lack of differentiability. We present an in-depth study of the target…

In this paper, we formulate newly a hierarchical convex optimization for multiclass SVM achieving maximum pairwise margins with least empirical hinge-loss. This optimization problem is a most faithful as well as robust multiclass extension…

We introduce a new Bayesian multi-class support vector machine by formulating a pseudo-likelihood for a multi-class hinge loss in the form of a location-scale mixture of Gaussians. We derive a variational-inference-based training objective…

Recent works have studied implicit biases in deep learning, especially the behavior of last-layer features and classifier weights. However, they usually need to simplify the intermediate dynamics under gradient flow or gradient descent due…

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…

The choice of loss function in classification involves a fundamental trade-off: smooth losses (like Cross-Entropy) enable fast optimization rates but yield slow square-root consistency bounds, while piecewise-linear losses (like Hinge)…

Multiclass extensions of the support vector machine (SVM) have been formulated in a variety of ways. A recent empirical comparison of nine such formulations [Do\v{g}an et al. 2016] recommends the variant proposed by Weston and Watkins (WW),…

Classification is often the first problem described in introductory machine learning classes. Generalization guarantees of classification have historically been offered by Vapnik-Chervonenkis theory. Yet those guarantees are based on…

Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more…

We propose a novel criterion for support vector machine learning: maximizing the margin in the input space, not in the feature (Hilbert) space. This criterion is a discriminative version of the principal curve proposed by Hastie et al. The…

Estimation of convex functions finds broad applications in engineering and science, while convex shape constraint gives rise to numerous challenges in asymptotic performance analysis. This paper is devoted to minimax optimal estimation of…

In this paper, we propose a maximum margin classifier that deals with uncertainty in data input. More specifically, we reformulate the SVM framework such that each training example can be modeled by a multi-dimensional Gaussian distribution…

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…