Related papers: Maximing the Margin in the Input Space

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…

Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers.…

The support vector machines (SVM) is one of the most widely used and practical optimization based classification models in machine learning because of its interpretability and flexibility to produce high quality results. However, the big…

Extracting a small subset of crucial rationales from the full input is a key problem in explainability research. The most widely used fundamental criterion for rationale extraction is the maximum mutual information (MMI) criterion. In this…

We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets…

Semi-supervised clustering is an very important topic in machine learning and computer vision. The key challenge of this problem is how to learn a metric, such that the instances sharing the same label are more likely close to each other on…

Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how…

This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu \in \mathbb{R}^P$. The design of reliable and efficient algorithms for addressing this task…

Flexible optical network is a promising technology to accommodate high-capacity demands in next-generation networks. To ensure uninterrupted communication, existing lightpath provisioning schemes are mainly done with the assumption of…

We propose a new algorithm to identify a Wiener-Hammerstein system. This model represents a communication channel where two linear filters are separated by a non-linear function modelling an amplifier. The algorithm enables to recover each…

We present and analyze a momentum-based gradient method for training linear classifiers with an exponentially-tailed loss (e.g., the exponential or logistic loss), which maximizes the classification margin on separable data at a rate of…

Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an…

Boosting algorithms produce a classifier by iteratively combining base hypotheses. It has been observed experimentally that the generalization error keeps improving even after achieving zero training error. One popular explanation…

We consider an unconstrained problem of minimizing a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is…

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…

We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…

Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…