Related papers: Efficient Classification for Metric Data

With the increasing penetration of machine learning applications in critical decision-making areas, calls for algorithmic fairness are more prominent. Although there have been various modalities to improve algorithmic fairness through…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…

Proximities are at the heart of almost all machine learning methods. If the input data are given as numerical vectors of equal lengths, euclidean distance, or a Hilbertian inner product is frequently used in modeling algorithms. In a more…

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

The generalization performance of deep neural networks in classification tasks is a major concern in machine learning research. Despite widespread techniques used to diminish the over-fitting issue such as data augmentation,…

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…

Most research into similarity search in metric spaces relies upon the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common…

A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…

Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…

A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0,1] and the loss is logarithmic. This setting presents novel computational and statistical…

Lipschitz constrained networks have gathered considerable attention in the deep learning community, with usages ranging from Wasserstein distance estimation to the training of certifiably robust classifiers. However they remain commonly…

In this paper, we establish a comprehensive characterization of the generalized Lipschitz classes through the study of the rate of convergence of a family of semi-discrete sampling operators, of Durrmeyer type, in $L^p$-setting. To achieve…

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimensionality reduction.…

Optimization problems arising in data science have given rise to a number of new derivative-based optimization methods. Such methods often use standard smoothness assumptions -- namely, global Lipschitz continuity of the gradient function…

Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes. Motivated by…