Related papers: Efficient Classification for Metric Data
Lipschitz extensions were recently proposed as a tool for designing node differentially private algorithms. However, efficiently computable Lipschitz extensions were known only for 1-dimensional functions (that is, functions that output a…
This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$…
This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that…
In the literature surrounding the theory of Banach spaces, considerable effort has been invested in exploring the conditions on a Banach space X that characterise X as being an inner product space or as a linearly isomorphic copy of a…
Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
Given a black-box classification model and an unlabeled evaluation dataset from some application domain, efficient strategies need to be developed to evaluate the model. Random sampling allows a user to estimate metrics like accuracy,…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…
We consider classification and regression tasks where we have missing data and assume that the (clean) data resides in a low rank subspace. Finding a hidden subspace is known to be computationally hard. Nevertheless, using a non-proper…
We present a Gaussian kernel loss function and training algorithm for convolutional neural networks that can be directly applied to both distance metric learning and image classification problems. Our method treats all training features…
Supervised statistical classification is a vital tool for satellite image processing. It is useful not only when a discrete result, such as feature extraction or surface type, is required, but also for continuum retrievals by dividing the…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
We find a new finite algorithm for evaluation of Lipschitz-free $p$-space norm in finite-dimensional Lipschitz-free $p$-spaces. We use this algorithm to deal with the problem of whether given $p$-metric spaces $N\subset M$, the canonical…
Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
Space-filling curves (SFC, also known as FASS-curves) are a useful tool in scientific computing and other areas of computer science to sequentialize multidimensional grids in a cache-efficient and parallelization-friendly way for storage in…
This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially…