Related papers: Efficient Classification for Metric Data
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate…
In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…
In this note, we show that one can use average embeddings, introduced recently in [Naor'20, arXiv:1905.01280], to obtain efficient algorithms for approximate nearest neighbor search. In particular, a metric $X$ embeds into $\ell_2$ on…
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings,…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
The article deals with the issue of modification of metric classification algorithms. In particular, it studies the algorithm k-Nearest Neighbours for its application to sequential data. A method of generalization of metric classification…
Classifying large-scale image data into object categories is an important problem that has received increasing research attention. Given the huge amount of data, non-parametric approaches such as nearest neighbor classifiers have shown…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from [1] is extended from finite-dimensional problems to general Hilbert spaces. The method iteratively computes Pareto critical points,…
Smoothness is crucial for attaining fast rates in first-order optimization. However, many optimization problems in modern machine learning involve non-smooth objectives. Recent studies relax the smoothness assumption by allowing the…
The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first exact algorithm for computing a data-sensitive metric called…
We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this…