Related papers: No Dimensional Sampling Coresets for Classificatio…
Specific data compression techniques, formalized by the concept of coresets, proved to be powerful for many optimization problems. In fact, while tightly controlling the approximation error, coresets may lead to significant speed up of the…
Training machine learning models on massive datasets incurs substantial computational costs. To alleviate such costs, there has been a sustained effort to develop data-efficient training methods that can carefully select subsets of the…
How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
We present a novel coreset construction algorithm for solving classification tasks using Support Vector Machines (SVMs) in a computationally efficient manner. A coreset is a weighted subset of the original data points that provably…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…
This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…
We study distribution-free property testing and learning problems where the unknown probability distribution is a product distribution over $\mathbb{R}^d$. For many important classes of functions, such as intersections of halfspaces,…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
We develop and analyze a method to reduce the size of a very large set of data points in a high dimensional Euclidean space R d to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set…
In this paper, we report on the largest labelled dataset constructed so far for solving zero-dimensional square nonlinear systems with subdivision-based methods. A brief, non-exhaustive survey with emphasis on the literature from the past…
When model predictions inform downstream decision making, a natural question is under what conditions can the decision-makers simply respond to the predictions as if they were the true outcomes. Calibration suffices to guarantee that simple…
We propose a pair of completely data-driven algorithms for unsupervised classification and dimension reduction, and we empirically study their performance on a number of data sets, both simulated data in three-dimensions and images from the…
Deep learning models achieve state-of-the-art performance across domains but face scalability challenges in real-time or resource-constrained scenarios. To address this, we propose Loss Trajectory Correlation (LTC), a novel metric for…
We study the robust geometric median problem in Euclidean space $\mathbb{R}^d$, with a focus on coreset construction.A coreset is a compact summary of a dataset $P$ of size $n$ that approximates the robust cost for all centers $c$ within a…
Training neural networks on a large dataset requires substantial computational costs. Dataset reduction selects or synthesizes data instances based on the large dataset, while minimizing the degradation in generalization performance from…
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…