Related papers: Computationally Efficient Approximations for Matri…
Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…
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 design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
In this work, we analyze alternative effective sample size (ESS) metrics for importance sampling algorithms, and discuss a possible extended range of applications. We show the relationship between the ESS expressions used in the literature…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
The purpose of Secure Multi-Party Computation is to enable protocol participants to compute a public function of their private inputs while keeping their inputs secret, without resorting to any trusted third party. However, opening the…
Sharpness (of the loss minima) is a common measure to investigate the generalization of neural networks. Intuitively speaking, the flatter the landscape near the minima is, the better generalization might be. Unfortunately, the correlation…
The entropy is one of the most applicable uncertainty measures in many statistical and en- gineering problems. In statistical literature, the entropy is used in calculation of the Kullback- Leibler (KL) information which is a powerful mean…
Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
In recent years, kernel methods are widespread in tasks of similarity measuring. Specifically, graph kernels are widely used in fields of bioinformatics, chemistry and financial data analysis. However, existing methods, especially entropy…
In this paper we examine the average R\'{e}nyi entropy $S_{\alpha}$ of a subsystem $A$ when the whole composite system $AB$ is a random pure state. We assume that the Hilbert space dimensions of $A$ and $AB$ are $m$ and $m n$ respectively.…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is…
In [1] it is shown that recurrent neural networks (RNNs) can learn - in a metric entropy optimal manner - discrete time, linear time-invariant (LTI) systems. This is effected by comparing the number of bits needed to encode the…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…