Related papers: Optimal Randomized Approximations for Matrix based…
Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…
The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been…
The joint eigenvalue distributions of random-matrix ensembles are derived by applying the principle maximum entropy to the Renyi, Abe and Kaniadakis entropies. While the Renyi entropy produces essentially the same matrix-element…
We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for $n$ data points requires $\Omega(n^2)$ similarity computations. This quadratic…
We introduce the first differentiable approximation of range-partition entropy, a complexity measure from computational geometry that directly bounds algorithmic runtime. Unlike architectural modifications, our method is a complementary…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
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,…
Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is…
We present a new sublinear time algorithm for approximating the spectral density (eigenvalue distribution) of an $n\times n$ normalized graph adjacency or Laplacian matrix. The algorithm recovers the spectrum up to $\epsilon$ accuracy in…
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…
We study the problem of entrywise $\ell_1$ low rank approximation. We give the first polynomial time column subset selection-based $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an…
The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…
Information retrieval (IR) systems traditionally aim to maximize metrics built on rankings, such as precision or NDCG. However, the non-differentiability of the ranking operation prevents direct optimization of such metrics in…
We present randomized algorithms for estimating the trace and deter- minant of Hermitian positive semi-definite matrices. The algorithms are based on subspace iteration, and access the matrix only through matrix vector products. We analyse…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…