Related papers: New bounds and efficient algorithm for sparse diff…
No polynomial-time algorithm is known to test whether a sparse polynomial G divides another sparse polynomial $F$. While computing the quotient Q=F quo G can be done in polynomial time with respect to the sparsities of F, G and Q, this is…
We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…
We propose a novel numerical approach to compute the Pareto front in multivariate polynomial multi-objective optimization problems. When the objective functions and (equality) constraints are multivariate polynomials, the Pareto front,…
The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…
This paper investigates the idea of designing data-driven partial estimators for nonlinear systems showing parametric uncertainties using sparse multivariate polynomial relationships. A general framework is first presented and then…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We give two new expressions of subresultants, nested subresultant and reduced nested subresultant, for the recursive polynomial remainder sequence (PRS) which has been introduced by the author. The reduced nested subresultant reduces the…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse…
Many high dimensional classification techniques have been proposed in the literature based on sparse linear discriminant analysis (LDA). To efficiently use them, sparsity of linear classifiers is a prerequisite. However, this might not be…
In this work we introduce the concept of $s$-sparse observability for large systems of ordinary differential equations. Let $\dot x=f(t,x)$ be such a system. At time $T>0$, suppose we make a set of observations $b=Ax(T)$ of the solution of…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
Process Outcome Prediction entails predicting a discrete property of an unfinished process instance from its partial trace. High-capacity outcome predictors discovered with ensemble and deep learning methods have been shown to achieve top…
A fully algebraic approach to reconstructing one-dimensional reflectionless potentials is described. A simple and easily applicable general formula is derived, using the methods of the theory of determinants. In particular, useful…
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we…
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…