Related papers: About the Kannan-Bachem algorithm
The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman…
The number of parameters in deep neural networks (DNNs) is rapidly increasing to support complicated tasks and to improve model accuracy. Correspondingly, the amount of computations and required memory footprint increase as well.…
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via…
Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
Bayesian Knowledge Tracing (BKT) is a probabilistic model of a learner's state of mastery corresponding to a knowledge component. It considers the learner's state of mastery as a "hidden" or latent binary variable and updates this state…
Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common…
Relief algorithm is a feature selection algorithm used in binary classification proposed by Kira and Rendell, and its computational complexity remarkable increases with both the scale of samples and the number of features. In order to…
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approximation of a solution. In particular, when all solutions have…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
Let $M_q(n)$ be the standard quantized matrix algebra, introduced by Faddeev, Reshetikhin, and Takhtajan. It is shown, by constructing an appropriate monomial ordering $\prec$ on its PBW $K$-basis ${\cal B}$ , that $M_q(n)$ is a solvable…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
We define a variant of k-of-n testing that we call conservative k-of-n testing. We present a polynomial-time, combinatorial algorithm for the problem of maximizing throughput of conservative k-of-n testing, in a parallel setting. This…
We describe a novel way of representing a symbolic knowledge base (KB) called a sparse-matrix reified KB. This representation enables neural modules that are fully differentiable, faithful to the original semantics of the KB, expressive…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
The problem of finding the distance from a given $n \times n$ matrix polynomial of degree $k$ to the set of matrix polynomials having the elementary divisor $(\lambda-\lambda_0)^j, \, j \geqslant r,$ for a fixed scalar $\lambda_0$ and $2…
Over the years, computational imaging with accurate nonlinear physical models has garnered considerable interest due to its ability to achieve high-quality reconstructions. However, using such nonlinear models for reconstruction is…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…