Related papers: Arb: Efficient Arbitrary-Precision Midpoint-Radius…
There are several efficient methods to solve linear interval polynomial systems in the context of interval computations, however, the general case of interval polynomial systems is not yet covered as well. In this paper we introduce a new…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
This paper introduces the Adaptive Base Representation (ABR) Theorem and proposes a novel number system that offers a structured alternative to the binary number system for digital computers. The ABR number system enables each decimal…
Automatic amortized resource analysis (AARA) is a type-based technique for inferring concrete (non-asymptotic) bounds on a program's resource usage. Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs.…
We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, the…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
A regularized artificial neural network (RANN) is proposed for interval-valued data prediction. The ANN model is selected due to its powerful capability in fitting linear and nonlinear functions. To meet mathematical coherence requirement…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Adaptive randomized pivoting (ARP) is a recently proposed and highly effective algorithm for column subset selection. This paper reinterprets the ARP algorithm by drawing connections to the volume sampling distribution and active learning…
We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B \subseteq Rn is a product of closed real intervals and f : B \rightarrow Rn is a real-valued continuous function given in the form of arithmetical…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…
Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming…
Implicit Neural Representation (INR) has gained increasing popularity as a data representation method, serving as a prerequisite for innovative generation models. Unlike gradient-based methods, which exhibit lower efficiency in inference,…
Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly…
We introduce a framework for efficient Markov Chain Monte Carlo (MCMC) algorithms targeting discrete-valued high-dimensional distributions, such as posterior distributions in Bayesian variable selection (BVS) problems. We show that many…
Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to…
Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem,…
Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally…