Related papers: Randomized matrix computations: Themes and variati…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
Randomization has emerged as a powerful set of tools for large-scale matrix and tensor decompositions. Randomized algorithms involve computing sketches with random matrices. A prevalent approach is to take the random matrix as a standard…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category…
This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…
This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…
I describe my path to unconventionality in my exploration of theoretical and applied aspects of computation towards revealing the algorithmic and reprogrammable properties and capabilities of the world, in particular related to applications…
In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
The paper considers implementations of some randomized algorithms in connection with obtaining a random $n^2 \times n^2$ Sudoku matrix with programming language C++. For this purpose we describes the set $\Pi_n$ of all $(2n) \times n$…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
We provide a general framework to improve trade-offs between the number of full batch and sample queries used to solve structured optimization problems. Our results apply to a broad class of randomized optimization algorithms that…