Related papers: Scientific Applications Leveraging Randomized Line…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
Real-world problems of operations research are typically high-dimensional and combinatorial. Linear programs are generally used to formulate and efficiently solve these large decision problems. However, in multi-period decision problems, we…
Various fields of science and engineering rely on linear algebra for large scale data analysis, modeling and simulation, machine learning, and other applied problems. Linear algebra computations often dominate the execution time of such…
It is common practice in reinforcement learning (RL) research to train and deploy agents in bespoke simulators, typically implemented by engineers directly in general-purpose programming languages or hardware acceleration frameworks such as…
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms,…
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in…
There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing…
Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…
Machine learning (ML) provides a broad spectrum of tools and architectures that enable the transformation of data from simulations and experiments into useful and explainable science, thereby augmenting domain knowledge. Furthermore,…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
We propose efficient parallel algorithms and implementations on shared memory architectures of LU factorization over a finite field. Compared to the corresponding numerical routines, we have identified three main difficulties specific to…
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
In multi-core systems, various factors like inter-process communication, dependency, resource sharing and scheduling, level of parallelism, synchronization, number of available cores etc. influence the extent of possible High Performance…
Reinforcement Learning (RL), bolstered by the expressive capabilities of Deep Neural Networks (DNNs) for function approximation, has demonstrated considerable success in numerous applications. However, its practicality in addressing various…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains…
Many modern multiclass and multilabel problems are characterized by increasingly large output spaces. For these problems, label embeddings have been shown to be a useful primitive that can improve computational and statistical efficiency.…