Related papers: A low-rank complexity reduction algorithm for the …
In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial…
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is state space explosion problem. To address this issue,…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…
This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…
Low-rank representation~(LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Molecular circuits capable of autonomous learning could unlock novel applications in fields such as bioengineering and synthetic biology. To this end, existing chemical implementations of neural computing have mainly relied on emulating…
In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
Multienzyme cascaded reactions are widely utilized because they can generate value-added biomaterials and biodevices from simple raw materials. However, how to promote the catalytic efficiency and synergistic effect of the multienzyme…
Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying…
Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of the underlying physical problem. For…
In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
In deep learning inference, model parameters are pruned and quantized to reduce the model size. Compression methods and common subexpression (CSE) elimination algorithms are applied on sparse constant matrices to deploy the models on…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…