Related papers: Towards More Efficient SPSD Matrix Approximation a…
The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected…
We propose semidefinite trajectory optimization (STROM), a framework that computes fast and certifiably optimal solutions for nonconvex trajectory optimization problems defined by polynomial objectives and constraints. STROM employs sparse…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…
While semidefinite programming (SDP) has traditionally been limited to moderate-sized problems, recent algorithms augmented with matrix sketching techniques have enabled solving larger SDPs. However, these methods achieve scalability at the…
In this paper, we demonstrate the design of efficient and high-performance AI/Deep Learning accelerators with customized STT-MRAM and a reconfigurable core. Based on model-driven detailed design space exploration, we present the design…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
Motivated by the needs of estimating the proximity clustering with partial distance measurements from vantage points or landmarks for remote networked systems, we show that the proximity clustering problem can be effectively formulated as…
As a successful deep model applied in image super-resolution (SR), the Super-Resolution Convolutional Neural Network (SRCNN) has demonstrated superior performance to the previous hand-crafted models either in speed and restoration quality.…
Adaptive gradient methods are computationally efficient and converge quickly, but they often suffer from poor generalization. In contrast, second-order methods enhance convergence and generalization but typically incur high computational…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu \in \mathbb{R}^P$. The design of reliable and efficient algorithms for addressing this task…
The accuracy and complexity of machine learning algorithms based on kernel optimization are determined by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
The application of kernel-based Machine Learning (ML) techniques to discrete choice modelling using large datasets often faces challenges due to memory requirements and the considerable number of parameters involved in these models. This…
Recently, diffusion models have achieved significant advances in vision, text, and robotics. However, they still face slow generation speeds due to sequential denoising processes. To address this, a parallel sampling method based on Picard…
Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…