相关论文: Generation of Nested Quadrature Rules for Generic …

The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). However when the spatial dimensions are high, the number of…

In this paper we study the well-known greedy coordinate descent (GCD) algorithm to solve $\ell_1$-regularized problems and improve GCD by the two popular strategies: Nesterov's acceleration and stochastic optimization. Firstly, we propose a…

Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…

Deep neural networks (DNNs) have been proven to be effective in solving many real-life problems, but its high computation cost prohibits those models from being deployed to edge devices. Pruning, as a method to introduce zeros to model…

This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the…

A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…

We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…

Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…

For the purpose of uncertainty quantification with collocation, a method is proposed for generating families of one-dimensional nested quadrature rules with positive weights and symmetric nodes. This is achieved through a reduction…

This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized polynomial chaos (gPC) expansions for applications to uncertainty quantification (UQ) in aerodynamic computations. A core…

In this paper, we study the optimal general convergence rates for quadratures derived from Chebyshev points. By building on the aliasing errors on integration of Chebyshev polynomials, together with the asymptotic formulae on the…

Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…

We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares…

We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…

In this paper, we develop a new algorithm, Annealed Skewed SGD - AskewSGD - for training deep neural networks (DNNs) with quantized weights. First, we formulate the training of quantized neural networks (QNNs) as a smoothed sequence of…

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

The family of $(k, \ell)$-sparse graphs, introduced by Lorea, plays a central role in combinatorial optimization and has a wide range of applications, particularly in rigidity theory. A key algorithmic challenge is to compute a…

Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal…