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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Barron Type Spaces in Neural Network Approximation
神经网络 巴伦类型空间 经典函数空间
2023/4/13
We shall discuss various Barron type spaces arising from neural networks. The relations among these spaces will be clarified, and we shall also establish the relationship between Barron type spaces an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep neural network approximation to inverse conductivity problems for elliptic equations
椭圆方程 反电导率 深度神经网络
2023/4/14
The focus of this talk is on the numerical methods used to identify parameters in partial differential equations. Typically, an optimization approach is used to solve this class of inverse problems, w...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Graph Refinement via Simultaneously Low-rank and Sparse Approximation
低秩 稀疏近似 图细化
2023/4/18
Graphs play an important role in many fields of machine learning such as clustering. Many graph-based machine learning approaches assume that the graphs have hidden group structures. However, the grou...
Stochastic Combinatorial Optimization via Poisson Approximation
Stochastic Knapsack Stochastic Bin Packing Expected Util- ity Maximization
2016/1/23
We study several stochastic combinatorial problems, includ-ing the expected utility maximization problem, the stochas-tic knapsack problem and the stochastic bin packing prob-lem. A common technical c...
A Fully Polynomial Approximation Scheme for Approximating a Sum of Random Variables
Threshold probability Tail probability Approximate counting Counting knapsack FPTAS
2016/1/22
Given n independent integer-valued random variables X 1 , X 2 ,..., X n and an integer C, we study the fundamental problem of computing the probability that the sum X = X 1 + X 2 +···+ X n is at most ...
Linear Time Approximation Schemes for Geometric Maximum Coverage
Maximum coverage Geometric set cover Polynomial-time approximation scheme
2016/1/22
We study approximation algorithms for the following geo-metric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a × b rectangles such that ...
Saddlepoint Approximation for Moments of Random Variables
Saddlepoint Approximation Higher moments Sums of i.i.d.ran- dom variables
2016/1/19
In this paper we introduce a saddlepoint approximation method for higher-order moments like E(S − a) m+ ,a > 0, where the random variable S in these expectations could be a single random variabl...
Approximation of bivariate copulas by patched bivariate Fréchet copulas
Bivariate Fréchet copulas patched bivariate Fréchet copula approximation of bivariate copulas
2016/1/19
Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, in-dependence and countermonotonicity. They are easily interpretable but have limitation...
A rank minimization heuristic with application to minimum order system approximation
Variable control system analysis and controller synthesis matrix rank linear matrix inequality (lmi) the positive semi-definite matrix variables
2015/8/11
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
Data Cube Approximation and Mining using Probabilistic Modeling
data cubes OLAP data warehouses multidimensional data non-negative multi-way array factorization log-linear modeling
2015/7/29
On-line Analytical Processing (OLAP) techniques commonly used in data warehouses allow the exploration of data cubes according to different analysis axes (dimensions) and under different abstraction l...
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
Rank Minimization Heuristic Minimum Order System Approximation
2015/7/10
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
An Ellipsoidal Approximation to the Hadamard Product of Ellipsoids
Ellipsoidal Approximation Hadamard Product Ellipsoids
2015/7/10
This paper introduces a computationally efficient outer approximation to the Hadamard, i.e., element-wise, product of two ellipsoids. This element-wise product corresponds to multiplicative uncertaint...
A Diffusion Approximation for a Network of Reservoirs with Power Law Release Rule
Diffusion network reservoir power law
2015/7/8
A diffusion approximation for a network of continuous time reservoirs with power law release rules is examined. Under a mild assumption on the inflow processes, we show that for physically reasonable ...
Confidence Regions for Stochastic Approximation Algorithms
Confidence Regions Stochastic Approximation Algorithms
2015/7/8
In principle, known central limit theorems for stochastic approximation schemes permit the simulationist to provide confidence regions for both the optimum and optimizer of a stochastic optimization p...
A Diffusion Approximation for a Markovian Queue with Reneging
Markovian queues reneging impatience deadlines refl ected Ornstein–Uhlenbeck process
2015/7/8
Consider a single-server queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establ...