Related papers: Learning Decision-Sufficient Representations for L…
Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming…
We consider the problem of optimally compressing and caching data across a communication network. Given the data generated at edge nodes and a routing path, our goal is to determine the optimal data compression ratios and caching decisions…
We consider constrained sampling problems in paid research studies or clinical trials. When qualified volunteers are more than the budget allowed, we recommend a D-optimal sampling strategy based on the optimal design theory and develop a…
Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
Model compression and model defense for deep neural networks (DNNs) have been extensively and individually studied. Considering the co-importance of model compactness and robustness in practical applications, several prior works have…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
Best subset selection in linear regression is well known to be nonconvex and computationally challenging to solve, as the number of possible subsets grows rapidly with increasing dimensionality of the problem. As a result, finding the…
We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by D the largest absolute value of the subdeterminants of the constraint matrix. In this paper we…
Deep neural networks (DNNs) achieve remarkable predictive performance but remain difficult to interpret, largely due to overparameterization that obscures the minimal structure required for interpretation. Here we introduce DeepIn, a…
There has been a lot of interest recently in proving lower bounds on the size of linear programs needed to represent a given polytope P. In a breakthrough paper Fiorini et al. [Proceedings of 44th ACM Symposium on Theory of Computing 2012,…
Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…
We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
Recently, many neural network-based image compression methods have shown promising results superior to the existing tool-based conventional codecs. However, most of them are often trained as separate models for different target bit rates,…
Determinantal Point Processes (DPPs) provide an elegant and versatile way to sample sets of items that balance the point-wise quality with the set-wise diversity of selected items. For this reason, they have gained prominence in many…
Large-scale 3D point clouds (LS3DPC) obtained by LiDAR scanners require huge storage space and transmission bandwidth due to a large amount of data. The existing methods of LS3DPC compression separately perform rule-based point sampling and…
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…
Consider recovering a rank-one tensor of size $n_1 \times \cdots \times n_d$ from exact or noisy observations of a few of its entries. We tackle this problem via semidefinite programming (SDP). We derive deterministic combinatorial…