Related papers: Approximate Model Counting, Sparse XOR Constraints…
Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…
The main focus of this paper is a pair of new approximation algorithms for certain integer programs. First, for covering integer programs {min cx: Ax >= b, 0 <= x <= d} where A has at most k nonzeroes per row, we give a k-approximation…
Machine learning has played an important role in information retrieval (IR) in recent times. In search engines, for example, query keywords are accepted and documents are returned in order of relevance to the given query; this can be cast…
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…
Model counting is a fundamental problem in automated reasoning with applications in probabilistic inference, network reliability, neural network verification, and more. Although model counting is computationally intractable from a…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…
Multiple systems estimation strategies have recently been applied to quantify hard-to-reach populations, particularly when estimating the number of victims of human trafficking and modern slavery. In such contexts, it is not uncommon to see…
We present a general framework for good CNF-representations of boolean constraints, to be used for translating decision problems into SAT problems (i.e., deciding satisfiability for conjunctive normal forms). We apply it to the…
In this paper we introduce a new approach for approximately counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula $\Phi$ when the…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the $0/1$ loss function which results in…
Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
Answer Set Programming (ASP) has emerged as a promising paradigm in knowledge representation and automated reasoning owing to its ability to model hard combinatorial problems from diverse domains in a natural way. Building on advances in…
We consider the problem of \textit{online sparse linear approximation}, where one predicts the best sparse approximation of a sequence of measurements in terms of linear combination of columns of a given measurement matrix. Such online…
Neural network models are widely used in solving many challenging problems, such as computer vision, personalized recommendation, and natural language processing. Those models are very computationally intensive and reach the hardware limit…
In this paper, we propose a novel sparse coding and counting method under Bayesian framwork for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear…