Related papers: Combinatorial Characterizations of Algebraic Manip…
We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional. The…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we…
This chapter introduces and elaborates on the fruitful interplay of coding theory and algebraic combinatorics, with most of the focus on the interaction of codes with combinatorial designs, finite geometries, simple groups, sphere packings,…
In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas-Rachford splitting, or equivalently ADMM. When an optimization program is infeasible, unbounded, or pathological, the…
Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…
This manuscript describes the notions of blocker and interdiction applied to well-known optimization problems. The main interest of these two concepts is the capability to analyze the existence of a combinatorial structure after some…
In this paper, we construct new families of convolutional codes. Such codes are obtained by means of algebraic geometry codes. Additionally, more families of convolutional codes are constructed by means of puncturing, extending, expanding…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate…
Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…
Classifiers such as deep neural networks have been shown to be vulnerable against adversarial perturbations on problems with high-dimensional input space. While adversarial training improves the robustness of image classifiers against such…
Adaptive filters are at the core of many signal processing applications, ranging from acoustic noise supression to echo cancelation, array beamforming, channel equalization, to more recent sensor network applications in surveillance, target…
This paper studies the problem of detecting anomalous graphs using a machine learning model trained on only normal graphs, which has many applications in molecule, biology, and social network data analysis. We present a self-discriminative…
A linear code with parameters $[n,k,n-k]$ is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as an near maximum distance separable (NMDS for short) code. NMDS codes have…
This work contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two…
Traditional multi-armed bandit (MAB) formulations usually make certain assumptions about the underlying arms' distributions, such as bounds on the support or their tail behaviour. Moreover, such parametric information is usually 'baked'…
Machine learning models have demonstrated vulnerability to adversarial attacks, more specifically misclassification of adversarial examples. In this paper, we propose a one-off and attack-agnostic Feature Manipulation (FM)-Defense to detect…
We study the combinatorial pure exploration problem Best-Set in stochastic multi-armed bandits. In a Best-Set instance, we are given $n$ arms with unknown reward distributions, as well as a family $\mathcal{F}$ of feasible subsets over the…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…