Related papers: Exploiting Hidden Structure in Selecting Dimension…
We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, second order cone, and semidefinite programming. This allows…
Motivated by complexity questions in integer programming, this paper aims to contribute to the understanding of combinatorial properties of integer matrices of row rank $r$ and with bounded subdeterminants. In particular, we study the…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…
In connection with machine arithmetic, we are interested in systems of constraints of the form x + k \leq y + k'. Over integers, the satisfiability problem for such systems is polynomial time. The problem becomes NP complete if we restrict…
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are…
Let $\K$ be a field of characteristic zero and $\Kbar$ be an algebraic closure of $\K$. Consider a sequence of polynomials$G=(g\_1,\dots,g\_s)$ in $\K[X\_1,\dots,X\_n]$, a polynomial matrix $\F=[f\_{i,j}] \in \K[X\_1,\dots,X\_n]^{p \times…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
Sequence classification has numerous applications in various fields. Despite extensive studies in the last decades, many challenges still exist, particularly in pattern-based methods. Existing pattern-based methods measure the…
Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the…
We study the complexity of the Hitting Set problem in set systems (hypergraphs) that avoid certain sub-structures. In particular, we characterize the classical and parameterized complexity of the problem when the Vapnik-Chervonenkis…
Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…
In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both…
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
Previous literature suggests that perceptual similarity is an emergent property shared across deep visual representations. Experiments conducted on a dataset of human-judged image distortions have proven that deep features outperform…
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection,…