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Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
We study clustering algorithms based on neighborhood graphs on a random sample of data points. The question we ask is how such a graph should be constructed in order to obtain optimal clustering results. Which type of neighborhood graph…
Training quantum neural networks (QNNs) using gradient-based or gradient-free classical optimisation approaches is severely impacted by the presence of barren plateaus in the cost landscapes. In this paper, we devise a framework for…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Part-based representations have been shown to be very useful for image classification. Learning part-based models is often viewed as a two-stage problem. First, a collection of informative parts is discovered, using heuristics that promote…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
Consider the following toy problem. There are $m$ rectangles and $n$ points on the plane. Each rectangle $R$ is a consumer with budget $B_R$, who is interested in purchasing the cheapest item (point) inside R, given that she has enough…
The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
Informative path planning algorithms are of paramount importance in applications like disaster management to efficiently gather information through a priori unknown environments. This is, however, a complex problem that involves finding a…
Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization…
The gradient mapping norm is a strong and easily verifiable stopping criterion for first-order methods on composite problems. When the objective exhibits the quadratic growth property, the gradient mapping norm minimization problem can be…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…