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Many existing federated learning (FL) algorithms are designed for supervised learning tasks, assuming that the local data owned by the clients are well labeled. However, in many practical situations, it could be difficult and expensive to…
This paper studies a generalization of hyperinterpolation over the high-dimensional unit cube. Hyperinterpolation of degree \( m \) serves as a discrete approximation of the \( L_2 \)-orthogonal projection of the same degree, using Fourier…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Process calculi based on logic, such as $\pi$DILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of…
In this paper, we introduce a new problem called the split feasibility and fixed point equality problems (SFFPEP) and propose a new iterative algorithm for solving the problem (SFFPEP) for the class of quasi-nonexpansive mappings in Hilbert…
Iterative Refinement (IR) is a classical computing technique for obtaining highly precise solutions to linear systems of equations, as well as linear optimization problems. In this paper, motivated by the limited precision of quantum…
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…
We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
Resolution and subtyping are two common mechanisms in programming languages. Resolution is used by features such as type classes or Scala-style implicits to synthesize values automatically from contextual type information. Subtyping is…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
In this paper, we consider the harmonic extension problem, which is widely used in many applications of machine learning. We find that the transitional method of graph Laplacian fails to produce a good approximation of the classical…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Clustering multivariate time series data is a crucial task in many domains, as it enables the identification of meaningful patterns and groups in time-evolving data. Traditional approaches, such as crisp clustering, rely on the assumption…
Fuzzy Cognitive Maps (FCMs) are considered a soft computing technique combining elements of fuzzy logic and recurrent neural networks. They found multiple application in such domains as modeling of system behavior, prediction of time…
Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the…
This paper proposes a novel algorithm for semisupervised learning. This algorithm learns graph cuts that maximize the margin with respect to the labels induced by the harmonic function solution. We motivate the approach, compare it to…