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The task of hyper-parameter optimization (HPO) is burdened with heavy computational costs due to the intractability of optimizing both a model's weights and its hyper-parameters simultaneously. In this work, we introduce a new class of HPO…
The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with…
Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new…
Particle MCMC is a class of algorithms that can be used to analyse state-space models. They use MCMC moves to update the parameters of the models, and particle filters to propose values for the path of the state-space model. Currently the…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
Reconstruction of structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine…
The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…
In this paper we shall consider optimal scaling problems for high-dimensional Metropolis--Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the…
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively…
We present a novel, real-time algorithm to track the trajectory of each pedestrian in moderately dense crowded scenes. Our formulation is based on an adaptive particle-filtering scheme that uses a combination of various multi-agent…
Machine learning models are often tuned by nesting optimization of model weights inside the optimization of hyperparameters. We give a method to collapse this nested optimization into joint stochastic optimization of weights and…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
Weight optimization of frame structures with continuous cross-section parametrization is a challenging non-convex problem that has traditionally been solved by local optimization techniques. Here, we exploit its inherent semi-algebraic…
The performance of land surface models (LSMs) significantly affects the understanding of atmospheric and related processes. Many of the LSMs' soil and vegetation parameters were unknown so that it is crucially important to efficiently…
Natural image matting, which separates foreground from background, is a very important intermediate step in recent computer vision algorithms. However, it is severely underconstrained and difficult to solve. State-of-the-art approaches…
The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the…