Related papers: Tent-transformed lattice rules for integration and…
In this notes we describe an algorithm for non-linear fitting which incorporates some of the features of linear least squares into a general minimum $\chi^2$ fit and provide a pure Python implementation of the algorithm. It consists of the…
We investigate convexification for convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step…
Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, can be exploited. A relevant tool for analysing sparse…
The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic…
This work proposes a low complexity nonlinearity model and develops adaptive algorithms over it. The model is based on the decomposable---or rank-one, in tensor language---Volterra kernels. It may also be described as a product of FIR…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest paths, minimum weight spanning trees,…
We develop a symmetry-aware toolkit for finite mixtures whose components are only identifiable up to a finite \emph{folding} group action. The correct estimand is the multiset of parameter orbits in the quotient space, not an ordered list…
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…
In this paper we investigate quasi-Monte Carlo (QMC) integration using digital nets over $\mathbb{Z}_b$ in reproducing kernel Hilbert spaces. The tent transformation, or the baker's transformation, was originally used for lattice rules by…
We propose a simple and effective method for designing approximation formulas for weighted analytic functions. We consider spaces of such functions according to weight functions expressing the decay properties of the functions. Then, we…
This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank…
Weight-space merging aims to combine multiple fine-tuned LLMs into a single model without retraining, yet most existing approaches remain fundamentally parameter-space heuristics. This creates three practical limitations. First, linear…
This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
We investigate the numerical approximation of integrals over $\mathbb{R}^d$ equipped with the standard Gaussian measure $\gamma$ for integrands belonging to the Gaussian-weighted Sobolev spaces $W^\alpha_p(\mathbb{R}^d, \gamma)$ of mixed…
We exploit knowledge of linear substructure in the linear-regression Kalman filters (LRKFs) to simplify the problem of moment matching. The theoretical results yield quantifiable and significant computational speedups at no cost of…
We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovi\v{c}s, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields arbitrary high order weak approximations to stochastic differential equations, extending the cubature…