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We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can…
Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for…
The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically is computed by first discretizing the problem and then…
In this paper we consider the problem of decentralized (distributed) adaptive learning, where the aim of the network is to train the coefficients of a widely linear autoregressive moving average (ARMA) model by measurements collected by the…
Integrating multimodal knowledge for abstractive summarization task is a work-in-progress research area, with present techniques inheriting fusion-then-generation paradigm. Due to semantic gaps between computer vision and natural language…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Multivariate imputation by chained equations (MICE) is one of the most popular approaches to address missing values in a data set. This approach requires specifying a univariate imputation model for every variable under imputation. The…
Most data analytics systems that require low-latency execution and efficient utilization of computing resources, increasingly adopt two computational paradigms, namely, incremental and approximate computing. Incremental computation updates…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform…
A new recalibration post-processing method is presented to improve the quality of the posterior approximation when using Approximate Bayesian Computation (ABC) algorithms. Recalibration may be used in conjunction with existing…
The combinatorial integral approximation (CIA) is a solution technique for integer optimal control problems. In order to regularize the solutions produced by CIA, one can minimize switching costs in one of its algorithmic steps. This leads…
By leveraging contrastive learning, clustering, and other pretext tasks, unsupervised methods for learning image representations have reached impressive results on standard benchmarks. The result has been a crowded field - many methods with…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
Independent component analysis (ICA) is a widely used method in various applications of signal processing and feature extraction. It extends principal component analysis (PCA) and can extract important and complicated components with small…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Work in Counterfactual Explanations tends to focus on the principle of "the closest possible world" that identifies small changes leading to the desired outcome. In this paper we argue that while this approach might initially seem…