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A new modeling approach for large-eddy simulation (LES) is obtained by combining a `regularization principle' with an explicit filter and its inversion. This regularization approach allows a systematic derivation of the implied…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Accumulated Local Effects (ALE) is a model-agnostic approach for global explanations of the results of black-box machine learning (ML) algorithms. There are at least three challenges with conducting statistical inference based on ALE:…

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…

In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…

We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

While much work has been devoted to understanding the implicit (and explicit) regularization of deep nonlinear networks in the supervised setting, this paper focuses on unsupervised learning, i.e., autoencoders are trained with the…

Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…

Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…

Simultaneously addressing multiple objectives is becoming increasingly important in modern machine learning. At the same time, data is often high-dimensional and costly to label. For a single objective such as prediction risk, conventional…

Regularization of neural machine translation is still a significant problem, especially in low-resource settings. To mollify this problem, we propose regressing word embeddings (ReWE) as a new regularization technique in a system that is…

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…

Conventional reinforcement learning (RL) algorithms exhibit broad generality in their theoretical formulation and high performance on several challenging domains when combined with powerful function approximation. However, developing RL…

Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems. In high-dimensional settings, however, ELA suffers from sparsity effects, high estimator variance, and the prohibitive cost…

In the field of machine learning there is a growing interest towards more robust and generalizable algorithms. This is for example important to bridge the gap between the environment in which the training data was collected and the…

Accumulated Local Effects (ALE) is a widely-used explainability method for isolating the average effect of a feature on the output, because it handles cases with correlated features well. However, it has two limitations. First, it does not…