Related papers: Model reduction by separation of variables: a comp…

This paper describes the many image decomposition models that allow to separate structures and textures or structures, textures, and noise. These models combined a total variation approach with different adapted functional spaces such as…

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…

Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many…

We classify two types of Hierarchical Bayesian Model found in the literature as Hierarchical Prior Model (HPM) and Hierarchical Stochastic Model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of…

Statistic modeling and data-driven learning are the two vital fields that attract many attentions. Statistic models intend to capture and interpret the relationships among variables, while data-based learning attempt to extract information…

A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical…

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…

This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization. We provide improved running time estimates for the state-of-the-art continuous algorithms for the problem…

Proxy-based metric learning losses are superior to pair-based losses due to their fast convergence and low training complexity. However, existing proxy-based losses focus on learning class-discriminative features while overlooking the…

Constructing disentangled representations is known to be a difficult task, especially in the unsupervised scenario. The dominating paradigm of unsupervised disentanglement is currently to train a generative model that separates different…

High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…

Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…

Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…

Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…

Previous face inverse rendering methods often require synthetic data with ground truth and/or professional equipment like a lighting stage. However, a model trained on synthetic data or using pre-defined lighting priors is typically unable…

Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural…

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…

In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related…