Related papers: Decoupling multivariate functions using second-ord…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Encoding and decoding models are widely used in systems, cognitive, and computational neuroscience to make sense of brain-activity data. However, the interpretation of their results requires care. Decoding models can help reveal whether…

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Low-rank tensor estimation offers a powerful approach to addressing high-dimensional data challenges and can substantially improve solutions to ill-posed inverse problems, such as image reconstruction under noisy or undersampled conditions.…

Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While…

Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…

Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…

In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analysis are not lost. The traditional workhorse for data…

We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range…

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

Tensor Network (TN) decompositions have emerged as an indispensable tool in Big Data analytics owing to their ability to provide compact low-rank representations, thus alleviating the ``Curse of Dimensionality'' inherent in handling…

In this technical report, we analyze Legendre decomposition for non-negative tensor in theory and application. In theory, the properties of dual parameters and dually flat manifold in Legendre decomposition are reviewed, and the process of…

We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…

One of the biggest challenges for deep learning algorithms in medical image analysis is the indiscriminate mixing of image properties, e.g. artifacts and anatomy. These entangled image properties lead to a semantically redundant feature…

Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

Investigating relationships between variables in multi-dimensional data sets is a common task for data analysts and engineers. More specifically, it is often valuable to understand which ranges of which input variables lead to particular…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…