Related papers: Tensor Decomposition with Unaligned Observations
The CANDECOMP/PARAFAC (or Canonical polyadic, CP) decomposition of tensors has numerous applications in various fields, such as chemometrics, signal processing, machine learning, etc. Tensor CP decomposition assumes the knowledge of the…
We analyze a new algorithm for probability forecasting of binary observations on the basis of the available data, without making any assumptions about the way the observations are generated. The algorithm is shown to be well calibrated and…
This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density…
Task-evoked functional magnetic resonance imaging studies, such as the Human Connectome Project (HCP), are a powerful tool for exploring how brain activity is influenced by cognitive tasks like memory retention, decision-making, and…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
We propose algorithms to take point sets for kernel-based interpolation of functions in reproducing kernel Hilbert spaces (RKHSs) by convex optimization. We consider the case of kernels with the Mercer expansion and propose an algorithm by…
It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical…
Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: we prove that given a tensor whose decomposition satisfies a robust form of Kruskal's rank condition, it is possible to approximately…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
We study symmetric tensor decompositions, i.e. decompositions of the input symmetric tensor T of order 3 as sum of r 3rd-order tensor powers of u_i where u_i are vectors in \C^n. In order to obtain efficient decomposition algorithms, it is…
In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…
We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…
Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. In this paper we address the application of CS to the scenario of progressive acquisition of 2D visual…
The canonical polyadic decomposition (CPD) is a compact decomposition which expresses a tensor as a sum of its rank-1 components. A common step in the computation of a CPD is computing a generalized eigenvalue decomposition (GEVD) of the…
Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…