Related papers: A Bilevel Optimization Method for Tensor Recovery …

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric.…

Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and…

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

We give an algorithm for completing an order-$m$ symmetric low-rank tensor from its multilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning…

Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…

We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing…

Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired…

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low…

We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…

Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the…

We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring…

In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…

How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental…