Related papers: An Efficient Memory Gradient Method for Extreme M-…

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…

Training RNNs to learn long-term dependencies is difficult due to vanishing gradients. We explore an alternative solution based on explicit memorization using linear autoencoders for sequences, which allows to maximize the short-term memory…

Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Virtual element methods is a new promising finite element methods using general polygonal meshes. Its optimal a priori error estimates are well established in the literature. In this paper, we take a different viewpoint. We try to uncover…

We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly…

The tracking method based on the extreme learning machine (ELM) is efficient and effective. ELM randomly generates input weights and biases in the hidden layer, and then calculates and computes the output weights by reducing the iterative…

Extreme Multi-label classification (XML) is an important yet challenging machine learning task, that assigns to each instance its most relevant candidate labels from an extremely large label collection, where the numbers of labels, features…

In this work, we study the numerical solution of inverse eigenvalue problems from a machine learning perspective. Two different problems are considered: the inverse Strum-Liouville eigenvalue problem for symmetric potentials and the inverse…

Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…

We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…

The choice of how to retain information about past gradients dramatically affects the convergence properties of state-of-the-art stochastic optimization methods, such as Heavy-ball, Nesterov's momentum, RMSprop and Adam. Building on this…

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…

We investigate an inertial viscosity-type Tseng's extragradient algorithm with a new step size to solve pseudomonotone variational inequality problems in real Hilbert spaces. A strong convergence theorem of the algorithm is obtained without…

Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by…

Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…

The classification of all fourth-order anisotropic tensor classes for classical linear elasticity is well known. In this article, we review the related problem of explicitly computing the dimension and the expressions of the elements…