Related papers: Experimental observation on a low-rank tensor mode…
This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success…
This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with $n$ agents (users) $\{x_i\}_{i \in [n]}$ and $m$…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN)…
We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form $T(\lambda)v=0$ that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are…
The problem of recovering a low $n$-rank tensor is an extension of sparse recovery problem from the low dimensional space (matrix space) to the high dimensional space (tensor space) and has many applications in computer vision and graphics…
We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank…
Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…
We explore the usage of the Levenberg-Marquardt (LM) algorithm for regression (non-linear least squares) and classification (generalized Gauss-Newton methods) tasks in neural networks. We compare the performance of the LM method with other…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
The use of fractional differential equations is a key tool in modeling non-local phenomena. Often, an efficient scheme for solving a linear system involving the discretization of a fractional operator is evaluating the matrix function $x =…
Regularized nonnegative low-rank approximations, such as sparse Nonnegative Matrix Factorization or sparse Nonnegative Tucker Decomposition, form an important branch of dimensionality reduction models known for their enhanced…
Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…
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…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
Pre-trained language models (PLM) are effective components of few-shot named entity recognition (NER) approaches when augmented with continued pre-training on task-specific out-of-domain data or fine-tuning on in-domain data. However, their…
Matrix rank minimization problem is in general NP-hard. The nuclear norm is used to substitute the rank function in many recent studies. Nevertheless, the nuclear norm approximation adds all singular values together and the approximation…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…