arXiv research

New algorithm for low-rank optimal transport with improved interpretability and efficiency.

New algorithm tackles low-rank constraints in optimal transport problems.

Faster GW alignment for incomparable point clouds via low-rank couplings.

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, w…

Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.

There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender systems, under machine learning. From a statistical estimation point of view, the…

We introduce a new framework for optimal transport using Schatten-p regularization to recover low-rank structures.

Proposes a low-rank PGD attack for more efficient adversarial training.

Partial convexification improves tractability of low-rank spectral optimization problems.

Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intu…

Proposes BHT-ARIMA for forecasting multiple short time series.

A new method classifies color images using quaternion algebra.

LOT improves optimal transport for large datasets.

Paper proposes diagnostics for error and variance estimation in randomized matrix computations.

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single…

A new EnKF method for elliptic PDEs reduces dimensionality for accurate state estimation.

How can we correlate neural activity in the human brain as it responds to words, with behavioral data expressed as answers to questions about these same words? In short, we want to find latent variables, that explain both the brain activity, as well as the behavioral responses. We show that this is an instance of the C…

New algorithm catches moving subspaces in bandit problems.

A fast method learns plasma collision kernels from simulations, improving kinetic models.

We propose an extension of the canonical polyadic (CP) tensor model where one of the latent factors is allowed to vary through data slices in a constrained way. The components of the latent factors, which we want to retrieve from data, can vary from one slice to another up to a diffeomorphism. We suppose that the diffe…

Dual-Channel Tensor Neural Network (DC-TNN) decomposes tensor data into low-rank and sparse components for better estimation and inference.

Bayesian hierarchical tensor factorization model for international trade flows

Exploiting low-rank structure of the user-item rating matrix has been the crux of many recommendation engines. However, existing recommendation engines force raters with heterogeneous behavior profiles to map their intrinsic rating scales to a common rating scale (e.g. 1-5). This non-linear transformation of the rating…

This paper solves tensor robust principal component analysis via scaled gradient descent.

Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after normalisation, they follow the same target distribution for each sample. Choosing a "g…

Graph-coupled causal Bayesian optimization transfers information across related interventions.

The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors, which can be interpreted as multiple feature maps of size 1x1. Such representations…

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algori…

NA$_0$CT$^2$ improves tensor regression predictions with $\ell_0$ regularization.

This work shows how to use simulators to learn efficient exploration in real-world RL.

SGD with mini-batches can solve convex low-rank matrix problems efficiently.

New spectral methods improve matrix estimation in RL with low-rank structure.

Novel method for efficient low-rank matrix estimation and bandit algorithms.

In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to …

Paper improves MVSC using tensor low-rank modeling.

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy becau…

The paper proposes using low rank assumption to improve causal structure learning in DAGs.

Algorithm recovers multiple low-rank matrices from unlabeled data.

Paper tackles fair low-rank approximation and column subset selection.

Research reveals deep networks often learn low-rank structures, leading to more efficient training and fine-tuning.

New insights into training deep networks with low rank layers.

New algorithm improves deep learning models' robustness without sacrificing accuracy.

Extreme multi-label classification refers to supervised multi-label learning involving hundreds of thousands or even millions of labels. Datasets in extreme classification exhibit fit to power-law distribution, i.e. a large fraction of labels have very few positive instances in the data distribution. Most state-of-the-…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…

FedLoRU improves FL efficiency by using low-rank updates.

A low-rank tensor model simplifies multi-dimensional Markov chains.

New nonconvex regularizer speeds up low-rank matrix completion.

A new method for efficient neural network fine-tuning using queryable low-rank update atoms.