arXiv research

Paper develops fast low-rank approximation for smoothing splines.

Develops PRPCA for smooth image recovery combining low-rank and smoothness.

Bayesian framework for sequential learning tasks with low-rank approximations.

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminisce…

A new federated learning algorithm improves on existing methods by exploiting data smoothness.

Optimal smooth subspaces approximate large data sets efficiently.

In designing personalized ranking algorithms, it is desirable to encourage a high precision at the top of the ranked list. Existing methods either seek a smooth convex surrogate for a non-smooth ranking metric or directly modify updating procedures to encourage top accuracy. In this work we point out that these methods…

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world …

Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the pe…

A new method for quantized matrix completion using Huber loss.

Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to matrices with linear structures which appear in applications such as system identificat…

Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. …

Top-N-Rank improves top N item recommendations in scalable recommender systems.

Matrix completion works well for smooth non-linear structures, even without low-rank assumptions.

Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximatio…

New method extends low-rank MDPs to continuous action spaces.

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between $X$ and $W^T H$ to model the Poisson noise or the Gaussian noise.…

The study optimizes Gaussian process approximations for finite-rank models.

Tree tensor networks balance model complexity and empirical risk for high-dimensional function approximation.

A new method reduces high-dimensional filtering to quadratic complexity.

New method improves Kalman filtering and smoothing for large state spaces.

New concept of attitude towards probability introduced in risk sharing problems.

It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is random…

Proposes a new method for multivariate functional regression.

Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In practical settings, the task often reduces to estimating a rank functional of an object …

We consider semidefinite programs (SDPs) of size n with equality constraints. In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size $n$ by $k$ such that $X = YY^*$ is the SDP variable. The advantages of such formulation are twofold: the di…

Recent developments in linear system identification have proposed the use of non-parameteric methods, relying on regularization strategies, to handle the so-called bias/variance trade-off. This paper introduces an impulse response estimator which relies on an $\ell_2$-type regularization including a rank-penalty derive…

Derives smooth homogeneous structures for low-rank tensors.

Efficiently reduces tensor ranks using mean-field approximation.

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to recover such model structures from large covariance matrix estimation. We propos…

Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.

In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sampl…

This work learns low-rank hyperbolic embeddings for tasks with hierarchical structures.

In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within classical algorithms for low-rank approximation in order to exploit the possible sp…

UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.

Paper proposes a new technique to compress CNNs while maintaining accuracy.

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

Gradient descent solves asymmetric low-rank matrix factorization efficiently.

We develop an efficient algorithm for low-rank approximation with improved approximation guarantees.

New algorithms solve large-scale low-rank and nonsmooth optimization problems efficiently.

New methods recover best rank-r approximations from few entries.

Paper develops methods for non-quadratic loss low-rank matrix recovery.

We accelerate the power method for strong low-rank approximation using fast sketching.

New algorithm for weighted low rank approximation with provable guarantees.

The study assesses low-rank approximations in Gaussian Process regression.

The study assesses low-rank approximations in Gaussian Process regression.

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…

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…