arXiv research

New method for matrix completion under complex missing data patterns.

New method estimates missingness probabilities for MNAR matrix completion.

Improved matrix completion for non-uniformly sampled data.

Paper improves compressed sensing with prior probability information.

To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are inconsistent. In particular, we would like to present that the constrained quadratic …

A new method for matrix completion with model-free weights.

Method determines credit transition matrix from cumulative default probabilities.

We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability measure. We interpret the probability measure as arising via the Born rule from a translation invariant matrix product state.

SC-InfoNCE improves InfoNCE for feature clustering in contrastive learning.

The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong a…

Analyze message passing algorithms using free probability theory.

Paper proposes a matrix optimization model for reliable Euclidean embedding from noisy data.

Active seriation recovers item order from noisy pairwise similarity measurements.

We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a $0-1$ Bernoulli random variable. We analyze an unbiased covariance estimator under this mod…

Develops a gradient flow for Muon optimizer, a method for optimization.

A new method for comparing image probability measures using convolution operators.

We address the rectangular matrix completion problem by lifting the unknown matrix to a positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over the semidefinite factor using a simple gradient descent scheme. With $O( μr^2 κ^2 n \max(μ, \log n))$ random observations of a $n_1 \times n…

New method improves sampling from high-dimensional target densities.

Paper proposes a new Markov model for efficient PLC system design.

Study on random matrices in deep neural networks with IID entries.

New method estimates large matrices' spectra from small sub-matrices.

A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank …

Two methods estimate rating transition probabilities, one Markov, one non-Markov, differing in default probabilities.

Study the distribution for low-rank matrix learning, improving inference methods.

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries an…

In this paper, we use a new approach to prove that the largest eigenvalue of the sample covariance matrix of a normally distributed vector is bigger than the true largest eigenvalue with probability 1 when the dimension is infinite. We prove a similar result for the smallest eigenvalue.

Improved statistical computation through efficient matrix sampling.

We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition proba…

New estimator for causal effects in large datasets.

Predicting unobserved entries of a partially observed matrix has found wide applicability in several areas, such as recommender systems, computational biology, and computer vision. Many scalable methods with rigorous theoretical guarantees have been developed for algorithms where the matrix is factored into low-rank co…

Spectral algorithm recovers clusters in hypergraph with high probability.

For any matrix A in R^(m x n) of rank ρ, we present a probability distribution over the entries of A (the element-wise leverage scores of equation (2)) that reveals the most influential entries in the matrix. From a theoretical perspective, we prove that sampling at most s = O ((m + n) ρ^2 ln (m + n)) entries of the ma…

Unified framework for gradient-free MDS improves efficiency and accuracy.

An important application of Lebesgue integral quadrature arXiv:1807.06007 is developed. Given two random processes, $f(x)$ and $g(x)$, two generalized eigenvalue problems can be formulated and solved. In addition to obtaining two Lebesgue quadratures (for $f$ and $g$) from two eigenproblems, the projections of $f$- and…

MPSTime uses matrix-product states for efficient time-series ML.

A method to learn transition matrices without anchor points improves classifier performance.

Let X be a data matrix of rank ρ, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We pr…

We propose a route for the evaluation of risk based on a transformation of the covariance matrix. The approach uses a `potential' or `objective' function. This allows us to rescale data from different assets (or sources) such that each data set then has similar statistical properties in terms of their probability distr…

We simplify word embeddings by removing sigmoid in SGNS, revealing connections to hyperbolic spaces.

New method improves robustness of deep learning with noisy labels.

We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective f…

VAE enhances NMF for probabilistic non-negative matrix factorisation.

Estimates covariance matrices with correlations between samples.

Improves sparse recovery with non-linear Fourier features.

Estimates the probability of a random symmetric tensor being close to rank-one.

Optimizes ellipsoids for uncertainty regions in parameter estimation.

This paper clarifies vine copula structures using graph and matrix representations.

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies heavily on the assumption that every entry is observed with exactly the same pro…