相关论文: Nearest Neighbors for Matrix Estimation Interprete…

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…

Large margin nearest neighbor (LMNN) is a metric learner which optimizes the performance of the popular $k$NN classifier. However, its resulting metric relies on pre-selected target neighbors. In this paper, we address the feasibility of…

We propose a method to facilitate exploration and analysis of new large data sets. In particular, we give an unsupervised deep learning approach to learning a latent representation that captures semantic similarity in the data set. The core…

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise"…

High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…

We study transfer learning for matrix completion in a Missing Not-at-Random (MNAR) setting that is motivated by biological problems. The target matrix $Q$ has entire rows and columns missing, making estimation impossible without side…

We consider the visual feature selection to improve the estimation quality required for the accurate navigation of a robot. We build upon a key property that asserts: contributions of trackable features (landmarks) appear linearly in the…

This paper is concerned with estimating the column space of an unknown low-rank matrix $\boldsymbol{A}^{\star}\in\mathbb{R}^{d_{1}\times d_{2}}$, given noisy and partial observations of its entries. There is no shortage of scenarios where…

The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank $r$ reliably from the fewest possible random…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…

Synthetic Nearest Neighbors (SNN) provides a principled solution to causal matrix completion under missing-not-at-random (MNAR) by exploiting local low-rank structure through fully observed anchor submatrices. However, its effectiveness…

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…

The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…

Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor…

Neural networks are widely used to approximate unknown functions in control. A common neural network architecture uses a single hidden layer (i.e. a shallow network), in which the input parameters are fixed in advance and only the output…