Related papers: Rank-one matrix estimation: analysis of algorithmi…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
1. A standard Gaussian random matrix has full rank with probability 1 and is well-conditioned with a probability quite close to 1 and converging to 1 fast as the matrix deviates from square shape and becomes more rectangular. 2. If we…
Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…
Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature,…
Data for several applications in diverse fields can be represented as multiple matrices that are linked across rows or columns. This is particularly common in molecular biomedical research, in which multiple molecular "omics" technologies…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
Class imbalance and distributional differences in large datasets present significant challenges for classification tasks machine learning, often leading to biased models and poor predictive performance for minority classes. This work…
We consider the problem of estimating a rank-one nonsymmetric matrix under additive white Gaussian noise. The matrix to estimate can be written as the outer product of two vectors and we look at the special case in which both vectors are…
Reliable uncertainty quantification at unobserved spatial locations, especially in the presence of complex and heterogeneous datasets, remains a core challenge in spatial statistics. Traditional approaches like Kriging rely heavily on…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
We design a new distribution over $\poly(r \eps^{-1}) \times n$ matrices $S$ so that for any fixed $n \times d$ matrix $A$ of rank $r$, with probability at least 9/10, $\norm{SAx}_2 = (1 \pm \eps)\norm{Ax}_2$ simultaneously for all $x \in…
Estimating position and orientation change of a mobile platform from two consecutive point clouds provided by a high-resolution sensor is a key problem in autonomous navigation. In particular, scan matching algorithms aim to find the…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
In this paper the problem of forecasting high dimensional time series is considered. Such time series can be modeled as matrices where each column denotes a measurement. In addition, when missing values are present, low rank matrix…