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Why are big data matrices approximately low rank?
Matrices of (approximate) low rank are pervasive in data science, appearing in movie
preferences, text documents, survey data, medical records, and genomics. While there is a …
preferences, text documents, survey data, medical records, and genomics. While there is a …
Patch2Self: Denoising Diffusion MRI with Self-Supervised Learning
Diffusion-weighted magnetic resonance imaging (DWI) is the only non-invasive method for
quantifying microstructure and reconstructing white-matter pathways in the living human …
quantifying microstructure and reconstructing white-matter pathways in the living human …
Explaining the success of nearest neighbor methods in prediction
Many modern methods for prediction leverage nearest neighbor search to find past training
examples most similar to a test example, an idea that dates back in text to at least the 11th …
examples most similar to a test example, an idea that dates back in text to at least the 11th …
Causal matrix completion
Matrix completion is the study of recovering an underlying matrix from a sparse subset of
noisy observations. Traditionally, it is assumed that the entries of the matrix are “missing …
noisy observations. Traditionally, it is assumed that the entries of the matrix are “missing …
On robustness of principal component regression
Consider the setting of Linear Regression where the observed response variables, in
expectation, are linear functions of the p-dimensional covariates. Then to achieve vanishing …
expectation, are linear functions of the p-dimensional covariates. Then to achieve vanishing …
Rates of convergence of spectral methods for graphon estimation
This paper studies the problem of estimating the graphon function–a generative mechanism
for a class of random graphs that are useful approximations to real networks. Specifically, a …
for a class of random graphs that are useful approximations to real networks. Specifically, a …
Missing not at random in matrix completion: The effectiveness of estimating missingness probabilities under a low nuclear norm assumption
Matrix completion is often applied to data with entries missing not at random (MNAR). For
example, consider a recommendation system where users tend to only reveal ratings for …
example, consider a recommendation system where users tend to only reveal ratings for …
Algebraic variety models for high-rank matrix completion
We consider a non-linear generalization of low-rank matrix completion to the case where the
data belongs to an algebraic variety, ie, each data point is a solution to a system of …
data belongs to an algebraic variety, ie, each data point is a solution to a system of …
Counterfactual inference for sequential experiments
We consider after-study statistical inference for sequentially designed experiments wherein
multiple units are assigned treatments for multiple time points using treatment policies that …
multiple units are assigned treatments for multiple time points using treatment policies that …
Model agnostic time series analysis via matrix estimation
We propose an algorithm to impute and forecast a time series by transforming the observed
time series into a matrix, utilizing matrix estimation to recover missing values and de-noise …
time series into a matrix, utilizing matrix estimation to recover missing values and de-noise …