Related papers: Estimation and imputation in Probabilistic Princip…
This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…
Auxiliary information is frequently utilized in survey sampling to improve the efficiency of estimators of the finite population mean. However, the simultaneous use of multiple auxiliary variables often induces multicollinearity, which…
Missing data is a fundamental challenge in data science, significantly hindering analysis and decision-making across a wide range of disciplines, including healthcare, bioinformatics, social science, e-commerce, and industrial monitoring.…
This paper studies the principal components (PC) estimator for high dimensional approximate factor models with weak factors in that the factor loading ($\boldsymbol{\Lambda}^0$) scales sublinearly in the number $N$ of cross-section units,…
We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…
Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…
Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially…
We report assumption-free bounds for any contrast between the probabilities of the potential outcome under exposure and non-exposure when the confounders are missing not at random. We assume that the missingness mechanism is…
Current domain adaptation methods under missingness shift are restricted to Missing At Random (MAR) missingness mechanisms. However, in many real-world examples, the MAR assumption may be too restrictive. When covariates are Missing Not At…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
The presence of missing values makes supervised learning much more challenging. Indeed, previous work has shown that even when the response is a linear function of the complete data, the optimal predictor is a complex function of the…
Researchers addressing post-treatment complications in randomized trials often turn to principal stratification to define relevant assumptions and quantities of interest. One approach for estimating causal effects in this framework is to…
Many real-world datasets contain missing entries and mixed data types including categorical and ordered (e.g. continuous and ordinal) variables. Imputing the missing entries is necessary, since many data analysis pipelines require complete…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…