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Lack of data on which to perform experimentation is a recurring issue in many areas of research, particularly in machine learning. The inability of most automated data mining techniques to be generalized to all types of data is inherently…

We present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $n \times n$ distance matrix as input, where $n$ is the number of individuals,…

Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-explored in the literature. A common practice is to introduce measurement error into SAR models to separate…

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…

Deep learning architectures have achieved promising results in different areas (e.g., medicine, agriculture, and security). However, using those powerful techniques in many real applications becomes challenging due to the large labeled…

Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more…

We study an EM algorithm for estimating product-term regression models with missing data. The study of such problems in the likelihood tradition has thus far been restricted to an EM algorithm method using full numerical integration.…

Many datasets suffer from missing values due to various reasons,which not only increases the processing difficulty of related tasks but also reduces the accuracy of classification. To address this problem, the mainstream approach is to use…

Missing data is a crucial issue when applying machine learning algorithms to real-world datasets. Starting from the simple assumption that two batches extracted randomly from the same dataset should share the same distribution, we leverage…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

Unsupervised embedding learning aims to extract good representation from data without the need for any manual labels, which has been a critical challenge in many supervised learning tasks. This paper proposes a new unsupervised embedding…

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

Missing data imputation forms the first critical step of many data analysis pipelines. The challenge is greatest for mixed data sets, including real, Boolean, and ordinal data, where standard techniques for imputation fail basic sanity…

In this paper, we present a novel low rank representation (LRR) algorithm for data lying on the manifold of square root densities. Unlike traditional LRR methods which rely on the assumption that the data points are vectors in the Euclidean…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

Gaussian Mixture models (GMMs) are a powerful tool for clustering, classification and density estimation when clustering structures are embedded in the data. The presence of missing values can largely impact the GMMs estimation process,…

The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

Multi-contrast magnetic resonance imaging (MRI) is widely used in clinical practice as each contrast provides complementary information. However, the availability of each imaging contrast may vary amongst patients, which poses challenges to…