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Revealing latent structure in data is an active field of research, having introduced exciting technologies such as variational autoencoders and adversarial networks, and is essential to push machine learning towards unsupervised knowledge…

Machine unlearning focuses on the computationally efficient removal of specific training data from trained models, ensuring that the influence of forgotten data is effectively eliminated without the need for full retraining. Despite…

We investigate methods for parameter learning from incomplete data that is not missing at random. Likelihood-based methods then require the optimization of a profile likelihood that takes all possible missingness mechanisms into account.…

Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…

Machine unlearning aims to remove the influence of specific training data from a model without requiring full retraining. This capability is crucial for ensuring privacy, safety, and regulatory compliance. Therefore, verifying whether a…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning…

Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…

The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is…

Supervised learning with missing data aims at building the best prediction of a target output based on partially-observed inputs. Major approaches to address this problem can be decomposed into $(i)$ impute-then-predict strategies, which…

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

Recent work has suggested that a good embedding is all we need to solve many few-shot learning benchmarks. Furthermore, other work has strongly suggested that Model Agnostic Meta-Learning (MAML) also works via this same method - by learning…

This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…

Statistically correcting measured cross sections for detector effects is an important step across many applications. In particle physics, this inverse problem is known as unfolding. In cases with complex instruments, the distortions they…

Missing data is a ubiquitous challenge in data analysis, often leading to biased and inaccurate results. Traditional imputation methods usually assume that the missingness mechanism is missing-at-random (MAR), where the missingness is…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…

While data are the primary fuel for machine learning models, they often suffer from missing values, especially when collected in real-world scenarios. However, many off-the-shelf machine learning models, including artificial neural network…