Related papers: An evaluation framework for dimensionality reducti…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
In sentiment classification, the enormous amount of textual data, its immense dimensionality, and inherent noise make it extremely difficult for machine learning classifiers to extract high-level and complex abstractions. In order to make…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
Programmatic Weak Supervision (PWS) enables supervised model training without direct access to ground truth labels, utilizing weak labels from heuristics, crowdsourcing, or pre-trained models. However, the absence of ground truth…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…
Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
Despite their benefits in terms of simplicity, low computational cost and data requirement, parametric machine learning algorithms, such as linear discriminant analysis, quadratic discriminant analysis or logistic regression, suffer from…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. However, application of QR can become very challenging when dealing with high-dimensional data, making it necessary to use…
Evaluating the accuracy of dimensionality reduction (DR) projections in preserving the structure of high-dimensional data is crucial for reliable visual analytics. Diverse evaluation metrics targeting different structural characteristics…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in…
In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their…
The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…
A plethora of dimensionality reduction techniques have emerged over the past decades, leaving researchers and analysts with a wide variety of choices for reducing their data, all the more so given some techniques come with additional…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…