Related papers: Dimensionality Reduction and (Bucket) Ranking: a M…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
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…
High-dimensional classification has become an increasingly important problem. In this paper we propose a "Multivariate Adaptive Stochastic Search" (MASS) approach which first reduces the dimension of the data space and then applies a…
Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be…
We propose a framework to analyze how multivariate representations disentangle ground-truth generative factors. A quantitative analysis of disentanglement has been based on metrics designed to compare how one variable explains each…
The two-sample problem, which consists in testing whether independent samples on $\mathbb{R}^d$ are drawn from the same (unknown) distribution, finds applications in many areas. Its study in high-dimension is the subject of much attention,…
Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…
Social choice theory offers a wealth of approaches for selecting a candidate on behalf of voters based on their reported preference rankings over options. When voters have underlying utilities for these options, however, using preference…
Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole…
The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
The "curse of dimensionality" is a well-known problem in pattern recognition. A widely used approach to tackling the problem is a group of subspace methods, where the original features are projected onto a new space. The lower dimensional…
We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
We present a novel approach for the construction of ensemble classifiers based on dimensionality reduction. Dimensionality reduction methods represent datasets using a small number of attributes while preserving the information conveyed by…
Beyond accuracy, there are a variety of aspects to the quality of recommender systems, such as diversity, fairness, and robustness. We argue that many of the prevalent problems in recommender systems are partly due to low-dimensionality of…
We study the long-standing problem of determining the number of principal components in econometric applications from a selective inference perspective. We consider i.i.d. observations from a $p$-dimensional random vector with $p<n$ and…