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Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Preference optimization is widely used to align large language models (LLMs) with human preferences. However, many margin-based methods also suppress the chosen response when they try to suppress the rejected one, and there is no general…
With the onset of large language models (LLMs), the performance of artificial intelligence (AI) models is becoming increasingly multi-dimensional. Accordingly, there have been several large, multi-dimensional evaluation frameworks put…
Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…
Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Quadratic discriminant analysis (QDA) is a simple method to classify a subject into two populations, and was proven to perform as well as the Bayes rule when the data dimension p is fixed. The main purpose of this paper is to examine the…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
Particle accelerators are complex facilities that produce large amounts of structured data and have clear optimization goals as well as precisely defined control requirements. As such they are naturally amenable to data-driven research…
This paper is concerned with the problem of tracking single or multiple targets with multiple non-target specific observations (measurements). For such filtering problems with data association uncertainty, a novel feedback control-based…
We present a preference learning framework for multiple criteria sorting. We consider sorting procedures applying an additive value model with diverse types of marginal value functions (including linear, piecewise-linear, splined, and…
Reward models are pivotal for aligning Large Language Models (LLMs) with human preferences. Existing approaches face two key limitations: Discriminative reward models require large-scale annotated data, as they cannot exploit the preference…
Multi-criteria decision analysis (MCDA) is a quantitative approach to the drug benefit-risk assessment (BRA) which allows for consistent comparisons by summarising all benefits and risks in a single score. The MCDA consists of several…
One drawback of evolutionary multiobjective optimization algorithms (EMOA) has traditionally been high computational cost to create an approximation of the Pareto front: number of required objective function evaluations usually grows high.…
Multi-objective optimization (MOO) has been widely studied in literature because of its versatility in human-centered decision making in real-life applications. Recently, demand for dynamic MOO is fast-emerging due to tough market dynamics…
Topological Data Analysis (TDA) is a recent approach to analyze data sets from the perspective of their topological structure. Its use for time series data has been limited. In this work, a system developed for a leading provider of cloud…
Principal components analysis (PCA) is a standard tool for identifying good low-dimensional approximations to data in high dimension. Many data sets of interest contain private or sensitive information about individuals. Algorithms which…