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Quantum Machine Learning (QML) hasn't yet demonstrated extensively and clearly its advantages compared to the classical machine learning approach. So far, there are only specific cases where some quantum-inspired techniques have achieved…
Disjunctive Linear Arithmetic (DLA) is a major decidable theory that is supported by almost all existing theorem provers. The theory consists of Boolean combinations of predicates of the form $\Sigma_{j=1}^{n}a_j\cdot x_j \le b$, where the…
Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…
Lagrangian descriptors (LDs) based on the arc length of orbits previously demonstrated their utility in delineating structures governing the dynamics. Recently, a chaos indicator based on the second derivatives of the LDs, referred to as…
In practical applications, we often have to deal with high order data, such as a grayscale image and a video sequence are intrinsically 2nd-order tensor and 3rd-order tensor, respectively. For doing clustering or classification of these…
Classification methods that leverage the strengths of data from multiple sources (multi-view data) simultaneously have enormous potential to yield more powerful findings than two step methods: association followed by classification. We…
Temporal difference learning (TD) is a simple iterative algorithm used to estimate the value function corresponding to a given policy in a Markov decision process. Although TD is one of the most widely used algorithms in reinforcement…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…
Quadratic approximations form a fundamental building block of machine learning methods. E.g., second-order optimizers try to find the Newton step into the minimum of a local quadratic proxy to the objective function; and the second-order…
Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial…
We propose Stepwise cOnditional likelihood variable selection for Discriminant Analysis (SODA) to detect both main and quadratic interaction effects in logistic regression and quadratic discriminant analysis (QDA) models. In the forward…
Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…
Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the classic methods in high-dimensional settings. Asymptotic optimality has been established for some of these methods in high…
Recently proposed L2-norm linear discriminant analysis criterion via the Bhattacharyya error bound estimation (L2BLDA) is an effective improvement of linear discriminant analysis (LDA) for feature extraction. However, L2BLDA is only…
We aim to analyze the relation between two random vectors that may potentially have both different number of attributes as well as realizations, and which may even not have a joint distribution. This problem arises in many practical…
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which…
We study the estimation of the linear discriminant with projection pursuit, a method that is blind in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive…
Accurate image segmentation remains challenging, particularly in generating sharp, confident boundaries. While modern architectures have advanced the field, many of them still rely on standard loss functions like Cross-Entropy and Dice,…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…