Related papers: High Dimensional Quadratic Discriminant Analysis: …
Regularized discriminant analysis (RDA), proposed by Friedman (1989), is a widely popular classifier that lacks interpretability and is impractical for high-dimensional data sets. Here, we present an interpretable and computationally…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
We tackle the problem of bias mitigation of algorithmic decisions in a setting where both the output of the algorithm and the sensitive variable are continuous. Most of prior work deals with discrete sensitive variables, meaning that the…
Dimensionality reduction is the fundamental problem for machine learning and pattern recognition. During data preprocessing, the feature selection is often demanded to reduce the computational complexity. The problem of feature selection is…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
The focus of this paper is on classification of different vehicles using sound emanated from the vehicles. In this paper,quadratic discriminant analysis classifies audio signals of passing vehicles to bus, car, motor, and truck categories…
We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1- {\alpha}$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the…
High-dimensional data requires scalable algorithms. We propose and analyze three scalable and related algorithms for semi-supervised discriminant analysis (SDA). These methods are based on Krylov subspace methods which exploit the data…
Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types.…
Domain adaptation (DA) aims to generalize a learning model across training and testing data despite the mismatch of their data distributions. In light of a theoretical estimation of upper error bound, we argue in this paper that an…
We consider in this paper detection of signal regions associated with disease outcomes in whole genome association studies. Gene- or region-based methods have become increasingly popular in whole genome association analysis as a…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
In high-dimensional regression, feature selection methods, such as sequential feature selection (SeqFS), are commonly used to identify relevant features. When data is limited, domain adaptation (DA) becomes crucial for transferring…
Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…
We revisit the problem of feature selection in linear discriminant analysis (LDA), that is, when features are correlated. First, we introduce a pooled centroids formulation of the multiclass LDA predictor function, in which the relative…
In recent years many sparse linear discriminant analysis methods have been proposed for high-dimensional classification and variable selection. However, most of these proposals focus on binary classification and they are not directly…
We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbol{\lambda} \cdot \boldsymbol{\tilde{H}}$, $\boldsymbol{\lambda}= \{\lambda_1, \lambda_2,...\}$, $\boldsymbol{\tilde{H}}$ $=…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…
Unsupervised Domain Adaptation (UDA) aims at classifying unlabeled target images leveraging source labeled ones. In this work, we consider the Partial Domain Adaptation (PDA) variant, where we have extra source classes not present in the…