Related papers: High Dimensional Quadratic Discriminant Analysis: …
High dimensional classification has been highlighted for last two decades and much research has been conducted in order to circumvent challenges encountered in high dimensions. While existing methods have focused mainly on developing…
Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…
This paper proposes a quasi-binary encoding based algorithm for solving a specific quadratic optimization models with discrete variables, in the quantum approximate optimization algorithm (QAOA) framework. The quadratic optimization model…
In practical machine learning applications, it is often challenging to assign accurate labels to data, and increasing the number of labeled instances is often limited. In such cases, Weakly Supervised Learning (WSL), which enables training…
Much like the classical Fisher linear discriminant analysis (LDA), the recently proposed Wasserstein discriminant analysis (WDA) is a linear dimensionality reduction method that seeks a projection matrix to maximize the dispersion of…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
We propose a non-convex training objective for robust binary classification of data sets in which label noise is present. The design is guided by the intention of solving the resulting problem by adiabatic quantum optimization. Two…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as…
We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…
We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…
Medical image segmentation has made significant progress when a large amount of labeled data are available. However, annotating medical image segmentation datasets is expensive due to the requirement of professional skills. Additionally,…
Recent advancements in semi-supervised deep learning have introduced effective strategies for leveraging both labeled and unlabeled data to improve classification performance. This work proposes a semi-supervised framework that utilizes a…
Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical…
We study the problem of learning multi-index models (MIMs), where the label depends on the input $\boldsymbol{x} \in \mathbb{R}^d$ only through an unknown $\mathsf{s}$-dimensional projection $\boldsymbol{W}_*^\mathsf{T} \boldsymbol{x} \in…
One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In…
Partial domain adaptation (PDA), in which we assume the target label space is included in the source label space, is a general version of standard domain adaptation. Since the target label space is unknown, the main challenge of PDA is to…
After obtaining an accurate approximation for $ARL_0$, we first consider the optimal design of weight parameter for a multivariate EWMA chart that minimizes the stationary average delay detection time (SADDT). Comparisons with moving…
Semi-supervised domain adaptation (SSDA) adapts a learner to a new domain by effectively utilizing source domain data and a few labeled target samples. It is a practical yet under-investigated research topic. In this paper, we analyze the…
Few-shot anomaly detection (FSAD) plays a crucial role in industrial manufacturing. However, existing FSAD methods encounter difficulties leveraging a limited number of normal samples, frequently failing to detect and locate inconspicuous…