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Independent component analysis (ICA) is a fundamental problem in the field of signal processing, and numerous algorithms have been developed to address this issue. The core principle of these algorithms is to find a transformation matrix…
A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To…
In complex plasmas, the behavior of freely floating micrometer sized particles is studied. The particles can be directly visualized and recorded by digital video cameras. To analyze the dynamics of single particles, reliable algorithms are…
Static analysis techniques enhance the security, performance, and reliability of programs by analyzing and portraiting program behaviors without the need for actual execution. In essence, static analysis takes the Intermediate…
We reframe the analysis of progress in AI by incorporating into an overall framework both the task performance of a system, and the time and resource costs incurred in the development and deployment of the system. These costs include: data,…
We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses…
Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…
Independent component analysis is intended to recover the mutually independent components from their linear mixtures. This technique has been widely used in many fields, such as data analysis, signal processing, and machine learning. To…
We propose a general, prior-free approach for the uncalibrated non-rigid structure-from-motion problem for modelling and analysis of non-rigid objects such as human faces. The word general refers to an approach that recovers the non-rigid…
We study differentially private mean estimation in a high-dimensional setting. Existing differential privacy techniques applied to large dimensions lead to computationally intractable problems or estimators with excessive privacy loss.…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
We combine the metrics of distance and isolation to develop the Analytic Isolation and Distance-based Anomaly (AIDA) detection algorithm. AIDA is the first distance-based method that does not rely on the concept of nearest-neighbours,…
Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking…
Independent component analysis (ICA) is the problem of efficiently recovering a matrix $A \in \mathbb{R}^{n\times n}$ from i.i.d. observations of $X=AS$ where $S \in \mathbb{R}^n$ is a random vector with mutually independent coordinates.…
The goal of this thesis was to implement a tool that, given a digital audio input, can extract and represent rhythm and musical time. The purpose of the tool is to help develop better models of rhythm for real-time computer based…
Given a square integrable m-dimensional random variable $X$ on a probability space $(\Omega.\mathcal F,\Pr)$ and a sub sigma algebra $\mathcal A$, we show that there exists another m-dimensional random variable $Y$, independent of $\mathcal…
Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…
Artificial Intelligence (AI) has attracted a great deal of attention in recent years. However, alongside all its advancements, problems have also emerged, such as privacy violations, security issues and model fairness. Differential privacy,…
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…