相关论文: Fast Robust Subspace Tracking via PCA in Sparse Da…

Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the…

Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies…

We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…

Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to…

A streaming algorithm is adversarially robust if it is guaranteed to perform correctly even in the presence of an adaptive adversary. Recently, several sophisticated frameworks for robustification of classical streaming algorithms have been…

The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…

Robustness is a correctness notion for concurrent programs running under relaxed consistency models. The task is to check that the relaxed behavior coincides (up to traces) with sequential consistency (SC). Although computationally simple…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

Sparse subspace clustering (SSC) is an elegant approach for unsupervised segmentation if the data points of each cluster are located in linear subspaces. This model applies, for instance, in motion segmentation if some restrictions on the…

Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

The problem of quickest detection of a change in the distribution of a sequence of random variables is studied. The objective is to detect the change with the minimum possible delay, subject to constraints on the rate of false alarms and…

Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most…

Robots and autonomous vehicles should be aware of what happens in their surroundings. The segmentation and tracking of moving objects are essential for reliable path planning, including collision avoidance. We investigate this estimation…

Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…

We consider the problem of outlier robust PCA (OR-PCA) where the goal is to recover principal directions despite the presence of outlier data points. That is, given a data matrix $M^*$, where $(1-\alpha)$ fraction of the points are noisy…

This paper presents a solution for persistent monitoring of real-world stochastic phenomena, where the underlying covariance structure changes sharply across time, using a small number of mobile robot sensors. We propose an adaptive…

This paper uses network packet capture data to demonstrate how Robust Principal Component Analysis (RPCA) can be used in a new way to detect anomalies which serve as cyber-network attack indicators. The approach requires only a few…

We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated. Under a bounded-ness assumption on the true data and the noise,…