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In this letter, we propose a modified version of Fast Independent Component Analysis (FICA) algorithm to solve the self-interference cancellation (SIC) problem in In-band Full Duplex (IBFD) communication systems. The complex mixing problem…
This work focuses on the problem of unraveling nonlinearly mixed latent components in an unsupervised manner. The latent components are assumed to reside in the probability simplex, and are transformed by an unknown post-nonlinear mixing…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
This paper presents Cram\'er-Rao Lower Bound (CRLB) for the complex-valued Blind Source Extraction (BSE) problem based on the assumption that the target signal is independent of the other signals. Two instantaneous mixing models are…
Independent component analysis (ICA) is a popular tool for investigating brain organization in neuroscience research. In fMRI studies, an important goal is to study how brain networks are modulated by subjects' clinical and demographic…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
Encoding models provide a powerful framework for linking continuous stimulus features to neural activity; however, traditional voxelwise approaches are limited by measurement noise, inter-subject variability, and redundancy arising from…
Cosine similarity is widely used to measure the similarity between two embeddings, while interpretations based on angle and correlation coefficient are common. In this study, we focus on the interpretable axes of embeddings transformed by…
Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for…
Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
Identifiability of statistical models is a key notion in unsupervised representation learning. Recent work of nonlinear independent component analysis (ICA) employs auxiliary data and has established identifiable conditions. This paper…
In this paper, we investigate the problem of classifying feature vectors with mutually independent but non-identically distributed elements. First, we show the importance of this problem. Next, we propose a classifier and derive an…
We propose a new method for training iterative collective classifiers for labeling nodes in network data. The iterative classification algorithm (ICA) is a canonical method for incorporating relational information into classification. Yet,…
Dynamic nonlinear systems exhibit distortions arising from coupled static and dynamic effects. Their intertwined nature poses major challenges for data-driven modeling. This paper presents a theoretical framework grounded in structured…
Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…