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Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
This paper develops an asymptotically efficient recursive identification algorithm for autoregressive systems with exogenous inputs under one-bit communications. In particular, the proposed method asymptotically achieves the Cramer-Rao…
Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an…
Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems. However, prior AMP theory -- which focused mostly on high-dimensional asymptotics -- fell short of predicting…
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Construct, Merge, Solve and Adapt (CMSA) is a general hybrid metaheuristic for solving combinatorial optimization problems. At each iteration, CMSA (1) constructs feasible solutions to the tackled problem instance in a probabilistic way and…
We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when…
In the current data-intensive era, big data has become a significant asset for Artificial Intelligence (AI), serving as a foundation for developing data-driven models and providing insight into various unknown fields. This study navigates…
In this work we aim to solve the compressed sensing problem for the case of a complex unknown vector by utilizing the Bayesian-optimal structured signal approximate message passing (BOSSAMP) algorithm on the jointly sparse real and…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
We propose a new method for statistical inference in generalized linear models. In the overparameterized regime, Principal Component Regression (PCR) reduces variance by projecting high-dimensional data to a low-dimensional principal…
Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs) is a challenging task. Recently, a line of message-passing-based research has been proposed to solve CQA. However, they perform unsatisfactorily on negative queries and…
Iterative hard thresholding (IHT) and compressive sampling matching pursuit (CoSaMP) are two types of mainstream compressed sensing algorithms using hard thresholding operators for signal recovery and approximation. The guaranteed…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
We present a novel compressed sensing recovery algorithm - termed Bayesian Optimal Structured Signal Approximate Message Passing (BOSSAMP) - that jointly exploits the prior distribution and the structured sparsity of a signal that shall be…
The study of stability and sensitivity of statistical methods or algorithms with respect to their data is an important problem in machine learning and statistics. The performance of the algorithm under resampling of the data is a…