We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an - cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from com…
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48 results for “sparse minimizers”
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse v…
Smoothed Low Rank and Sparse Matrix Recovery by Iteratively Reweighted Least Squares Minimizationcs.LG
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables an…
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard formulation is as a non-convex optimization problem which is solved in practice by heuri…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficient…
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…
Sparse Generalized Canonical Correlation Analysis: Distributed Alternating Iteration based Approachcs.LG
Proposes GCCA for detecting latent relations in multiview data with sparse structures.
problem Sparse CCA limitations for multiple datasets.
method Developed a GCCA algorithm based on distributed alternating iteration approach.
result Demonstrated effectiveness on synthetic and real-world datasets.
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called norm. In this paper we develop a Momentumized Iterative Shrinkage Th…
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Fr…
The paper improves sparse Gaussian processes by optimizing predictive loss.
problem Optimizing predictive loss in sparse Gaussian processes.
method Direct loss minimization (DLM) for log-loss and square loss, with product sampling (uPS) and biased Monte Carlo (bMC) for non-conjugate cases.
result DLM shows significant performance improvement in both log-loss and square loss cases.
New algorithm minimizes regret in sparse reinforcement learning.
problem Sparse reinforcement learning with unknown sparsity.
method Doubly robust approach combining feature vectors of all actions and novel analysis.
result Regret bound of .
Research shows finiteness in triangulations with girth constraints.
problem Finiteness of cellular partial triangulations with girth constraints.
method Characterization of sparse graphs and contraction-minimal graphs.
result There are finitely many (3,6)-tight and (3,3)-tight graphs.
factor analysismath.OC
New method for factor analysis using nuclear and norms.
problem Finding a low-rank plus sparse decomposition from noisy covariance matrix.
method Formulated an optimization problem with nuclear norm, norm, and KL divergence. Used alternating minimization algorithm.
result Algorithm effectively decomposes covariance matrices in synthetic and real datasets.
Paper finds sparse representation of functions using inverse scale space flow.
problem Finding sparse representation of functions.
method Inverse scale space flow to minimize loss.
result Convergence to optimal solution in ideal and noisy cases.
Autoencoders fail to capture sparse structure in 1-bit data compression.
problem Proving the performance of shallow autoencoders on sparse data compression.
method Gradient descent analysis and approximate message passing.
result Gradient descent minimizer for sparse data is the identity (up to permutation) above critical sparsity.
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing IHT-style methods are designed for sparse minimization in primal form. It remains open t…
Proposes a new method for kernel density estimation using stagewise minimization and a simple dictionary.
problem Kernel density estimation with data-adaptive weighting parameters and sparse representation.
method Stagewise minimization algorithm based on -divergence and a simple dictionary.
result Develops non-asymptotic error bound for the proposed estimator.
ERFit identifies dynamic equations from data with minimal supervision.
problem Data-driven sparse system identification in science and engineering.
method Entropic Regression method.
result ERFit package simplifies sparse system identification for various applications.
The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC und…
Paper proposes an algorithm for robust estimation using Huber's criterion.
problem Non-convexity and non-robustness of joint maximum likelihood estimation.
method Block-wise minimization majorization framework with data-adaptive step sizes.
result Improved convergence and robustness in sparse learning.
We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such, our network leverages by design that signals have a sparse representation and t…
Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in \cite{tang2012csotg} to recove…
Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC appro…
Quasi-potential and drift decomposition in stochastic systems by sparse identificationcond-mat.stat-mech
Paper uses sparse learning to estimate quasi-potential and drift components in stochastic systems.
problem Estimating quasi-potential and drift components in stochastic systems.
method Sparse identification of non-linear dynamics (SINDy) combined with action minimization methods.
result Evaluation of quasi-potential landscape from a single trajectory.
This work proposes a method to learn sparse representations that are more efficient for large-scale data retrieval.
problem Efficient retrieval of high-dimensional representations from large databases is computationally challenging.
method The approach minimizes the number of floating-point operations (FLOPs) by learning sparse embeddings with uniform non-zero entries.
result The proposed method achieves a similar or better speed-vs-accuracy tradeoff compared to existing baselines.
Thresholded Lasso Banditstat.ML
Thresholded Lasso bandit minimizes regret in sparse linear bandits.
problem Sparse stochastic contextual linear bandits with large feature vectors.
method Uses Lasso framework with thresholding to estimate reward function and its sparse support.
result Non-asymptotic regret upper bounds scaling as .
Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Pathcs.LG
New algorithms minimize regret in SSP with optimal sparse updates.
problem Minimizing regret in Stochastic Shortest Path models.
method Implicit finite-horizon approximation for analysis, model-free and model-based algorithms developed.
result Minimax optimal regret for both model-free and model-based algorithms.
Paper addresses regret minimization and inference in high-dimensional online decision-making.
problem Regret minimization and statistical inference in high-dimensional online decision-making.
method Integrates ε-greedy bandit algorithm with hard thresholding for sparse bandit parameters and debiasing method for inference.
result Achieves either regret or -consistent inference, with trade-off between exploration and exploitation.
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal splitting method for the iterative solution of hierarchical sparse coding problem…
New model leads to optimal test loss in sparse linear regression.
problem Sparse linear regression with low test loss despite interpolating training data.
method Developed a new parametrization of the model that combines benefits of ℓ1 and ℓ2 norms.
result Training via gradient descent leads to an interpolator with near-optimal test loss.
We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. regularization impedes the …
This letter proposes a sparse diffusion steepest-descent algorithm for one bit compressed sensing in wireless sensor networks. The approach exploits the diffusion strategy from distributed learning in the one bit compressed sensing framework. To estimate a common sparse vector cooperatively from only the sign of measur…
Most of the existing methods for sparse signal recovery assume a static system: the unknown signal is a finite-length vector for which a fixed set of linear measurements and a sparse representation basis are available and an L1-norm minimization program is solved for the reconstruction. However, the same representation…
In this paper we consider sparse approximation problems, that is, general minimization problems with the -"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) me…
Introduces PPMM algorithm for nonconvex robust regression problems.
problem Nonconvex tuning-free robust regression problems.
method PPMM algorithm with inner subproblems solved by SSN-PPA.
result Converges to d-stationary point with KL property.
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including , bridge, smoothly clipped absolute deviation, capped and mini…
We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity" and "usual recovery," (b) block-sparsity with possibly overlapping blo…
A new pruning method finds sparse minimizers in flat regions of deep neural networks.
problem Finding sparse minimizers in flat regions of deep neural networks.
method Directional pruning using an proximal gradient algorithm.
result Empirical results show promising sparsity (92%) and comparable minima to SGD.
New method learns sparse distributions by thresholding samples, improving performance and efficiency.
problem Sparse coding optimization in high-dimensional problems is computationally expensive and inefficient.
method Proposes a new variational sparse coding approach that learns sparse distributions by thresholding samples.
result Shows superior performance, statistical efficiency, and gradient estimation compared to other sparse distributions.
New ONMF model minimizes KL divergence for better sparse data modeling.
problem Clustering and data modeling with sparse vectors.
method Developed KL-ONMF algorithm based on alternating optimization.
result KL-ONMF outperforms Frobenius-norm ONMF for document classification and hyperspectral image unmixing.
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples into an appropriate basis (dictionary) and sparse vectors . Our algorithm …
3BASiL-TM decomposes LLMs into sparse and low-rank matrices for efficient compression.
problem Efficiently compressing large language models without significant performance loss.
method 3-Block ADMM method and transformer-matching refinement step for sparse plus low-rank decomposition.
result 3BASiL-TM reduces perplexity gap by over 30% and speeds up compression by 2.5x.
A novel approach tackles sparse linear bandits with reduced communication costs and minimal cumulative regret.
problem Sparse linear bandits with high-dimensional feature vectors and limited relevant features.
method Cooperative Thresholded Lasso using Lasso and ridge regression for dimension reduction and aggregation.
result Regret bound of with high probability.
Paper tackles outlier detection in signals modeled by generative models with theoretical guarantees.
problem Recovering signals from linear measurements with sparse outliers.
method Proposes an iterative ADMM algorithm and gradient descent algorithm for outlier detection using and squared norm minimization.
result Establishes theoretical recovery guarantees for signal reconstruction under sparse outliers.
Sparse Blind Source Separation (sparse BSS) is a key method to analyze multichannel data in fields ranging from medical imaging to astrophysics. However, since it relies on seeking the solution of a non-convex penalized matrix factorization problem, its performances largely depend on the optimization strategy. In this …
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems. Our key idea for making the proposed PMM to be efficient is to develop a sparse semismooth Newton method to solve the corresponding subproblem…
We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fr…