Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex or a nonconvex cost function, which is a generalization of the matching pursuit…
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48 results for “low-rank pursuit”
We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthet…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and stora…
Improved understanding of low-rank solutions in SDPs via smoothed analysis.
problem Finding low-rank solutions to semidefinite programs efficiently.
method Penalty function formulation and smoothed analysis to avoid worst-case matrices.
result All approximate local optima are global optima for rank-constrained SDPs under certain conditions.
Paper proposes a method for estimating sparse and low-rank tensors from sketchings.
problem Estimating sparse and low-rank tensors from limited data.
method Two-stage non-convex implementation using sparse tensor decomposition and thresholded gradient descent.
result Exact and stable recovery of tensors in noisy and noiseless cases with high probability.
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint/mixed relaxations (i.e., l_{1}-norm and tr…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on optimization problems with complexity that scales with the dimension of the data, which…
New model reconstructs networks by identifying regular components.
problem Uncovering the complexity of network structures.
method Low-rank pursuit based self-representation network model.
result Reconstructs networks and measures their regulability.
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…
Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …
Thompson Sampling improves pursuit-evasion coordination.
problem Optimizing pursuer behavior to capture an evader efficiently.
method Variant of Thompson Sampling applied to pursuit-evasion problems.
result Thompson Sampling reduces time-to-capture significantly.
Unified analysis of matching pursuit and coordinate descent methods.
problem Optimization of linear spaces using first-order methods.
method Unified analysis of matching pursuit and coordinate descent, providing rates for smooth and strongly convex objectives.
result Unified analysis leading to tightest known rates for steepest coordinate descent and accelerated convergence for matching pursuit.
Isometry pursuitstat.ML
Isometry pursuit identifies orthonormal submatrices from wide matrices.
problem Identifying isometric embeddings from wide matrices.
method A convex algorithm combining normalization and multitask basis pursuit.
result The method identifies isometric embeddings from interpretable dictionaries.
Efficiently recovers data corrupted by adversarial noise in structured settings.
problem Recovering clean data points from corrupted Gaussian data with low-rank noise and adversarial coordinate corruptions.
method Developed an efficient algorithm using a combinatorial approach to analyze Basis Pursuit (BP) method.
result Achieved nearly-optimal recovery of data points up to a error bound.
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses in finite time or converges to a closed geodesic. The main result is that this conjecture is …
A new algorithm improves SSC clustering accuracy with low complexity.
problem Sparse Subspace Clustering accuracy loss in time efficiency.
method Active Orthogonal Matching Pursuit (Active OMP-SSC) for improved clustering accuracy.
result Improves clustering accuracy of OMP-SSC with low computational complexity.
Study of pursuit-evasion game on sphere and its relation to planar Apollonius circle.
problem Analyzing pursuit-evasion game on a sphere and its properties.
method Extending classical planar pursuit-evasion game to spherical geometry, studying equilibrium intercept points and their relation to Apollonius domain.
result Condition for intercept point to belong to Apollonius domain on sphere, analogous to planar game.
New algorithms separate singing voices from accompaniment using complex and quaternionic principal component pursuit.
problem Separating singing voices from instrumental accompaniment using phase information.
method Extended principal component pursuit to complex and quaternionic cases, developed new proximity operators, applied inexact augmented Lagrange multiplier algorithm.
result Phase information improves singing voice separation.
This paper closes the gap on matching pursuit's convergence rate.
problem Improving the understanding of matching pursuit's convergence rate.
method Constructing a worst case dictionary to analyze matching pursuit's performance.
result Sharp characterization of matching pursuit's convergence rate as , with .
Blended Matching Pursuitmath.OC
New algorithm combines gradient and coordinate descent steps for faster convergence.
problem Optimizing smooth convex functions over atom-spans.
method Blended matching pursuit combining coordinate descent and gradient descent.
result Derives linear convergence rates for non-strongly convex functions.
Generative ML learns optimal pursuit trajectories in pursuit-evasion games.
problem Optimizing Blue's pursuit trajectory to intercept Red in a game of pursuit-evasion.
method Applying generative machine learning to learn optimal action policies for Blue.
result Generative ML models can learn relevant representations for pursuit-evasion dynamics.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
The paper compares PCA and PP for scRNA sequencing data.
problem Limitations of PCA in scRNA sequencing data.
method Applied PCA and PP (using negative Shannon's entropy) on scRNA sequencing data.
result PP outperforms PCA in scRNA sequencing data.
In this correspondence, we obtain exact recovery conditions for regularized modified basis pursuit (reg-mod-BP) and discuss when the obtained conditions are weaker than those for modified-CS or for basis pursuit (BP). The discussion is also supported by simulation comparisons. Reg-mod-BP provides a solution to the spar…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be solved in polynomial time via a natural convex relaxation, known as Compressive …
Insurance firms use RL to optimize customer offers for desired target portfolios.
problem Optimizing insurance offers to achieve a desired customer portfolio.
method Developed a novel reinforcement learning algorithm.
result The RL algorithm outperforms traditional methods in a synthetic market.
Enhances projection pursuit tree classifier with visual diagnostics for better multi-class classification.
problem Rigidity of original algorithm limits performance in complex high-dimensional classification problems.
method Allowing more splits and flexible class groupings in projection pursuit computation, and developing visual diagnostics.
result Demonstrates enhanced classifier performs as intended through interactive visual diagnostics.
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper devel…
PPF uses projections to improve classification accuracy.
problem Improving classification accuracy in multi-class problems.
method PPF constructs trees using projections of variables, enhancing traditional random forest.
result PPF outperforms traditional random forest in multi-class problems.
Paper extends principal component pursuit to hypercomplex numbers for improved audio data analysis.
problem Improving robust principal component analysis for audio data.
method Extends principal component pursuit to polar -complex and -bicomplex numbers, deriving proximity operators for - and trace-norm regularizers.
result Our approach outperforms tensor robust principal component analysis on audio data.
Product models of low dimensional experts are a powerful way to avoid the curse of dimensionality. We present the ``under-complete product of experts' (UPoE), where each expert models a one dimensional projection of the data. The UPoE is fully tractable and may be interpreted as a parametric probabilistic model for pro…
Paper proposes an accelerated algorithm for sparse subspace clustering.
problem Inefficient and inaccurate subspace clustering methods.
method Accelerated orthogonal least-squares for sparse subspace clustering.
result The proposed method is more accurate and efficient than existing methods.
Orthogonal Matching Pursuit (OMP) has long been considered a powerful heuristic for attacking compressive sensing problems; however, its theoretical development is, unfortunately, somewhat lacking. This paper presents an improved Restricted Isometry Property (RIP) based performance guarantee for T-sparse signal reconst…
Sharp results link DLN gradient flow to basis pursuit optimization and GHA phase transitions.
problem Understanding implicit regularization in Diagonal Linear Networks.
method Sharp convergence bounds and characterization of minimizers.
result Gradient flow of DLNs with tiny initialization approximates minimizers of basis pursuit optimization problem.
Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching pursuit methods in an optimization sense, for general sets of atoms. We derive …
Paper proposes a novel approach to density ratio estimation using projection pursuit.
problem Density ratio estimation challenges in high dimensions and model misspecification.
method The approach uses projection pursuit to approximate density ratios, addressing high dimensionality and model flexibility issues.
result The proposed estimator is consistent and converges at a certain rate, outperforming existing methods in experiments.
The problem of pursuing a moving target is always one of the main topics in navigation. In the literatures, there are two well-known algorithms called Pure Pursuit and Pure Rendezvous navigation in the 3-dimensional space . In this paper, these two methods are combined to introduce a novel family of pursu…
A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our approach incorporates a closed loop optimal control and the presentation is familiar wi…
Projection pursuit model improves Gaussian process regression for high-dimensional data.
problem Scalability issues with traditional Gaussian process models in high dimensions.
method Additive Gaussian process regression with dimension expansion and gradient descent.
result The proposed method approximates more complex functions and outperforms traditional models.
Improved SSC clustering with reduced computation time and accuracy.
problem Heavy computational burden in Sparse Subspace Clustering.
method RCOMP-SSC algorithm that restricts connections during OMP iterations.
result Improved clustering accuracy with reduced computational time.
New pursuit algorithm for ML-CSC model with improved stability and dictionary learning.
problem Lack of exact pursuit algorithms and conditions for non-empty model in ML-CSC.
method Projection approach for pursuit algorithm, stability bounds, practical alternatives, online dictionary learning.
result Sound pursuit algorithm and practical dictionary learning for ML-CSC model.
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
Paper proposes PPMM for fast estimation of large-scale OTM.
problem Estimation of large-scale optimal transport maps (OTM) is challenging due to the curse of dimensionality.
method Combines projection pursuit regression and sufficient dimension reduction to adaptively select projection directions.
result PPMM consistently estimates the most informative projection direction and weakly converges to the target OTM.
Lower bounds show OLS outperforms basis pursuit in overparameterized linear regression.
problem Excess risk of sparse interpolating procedures in overparameterized linear regression.
method Proved lower bounds on excess risk for OLS and basis pursuit.
result Excess risk of basis pursuit can converge at an exponentially slower rate than OLS.
Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.
problem SRPCP model robust matrix recovery with universal penalty parameter.
method Tuning-free alternating minimization (AltMin) algorithm with closed-form subproblems.
result Efficient AltMin algorithm confirms robustness and efficiency.
New technique RRT improves OMP performance without knowing sparsity or noise.
problem Recovering sparse high-dimensional vectors without knowing sparsity or noise statistics.
method Residual ratio thresholding (RRT) to operate OMP without a priori knowledge.
result RRT achieves comparable performance to OMP with known statistics.
Paper proves noise-tolerant SSC using greedy methods under coherence conditions.
problem Proving noise-tolerant SSC using greedy methods under coherence conditions.
method Derives coherence-based sufficient conditions for correct neighbor identification using MP/OMP in the presence of bounded noise.
result MP/OMP succeed in identifying correct neighbors under certain noise levels, leading to higher clustering accuracy.