Dual IHT algorithm solves NP-hard non-convex sparse minimization problems.
problem Non-convex sparse minimization with ℓ2-regularized loss function. method Developed a dual IHT algorithm for maximizing the non-smooth dual objective.
result Sparse recovery performance is invariant to RIP, superior to primal IHT algorithms.
Improved IHT with momentum accelerates convex optimization with non-convex constraints.
problem Optimizing convex criteria with non-convex constraints.
method Modified iterative hard thresholding with momentum.
result Acceleration leads to significant improvements over state-of-the-art methods.
A neural network, IHT-Net, improves DOA estimation with sparse arrays.
problem Single-snapshot DOA estimation with sparse arrays in dynamic settings.
method IHT-inspired neural network with recurrent neural network and autoencoders.
result IHT-Net achieves faster convergence and higher accuracy in DOA estimation.
IHT improves sparse distribution learning.
problem Learning sparse discrete distributions.
method Iterative hard thresholding as a solution, with a greedy approximate projection.
result IHT achieves state of the art results for sparse distribution learning.
Paper analyzes IHT's performance in sparse recovery problems.
problem Generalization performance of Iterative Hard Thresholding (IHT).
method Sparse generalization theory under algorithmic stability.
result IHT achieves convergence rates in sparse excess risk.
IHT reduces false positives and negatives in GWAS analysis.
problem Corrupted model selection in GWAS analysis.
method Iterative Hard Thresholding (IHT) algorithm for model selection.
result IHT reduces false positives and negatives while maintaining computational efficiency.
In this paper we consider l0 regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving l0 regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer.…
Improved iterative hard thresholding for faster, sparser solutions.
problem Finding sparser solutions without sacrificing runtime.
method Adaptive regularization framework applied to iterative hard thresholding.
result Returns solutions with sparsity O(sκ), improving over existing methods. We develop mask iterative hard thresholding algorithms (mask IHT and mask DORE) for sparse image reconstruction of objects with known contour. The measurements follow a noisy underdetermined linear model common in the compressive sampling literature. Assuming that the contour of the object that we wish to reconstruct i…
New methods solve graph sparsity optimization problems faster.
problem Complex graph sparsity optimization problems in disease outbreak monitoring and social network analysis.
method Stochastic variance-reduced gradient-based methods GraphSVRG-IHT and GraphSCSG-IHT.
result Our methods achieve linear convergence speed.
New algorithm resists contamination in high-dimensional regression with optimal performance.
problem Adversarial and measurement errors in high-dimensional data.
method Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm.
result Achieves minimax near-optimal estimation and signal-adaptive support recovery.
A hybrid ML model detects fraudulent transactions with high accuracy.
problem Detecting and preventing fraudulent credit card transactions.
method Intelligent combination of multiple algorithms with Grid search and IHT-LR.
result Achieves impressive accuracy rates of 99.66% for ENS model.
The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard L0 constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard thresholding (IHT)) methods is known to offer the fastest and most scalable sol…
New algorithm recovers signals from low-precision data in interferometry and imaging.
problem Signal loss in data compression for interferometry and medical imaging.
method Normalized Iterative Hard Thresholding with aggressive quantization.
result Recovery guarantees for low-precision data in compressive sensing.
FLIPHAT addresses joint differential privacy for high-dimensional sparse linear bandits.
problem Efficient sequential decision-making with high-dimensional sparse features and privacy concerns.
method FLIPHAT combines iterative forgetting and N-IHT for sparse linear regression, achieving optimal regret.
result FLIPHAT achieves optimal regret in terms of privacy parameters, context dimension, and time horizon.
Paper provides linear convergence guarantees for KZIHT and KZPT methods.
problem Solving linear equation systems with sparse constraints.
method Combines Kaczmarz and iterative thresholding methods, using reshuffling data sampling.
result KZIHT and KZPT converge linearly to sparse solutions.
ARHT algorithm improves sparsity guarantees in convex optimization.
problem Optimizing convex functions with sparsity constraints.
method Adaptively Regularized Hard Thresholding (ARHT) algorithm.
result ARHT achieves sparsity bound of γ=O(κ), matching theoretical limits.
Guarantees sparse recovery for neural networks with iterative hard thresholding.
problem Recovering sparse network weights in neural networks.
method Structural properties of sparse network weights and iterative hard thresholding algorithm.
result Simple iterative hard thresholding algorithm recovers sparse network weights exactly using linear memory.
Meta-learning with network pruning reduces overfitting and improves few-shot learning.
problem Overfitting in meta-learning models with over-parameterized neural networks.
method Network pruning to control capacity and explicitly reduce generalization gap.
result Uniform concentration analysis shows the benefit of network capacity constraint.
Guarantees recovery of compressible signals from adversarial noise.
problem Recovering compressible signals from noise and adversarial attacks.
method Extends adversarial defense framework to ℓ0, ℓ2, and ℓ∞ norms. result Recovery guarantees for various signal recovery methods under different noise types.
Entropy regularization improves sparse model discovery in federated learning.
problem Sparse model discovery in federated learning with limited data.
method Entropy regularization of gate distributions for probabilistic sparse model exploration.
result Entropy regularization leads to better sparse model recovery and performance.
This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz φ-radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz φ-radial addition of two star bodies, we derive a f…
Dual spherical conchoidal motion has been defined by Yapar. In this work, we define this motion on a dual hyperbolic unit sphere in the dual Lorentzian space with dual signature, and the results carried to the Lorentzian lines space by means of the Study s mapping. We also obtain the study maps of the orbits drawn on t…
Study of curves in dual space with constant curvature and torsion.
problem Classifying curves in dual space with specific geometric properties.
method Defined curvature and torsion for curves in dual space, classified curves with constant properties, and proved existence theorems.
result Established fundamental theorem of existence for dual curves with prescribed curvature and torsion.
Solves a problem related to dual Orlicz curvature measure.
problem Solving the dual Orlicz-Minkowski problem.
method Introduced dual Orlicz curvature measure and established a variational formula.
result Provided a solution to the dual Orlicz-Minkowski problem.
The paper classifies curves in dual affine and Lorentz-Minkowski planes with constant curvature.
problem Classifying curves with constant curvature in dual affine and Lorentz-Minkowski planes.
method Investigation of invariants under equiaffine transformations and explicit equations for curves with constant curvature.
result Curves with constant curvature in dual affine and Lorentz-Minkowski planes are classified.
Geodesic currents on hyperbolic surfaces have dual spaces that are metric trees.
problem Understanding the dual spaces of geodesic currents on hyperbolic surfaces.
method Analyzing the geometric properties of dual spaces, including their hyperbolicity and completeness.
result The dual spaces of geodesic currents are Gromov hyperbolic metric tree-graded spaces.
The paper explores dual learning, a technique that improves machine translation and image transformation.
problem Understanding and improving dual learning's effectiveness and conditions.
method Theoretical analysis and algorithmic extension of dual learning.
result Multi-step dual learning boosts performance under mild conditions.
New construction of self-dual black holes using quadrics.
problem Hidden features of self-dual black holes obscured by twistor theory.
method Holomorphic quadrics in dual twistor space.
result Directly encoded geometry of self-dual black holes in quadrics.
Dual supervised learning improves model performance for dual tasks.
problem Separate training of dual tasks misses probabilistic connections.
method Simultaneous training of dual tasks exploiting probabilistic correlations.
result Dual supervised learning improves practical performance across various applications.
Dehn surgery on a knot determines a dual knot in the surgered manifold, the core of the filling torus. We consider duals of knots in S3 that have a lens space surgery. Each dual supports a contact structure. We show that if a universally tight contact structure is supported, then the dual is in the same homology cla…
New formula for dual knots using involutions.
problem Understanding dual knots and their transformations.
method Involutive analog of knot surgery formula.
result Computed local equivalence class for involutive dual knots.
Introduces contact dual pairs using line bundles.
problem Understanding contact geometry and Jacobi structures.
method Line bundle approach to contact and Jacobi geometry.
result Characteristic Leaf Correspondence Theorem for contact dual pairs.
Notions of self-dual and anti self-dual almost quaternionic structures are introduced. The complete classification of self-dual and anti self-dual generalized Kaehler manifolds is obtained.
Construct dual F-manifolds for regular F-manifolds.
problem Constructing dual F-manifolds for non-semi-simple F-manifolds.
method Define eventual identity to ensure dual F-manifold, construct dual coordinate system.
result Construct families of Nijenhuis operators as an application.
Dual martingales improve primal optimal stopping problem efficiency.
problem Optimal stopping problem in the primal formulation.
method Investigation of dual martingales to improve primal methods.
result Accurate dual martingale approximations reduce primal problem variance.
This paper solves the dual Minkowski problem for q-torsional rigidity.
problem The dual Minkowski problem for q-torsional rigidity.
method Introduced the p-th dual q-torsional measure and solved the p-th dual Minkowski problem for q-torsional rigidity using a Gauss curvature flow.
result Existence of smooth even and non-even solutions to the p-th dual Minkowski problem for q-torsional rigidity.
We introduce the dual isoperimetrix which solves the isoperimetric problem in the dual Brunn-Minkowski theory. We then show how the dual isoperimetrix is related to the isoperimetrix from the Brunn-Minkowski theory.
Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.
problem Defining and studying weak dual pairs in Dirac-Jacobi structures.
method Adopting omni-Lie algebroid approach, proving equivalence and leaf correspondence theorems.
result Existence of self-dual pairs and alternative proof of normal form theorem.
Develops torsion dual connections for statistical manifolds.
problem Defining statistical manifolds using dual connections.
method Introduces torsion dual connections and proves their properties.
result Curvature tensor of torsion dual connections has specific divergence.
New algorithms exploit data's strong convexity for fast linear convergence without explicit regularization.
problem Empirical risk minimization with convex loss functions.
method Primal-dual first-order algorithms that exploit data's strong convexity.
result Adaptive primal-dual algorithms achieve linear convergence without explicit regularization.
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.
Dual matroids help embed 2-complexes in 3-space.
problem Characterizing embeddability of 2-dimensional simplicial complexes in 3-space.
method Introducing dual matroids and using them to extend Kuratowski's theorem.
result Dual matroids provide a new way to characterize embeddability.
Researchers prove uniqueness and continuity of solution to L_p dual Minkowski problem.
problem Proving uniqueness and continuity of solution to L_p dual Minkowski problem.
method Established new Minkowski-type inequalities related to optimization problem.
result Uniqueness and continuity of solution for general convex bodies when q<p. In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic trihedron (dual Darboux frame). We obtain the relationships between the invariants …
Dual representations for robust risk measures and uncertainty sets.
problem Characterizing continuity of robust risk measures and their uncertainty sets.
method Develop dual representations for robust risk measures and uncertainty sets based on distinct geometric assumptions.
result Two dual frameworks for consolidated uncertainty sets are complementary, not interchangeable.
A dual pair is constructed for contact groups, linking submanifolds and orbits.
problem Understanding the geometry of contact manifolds and their diffeomorphisms.
method Constructing an infinite-dimensional non-linear Stiefel manifold with a symplectic structure, and using equivariant moment maps.
result An EPContact dual pair is established, providing a geometric description of coadjoint orbits and solutions to geodesic equations.
Solves a generalized dual Minkowski problem for specific values of q.
problem Finding solutions to the generalized dual Minkowski problem for given q and star bodies.
method Variational methods
result Existence of solutions for q<0 and 0≤q≤1, sufficient condition for q>1.