In this paper, we study the Nystr{ö}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{ö}m type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretica…
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48 results for “Nyström regularization”
Paper develops a new kernel approximation framework.
problem High time and space complexity of kernel methods for large datasets.
method Perturbation-based kernel approximation framework using classical perturbation theory.
result Framework generalizes and improves upon existing methods.
In this paper, we study large-scale convex optimization algorithms based on the Newton method applied to regularized generalized self-concordant losses, which include logistic regression and softmax regression. We first prove that our new simple scheme based on a sequence of problems with decreasing regularization para…
In this paper we model the problem of learning preferences of a population as an active learning problem. We propose an algorithm can adaptively choose pairs of items to show to users coming from a heterogeneous population, and use the obtained reward to decide which pair of items to show next. We provide computational…
Recent work has focused on combining kernel methods and deep learning to exploit the best of the two approaches. Here, we introduce a new architecture of neural networks in which we replace the top dense layers of standard convolutional architectures with an approximation of a kernel function by relying on the Nystr{ö}…
We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We formulate two convex optimization problems to jointly learn the metric and the clas…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
Survey of kernels, RKHS, and their applications in machine learning.
problem Understanding kernels and their applications in machine learning.
method Review of historical context, mathematical definitions, and practical applications of kernels.
result Comprehensive overview of kernels, RKHS, and their applications.
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge regression. Despite its simplicity, the algorithm we study is the first to achieve the op…
This work improves knowledge distillation by transferring full kernel matrices efficiently.
problem Efficiently transferring full pairwise similarity matrices for model compression in deep learning.
method The authors propose a method to transfer the full similarity matrix effectively using the Nyström method, decomposing it into partial matrices.
result The difference between the full kernel matrices of teacher and student can be well bounded by partial matrices, improving optimization efficiency.
AIR-Net adapts low-rank regularization dynamically for better image completion.
problem Fixed low-rank regularization limits adaptability to different images.
method AIR-Net uses adaptive and implicit regularization parameterized by a dynamic Laplacian matrix.
result AIR-Net enhances implicit regularization and outperforms fixed methods in non-uniform missing data scenarios.
A 6-regular triangulation for hyperbolic plane created.
problem Creating a 6-regular triangulation for hyperbolic plane.
method Constructed a 6-regular geodesic triangulation.
result A 6-regular geodesic triangulation of the hyperbolic plane was successfully created.
Gradient descent implicitly regularizes neural networks by penalizing large loss gradients.
problem How to optimize deep neural networks without explicit regularization.
method Backward error analysis to calculate implicit gradient regularization and demonstrate its effectiveness empirically.
result Implicit gradient regularization biases gradient descent toward flat minima, improving model robustness and test errors.
Choquet regularization improves exploration in RL.
problem Improving exploration in reinforcement learning.
method Introducing Choquet regularizers to measure and manage exploration, reformulating RL problems and deriving explicit solutions.
result Explicit optimal distributions and Choquet regularizers for various exploratory samplers.
The paper explores optimal regularizers for data sources, linking them to star bodies.
problem Understanding optimal regularizers for data sources.
method Investigates optimal regularizers for data distributions using star bodies and dual Brunn-Minkowski theory.
result Identifies optimal regularizers and assesses amenability to convex regularization.
A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In…
In this article, we describe symplectic and complex toric spaces associated to the five regular convex polyhedra. The regular tetrahedron and the cube are rational and simple, the regular octahedron is not simple, the regular dodecahedron is not rational and the regular icosahedron is neither simple nor rational. We re…
The paper studies convergence rates of Tsallis entropic regularization in optimal transport.
problem Optimal transport with regularization.
method Γ-convergence and quantization/shadow arguments.
result Derives convergence rate of Tsallis entropic regularization.
Study uses property elicitation to understand how fairness regularizers affect optimal decisions.
problem Understanding how fairness regularizers change the optimal decision in predictive algorithms.
method Property elicitation to analyze the relationship between loss, regularization, and optimal decision.
result Necessary and sufficient condition for when a property changes with the addition of a regularizer.
Fiedler regularization uses spectral graph theory to improve neural network performance.
problem Improving neural network performance by penalizing weights based on connectivity.
method Uses the Fiedler value of the neural network's graph as a regularization tool, providing theoretical and computational methods.
result Demonstrates Fiedler regularization's effectiveness in improving neural network performance.
Study on convergence rates for optimal transport with regularization.
problem Convergence analysis of divergence-regularized optimal transport.
method Novel methodology using quantization and martingale couplings.
result Sharp rates for various divergences and transport costs.
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by i…
Improved optimal regularity for harmonic almost complex structures.
problem Establishing optimal regularity for harmonic almost complex structures.
method Quantitative stratification method and rectifiability of singular strata.
result Optimal regularity theory for energy minimizing harmonic almost complex structures.
Dropout is a simple but effective technique for learning in neural networks and other settings. A sound theoretical understanding of dropout is needed to determine when dropout should be applied and how to use it most effectively. In this paper we continue the exploration of dropout as a regularizer pioneered by Wager,…
Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their simplicity and effectiveness. However, we observe that imposing strong L1 or L2 reg…
Study on the regularity of -Gauss curvature flow near flat interfaces.
problem Regularity of -Gauss curvature flow near flat interfaces.
method Analysis of convex hypersurface near the interface.
result Regularity of the convex hypersurface near the interface.
Fast Learning Rate of Non-Sparse Multiple Kernel Learning and Optimal Regularization Strategiesstat.ML
In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper is dense type regularizations including \ellp-MKL. According to the recent numeri…
In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networ…
We study the evolution equations for a regularized version of Dirac-geodesics, which are the one-dimensional version of Dirac-harmonic maps. We show that for the regularization being sufficiently large, the evolution equations subconverge to a regularized Dirac-geodesic. In the end, we discuss the limiting process of r…
Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximationcs.LG
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
Regularized linear regression improves binary classification performance, especially with ridge and regularization.
problem Improving binary classification accuracy with noisy labels.
method Systematic study of regularization strengths on linear classifiers trained on noisy binary classification data.
result Ridge regression consistently improves classification error, while regularization can induce sparsity and regularization can concentrate weights to two values.
New algorithm adds Hessian regularization to improve neural network robustness.
problem Improving neural network robustness against adversarial attacks.
method Proposes an efficient algorithm to train neural networks with Hessian operator-norm regularization.
result Hessian operator-norm regularization increases neural network robustness over input gradient regularization.
Wasserstein distributionally robust optimization (DRO) has recently achieved empirical success for various applications in operations research and machine learning, owing partly to its regularization effect. Although connection between Wasserstein DRO and regularization has been established in several settings, existin…
Study slice-regular polynomial functions via twistor space group actions.
problem Characterize slice-regular functions and their polynomial subclasses.
method Employ the twistor construction and group actions of .
result Characterize slice-regular functions with planar twistor lifts and normal classes of polynomials.
Selective state-adaptive regularization improves offline RL performance.
problem Extrapolation errors and value overestimation in static dataset RL.
method State-adaptive regularization coefficients trust Bellman-driven results selectively.
result Significant improvement in performance on D4RL benchmark.
New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.
problem Comparative analysis of regularization norms in ill-posed problems.
method Small noise analysis framework for Tikhonov and RKHS regularizations.
result Optimal convergence rates achieved with adaptive fractional RKHS, but hyper-parameters decay too fast.
New iterative regularization method tackles non-smooth, non-strongly convex functionals.
problem Tackles non-smooth, non-strongly convex functionals in regularization problems.
method Primal-dual algorithm with convergence and stability analysis.
result First iterative regularization procedure for non-smooth, non-strongly convex functionals.
This study explores star-shaped regularizers learned from critic-based losses.
problem Understanding the structure of regularizers learned from critic-based losses.
method Optimizing critic-based loss functions over star-shaped regularizers.
result Derives exact expressions for optimal regularizers in certain cases.
Regularizers change the geometric properties of loss functions in neural networks.
problem Understanding how different regularizers affect the geometric properties of loss functions in neural networks.
method Examined several regularizers, including weight decay, to determine if the regularized loss function becomes Morse.
result For certain regularizers, the regularized loss function becomes Morse, indicating a change in geometric properties.
We investigate the learning rate of multiple kernel learning (MKL) with and elastic-net regularizations. The elastic-net regularization is a composition of an -regularizer for inducing the sparsity and an -regularizer for controlling the smoothness. We focus on a sparse setting where the total …
Introduces self-regularization for analyzing learning algorithms.
problem Analyzing and optimizing learning algorithms without explicit regularization.
method Develops a self-regularization framework for learning algorithms.
result Provides statistical analysis and minmax-optimal rates for self-regularized algorithms.
A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinator…
Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraintsmath.OC
New framework for robust regularization under uncertain data distributions.
problem Addressing ill-posed inverse problems and statistical estimation under distributional uncertainty.
method Distributionally robust optimal regularization using convex duality.
result Identifies robust regularizers that remain effective under data distributional perturbations.
Sharp bounds on diameter and eigenvalues for amply regular graphs.
problem Finding bounds for amply regular graphs' diameter and eigenvalues.
method New ideas relating discrete Ricci curvature to local matching properties, including a novel construction of a regular bipartite graph.
result Sharp diameter and eigenvalue bounds for amply regular graphs.
New regularizer improves neural network robustness and generalization.
problem Ineffective weight decay for networks with homogeneous activation functions.
method Proposes an invariant regularizer to penalize intrinsic weight norms.
result Improves generalization and adversarial robustness on various datasets.
The study limits how many parts regular simplicial partitions can overlap.
problem Bounding the intersection number of regular simplicial partitions.
method Analyzing the properties of regular simplicial partitions.
result Established a maximum limit for the intersection number.
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones. However, the resultant optimization problem is much harder. In this paper, for a …
Proves regularity for multiple membrane solutions.
problem Stationary solutions to the multiple membrane problem.
method Uses -regularity estimate.
result Proves regularity for stationary solutions.