Bayesian optimization gains efficiency by leveraging symmetries through a modified max kernel.
problem Improving Bayesian optimization efficiency for functions with group symmetries.
method Developed a PSD projection of the max kernel to exploit symmetries without violating kernel properties.
result The modified max kernel achieves lower regret compared to existing invariant and non-invariant kernels.
The min-max kernel is a generalization of the popular resemblance kernel (which is designed for binary data). In this paper, we demonstrate, through an extensive classification study using kernel machines, that the min-max kernel often provides an effective measure of similarity for nonnegative data. As the min-max ker…
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-χ2, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (γ). Interestingly, for a …
Adaptive kernel model for multi-view learning reduces overfitting and scales with data.
problem Overfitting and high computational cost in multi-view learning.
method Bayesian framework, Dirichlet process Gaussian mixtures, random Fourier features, max-margin constraints, MCMC sampler.
result Adaptive learning of shift-invariant kernels from data.
Following the very recent line of work on the ``generalized min-max'' (GMM) kernel, this study proposes the ``generalized intersection'' (GInt) kernel and the related ``normalized generalized min-max'' (NGMM) kernel. In computer vision, the (histogram) intersection kernel has been popular, and the GInt kernel generaliz…
Proposes a new feature preprocessing method using kernel density integral transformation.
problem Feature preprocessing for tabular data in machine learning and statistics.
method Kernel density integral transformation as a drop-in replacement or improved alternative to min-max scaling and quantile transformation.
result Frequently outperforms min-max scaling and quantile transformation with hyperparameter tuning.
The paper proposes a novel MKL approach for OCC using ℓp-norm constraints.
problem Addressing the MKL problem for one-class classification.
method A min-max saddle point Lagrangian optimisation problem is formulated and solved efficiently.
result The proposed method outperforms baselines and other algorithms on various data sets.
Max-sliced Wasserstein metric reduces high-dimensional data to 1D for better estimation.
problem Curse of dimensionality in optimal transport.
method Introduces max-sliced Wasserstein metric to reduce high-dimensional problems to 1D.
result Uniform ratio bounds of empirical measures on RKHS concentrate uniformly fast at parametric rates.
We propose a novel data-driven method to learn a mixture of multiple kernels with random features that is certifiabaly robust against adverserial inputs. Specifically, we consider a distributionally robust optimization of the kernel-target alignment with respect to the distribution of training samples over a distributi…
We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpret…
Paper develops KMS Wasserstein for high-dimensional data reduction.
problem Optimal transport's curse of dimensionality in high-dimensional data.
method Kernel max-sliced (KMS) Wasserstein distance for dimensionality reduction.
result Sharp finite-sample guarantees for KMS p-Wasserstein distance. New kernel connects deep learning to optimization, improving generalization.
problem Understanding why deep neural networks generalize well at over-parameterization.
method Established Neural Optimization Kernel (NOK) linking deep NN to optimization problems.
result New generalization bound for deep structured approximated NOK architecture.
The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM ker…
Adaptive kernels from neural networks improve model performance.
problem Improving neural network performance through adaptive kernels.
method Deriving adaptive kernels from infinite-width neural networks using feature learning and gradient flow training.
result Adaptive kernels achieve lower test loss compared to traditional kernels.
LCMQR improves prediction intervals by adapting to local heteroscedasticity.
problem Efficient and adaptive prediction intervals for local heteroscedasticity.
method LCMQR combines multi-quantile information with kernel-based localization.
result LCMQR constructs tighter intervals than prior methods, especially in heterogeneous environments.
Generalizes leverage score sampling for neural networks, accelerating kernel methods and deep learning.
problem Accelerating kernel methods and deep learning training.
method Generalizes leverage score sampling to neural networks and proves equivalence to neural tangent kernel ridge regression.
result Equivalence between regularized neural network and neural tangent kernel ridge regression under leverage score sampling initialization.
The study shows algebraic Bergman kernels imply finite type boundaries in complex domains.
problem Understanding the relationship between algebraic Bergman kernels and the finite type of boundaries in complex domains.
method Analyzing algebraic Bergman kernels and their implications on the finite type of boundaries in smoothly bounded pseudoconvex domains in C2. result The boundary of a smoothly bounded pseudoconvex domain with an algebraic Bergman kernel of degree d is of finite type with type r≤2d. We propose a novel adversarial training method in feature space that improves model robustness and computational efficiency.
problem Improving model robustness against adversarial input perturbations with computational efficiency.
method Shift from input to feature-space perturbations, reformulating the adversarial training problem in reproducing kernel Hilbert spaces, enabling exact solution of inner maximization and efficient optimization.
result The feature-perturbed formulation is a relaxation of the original problem and provides a regularized estimator that adapts to noise and function smoothness.
The recently proposed "generalized min-max" (GMM) kernel can be efficiently linearized, with direct applications in large-scale statistical learning and fast near neighbor search. The linearized GMM kernel was extensively compared in with linearized radial basis function (RBF) kernel. On a large number of classificatio…
Generative adversarial networks (GANs) are designed with the help of min-max optimization problems that are solved with stochastic gradient-type algorithms which are known to be non-robust. In this work we revisit a non-adversarial method based on kernels which relies on a pure minimization problem and propose a simple…
New group constructed from cube complex properties.
problem Creating a new group from cube complex properties.
method Cubical Rips construction for finitely presented groups.
result New group surjects onto a given group with specific properties.
While tree methods have been popular in practice, researchers and practitioners are also looking for simple algorithms which can reach similar accuracy of trees. In 2010, (Ping Li UAI'10) developed the method of "abc-robust-logitboost" and compared it with other supervised learning methods on datasets used by the deep …
Paper presents an efficient algorithm for estimating Lipschitz functions from noisy data.
problem Estimating unknown Lipschitz functions from noisy observations.
method Extends max-affine methods to Lipschitz setting using nonlinear feature expansion and adaptive partitioning.
result Achieves minimax convergence rate with respect to intrinsic dimension, up to logarithmic factors.
The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple normalization step as we theoretically demonstrate. We name the improved scheme …
pGMM kernel outperforms ordinary ridge regression and RBF kernel ridge regression without tuning.
problem Comparing pGMM kernel regression with other ridge regression methods.
method Implemented and compared pGMM kernel regression with ordinary ridge regression and RBF kernel ridge regression.
result pGMM kernel performs well without tuning and can match boosted trees with parameter tuning.
TML package uses tropical geometry for machine learning tasks.
problem Statistical learning problems.
method Tropical convexity computations, Hit and Run sampler, tropical metrics.
result First R package for tropical geometric machine learning.
Algorithm improves SVM classification in non-Euclidean spaces.
problem Limitations of traditional SVM in non-Euclidean spaces.
method Covariance-adjusted SVM using Cholesky Decomposition.
result Cholesky-SVM outperforms traditional SVM in non-Euclidean spaces.
This work develops a learning theory for inferring interaction kernels in complex agent systems.
problem Modeling complex interactions in systems of particles or agents.
method Nonparametric regression and approximation theory.
result Strong consistency and optimal convergence rates for estimators of interaction kernels.
Paper analyzes SGD in kernel regression, showing it outperforms offline methods.
problem Performance of SGD in kernel regression compared to offline methods.
method Analyzes Stochastic Gradient Descent (SGD) in kernel regression under misspecified models.
result SGD achieves min-max optimal rates up to constants, avoiding saturation.
This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.
problem Functional linear regression without target function in RKHS.
method Integral operator approach to establish upper bounds and prove asymptotic optimality.
result Sharp finite sample upper bounds and asymptotic optimality of divide-and-conquer estimators.
Generative Adversarial Networks (GANs) were intuitively and attractively explained under the perspective of game theory, wherein two involving parties are a discriminator and a generator. In this game, the task of the discriminator is to discriminate the real and generated (i.e., fake) data, whilst the task of the gene…
Tandem mass spectrometry (MS/MS) is a high-throughput technology used toidentify the proteins in a complex biological sample, such as a drop of blood. A collection of spectra is generated at the output of the process, each spectrum of which is representative of a peptide (protein subsequence) present in the original co…
We propose a procedure for supervised classification that is based on potential functions. The potential of a class is defined as a kernel density estimate multiplied by the class's prior probability. The method transforms the data to a potential-potential (pot-pot) plot, where each data point is mapped to a vector of …
Study introduces statistical mechanics for min-max problems.
problem Understanding the properties of min-max problems in high dimensions.
method Statistical mechanical formalism for analyzing min-max problems.
result Derives the relationship between training data and generalization error.
Recent works have shown that on sufficiently over-parametrized neural nets, gradient descent with relatively large initialization optimizes a prediction function in the RKHS of the Neural Tangent Kernel (NTK). This analysis leads to global convergence results but does not work when there is a standard ℓ2 regulari…
Study shows strong min-max principle for phase transitions.
problem Understanding nodal sets near minimal hypersurfaces.
method Analogous to White's principle, applies to Allen-Cahn energy.
result Strong min-max principle for phase transitions.
Equity-Transformer solves NP-hard min-max routing problems efficiently.
problem Min-max routing problems with multiple agents and large-scale applications.
method Sequential planning approach with Transformer and equitable workload distribution inductive biases.
result Significant runtime and cost reductions in min-max mTSP and min-max mPDP tasks.
Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.
problem Understanding max- and min-stability in stochastic dominance.
method Representation theorem for functionals satisfying max-stability, combining max- and min-stability to define Lambda-quantiles.
result New characterizations of functionals, including Lambda-quantiles, in finance and political science.
Max-min margin Markov networks improve consistency in structured prediction.
problem Statistical inconsistency in max-margin methods for structured prediction.
method Defining a max-min margin formulation to overcome statistical inconsistency.
result Proves consistency and provides an explicit algorithm with finite sample generalization bounds.
Upper bound for Morse index of min-max varifolds.
problem Bounding Morse index of varifolds.
method Proving upper bound for Morse index of min-max stationary integral varifolds.
result Upper bound for Morse index of min-max stationary integral varifolds.
Upper bound for max-sliced 2-Wasserstein distance between measures.
problem Estimating distance between probability measures and their empirical counterparts.
method Same technique as previous work, upper bound approach.
result Upper bound for expected max-sliced 2-Wasserstein distance.
Estimates parameters in max-linear Bayesian networks with noise.
problem Causal inference in extreme-value settings with noise parameters.
method Max-plus algebra and logarithm transformation, normal distribution estimation, EM algorithm and quadratic optimization.
result An estimator of a parameter for each edge in a DAG is normally distributed.
Localized min-max method proves minimal hypersurface existence.
problem Existence of minimal hypersurfaces in complete manifolds.
method Localized min-max approach to prove existence.
result Existence of complete embedded minimal hypersurface with index at most one.
The paper solves min-max widths on a 3-sphere and strengthens multiplicity theorems.
problem Which min-max widths of the unit 3-sphere lie between 2π2 and 8π? method Homological min-max theory and stronger versions of multiplicity one theorems.
result Proves the 10th to 13th min-max widths of the unit 3-sphere lie between 2π2 and 8π. Max flow/min cut theorem extended to currents and topology.
problem Continuous max flow/min cut theorem for complex domains.
method Continuous analogue of max flow/min cut theorem considering topology.
result Continuous max flow/min cut theorem proven for currents and laminations.
Paper corrects Max-Margin loss for multi-label tasks.
problem Max-Margin loss inconsistency in multi-label classification.
method Introduced Restricted-Max-Margin loss.
result Consistent loss for multi-label tasks under milder conditions.
In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, θ(⋅)) and "nature," who picks the matrix X of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel Wθ(X)/D(X), where Wθ(X) is the…
Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be used to obtain maximum a posteriori estimates). The limiting step to …