New lower bounds for linear classification problems in high dimensions.
problem Linear classification problems in high-dimensional spaces.
method Reduction from hardness conjectures for Affine Degeneracy testing and k-Sum problems.
result Matching lower bounds of Ω(n^d) and respectively Ω(1/ε^d) for Maximum Halfspace Discrepancy problem.
New non-existence results for harmonic maps into perturbed cones.
problem Proper harmonic maps into perturbed cones in \(\mathbb{R}^n\), horospheres in \(\mathbb{H}^n\).
method Extension of foliated maximum principle to non-compact settings.
result New non-existence results for proper harmonic maps.
While it is well known from examples that no interesting `halfspace theorem' holds for properly immersed complete n-dimensional self-translating mean curvature flow solitons in Euclidean space Rn+1, we show that they must all obey a general `bi-halfspace theorem': Two transverse vertical halfspaces can …
We study properly immersed ancient solutions of the codimension one mean curvature flow in n-dimensional Euclidean space, and classify the convex hulls of the subsets of space reached by any such flow. In particular, it follows that any compact convex ancient mean curvature flow can only have a slab, a halfspace or a…
Study finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.
problem Understanding convergence rates of maximum mean discrepancies for Farey sequences.
method Identifying positive-semidefinite kernels and their polynomial convergence rates.
result Polynomial convergence rate of maximum mean discrepancies of Farey sequences is equivalent to the Riemann hypothesis.
The paper proposes a method to produce well-calibrated predictions in regression tasks using maximum mean discrepancy.
problem The need for accurate uncertainty quantification in machine learning predictions.
method The method uses maximum mean discrepancy to minimize the kernel embedding measure and calibrate predictions.
result The method produces well-calibrated and sharp prediction intervals, outperforming state-of-the-art methods.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
New principle for harmonic maps helps study higher-dimensional submanifolds.
problem Understanding unboundedness of totally geodesic projections in higher codimension.
method Introducing a flexible notion of convexity and applying it to harmonic and conformal maps.
result New maximum principle for harmonic maps applicable to various geometric settings.
We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way of coupling Brownian motions on two minimal surfaces. This coupling is then used …
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
Generative neural network simulates characteristic functions.
problem Simulating from characteristic functions inaccessible in closed form.
method Generative neural network with Maximum-Mean-Discrepancy loss.
result Universal algorithm independent of dimensionality and function properties.
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
Generalizes halfspace theorems to higher dimensions for self-shrinkers.
problem Limitations of halfspace theorems in higher dimensions for self-shrinkers.
method Extends codimension 1 results to arbitrary codimension.
result Establishes new halfspace theorems for self-shrinkers in arbitrary codimension.
Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation to measure the discrepancy between the source and target domain distributions. Many existing domain adaptation approaches are based on the joint MMD, which is computed as the (weighted) sum of the marginal distribution discrepancy and the condi…
Paper proposes MMD-Sense-Analysis for detecting word sense shifts.
problem Detecting and interpreting shifts in word meanings over time.
method Leverages Maximum Mean Discrepancy (MMD) to identify and explain word sense changes.
result Demonstrates effectiveness of MMD-Sense-Analysis through empirical results.
A new gradient flow for MMD with closed-form implementation.
problem Existing gradient flows either lack tractable numerical implementation or require strong assumptions.
method Introduces a (de)-regularized Maximum Mean Discrepancy (DrMMD) and its gradient flow.
result Guarantees near-global convergence for a broad class of targets in both continuous and discrete time.
MMD test detects adversarial attacks by addressing kernel limitations and non-independence issues.
problem MMD test's failure to detect adversarial attacks.
method Replaced Gaussian kernel with deep kernel, maximized test power, and used wild bootstrap for non-independence.
result MMD test is aware of adversarial attacks.
We study the strong maximum principle for horizontal (p-) mean curvature operator and p-(sub)laplacian operator on subriemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher…
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
Polynomial-time tester-learner for general halfspaces with Gaussian adversarial noise.
problem Learning general halfspaces with adversarial label noise.
method Reduction to testable learning of nearly homogeneous halfspaces.
result First polynomial time tester-learner for general halfspaces with dimension-independent misclassification error.
Efficient algorithms for monophonic halfspaces in graphs simplify learning and compression.
problem Learning and compressing monophonic halfspaces in graphs.
method 2-satisfiability based decomposition theorem, efficient algorithms for various learning problems.
result Achieved efficient and nearly optimal algorithms for various learning problems.
Study efficient learning of robust halfspaces with noise.
problem Learning robust halfspaces in the presence of adversarial perturbations and random label noise.
method Provides conditions for robust learnability and a simple algorithm for any ℓ_p perturbation.
result Simple computationally efficient algorithm for robust learning with random label noise.
New lower bounds show learning intersections of halfspaces is hard even for a few halfspaces.
problem Learning intersections of halfspaces in polynomial time under standard assumptions.
method Unified connection to parallel pancakes distribution for proving hardness.
result Learning ω(loglogN) halfspaces in dimension N requires super-polynomial time under standard assumptions. We develop the Lorentzian geometry of a crooked halfspace in 2+1-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types, giving an explicit slice for the action of the automorphism group. The set of parall…
New conditions ensure MMDs separate and converge to target distributions.
problem Ensuring MMDs separate and converge to target distributions.
method Deriving new sufficient and necessary conditions for MMDs on separable metric spaces.
result First KSDs that exactly metrize weak convergence to P.
Efficiently learns monophonic halfspaces in graph vertices.
problem Learning binary classifiers on graph vertices using monophonic halfspaces.
method Polynomial-time algorithm for consistent hypothesis checking, based on structural insights and reduction to 2-satisfiability.
result Near-optimal passive sample complexity for monophonic halfspaces in polynomial time.
Optimizes MMD learning for generative models with theoretical guarantees.
problem Theoretical guarantees for optimizing non-convex MMD objectives.
method Analyzes MMD optimization landscape for specific distributions.
result Gradient-based methods globally minimize MMD objective for certain distributions.
New algorithms minimize MMD to approximate probability measures efficiently.
problem Approximating probability measures by representative point sets.
method Sequential greedy minimization of maximum mean discrepancy (MMD) over candidate sets, with mini-batch variants.
result Consistency of proposed algorithms and mini-batch variants established.
Non-convex SGD learns halfspaces with adversarial label noise efficiently.
problem Agnostically learning halfspaces in adversarial label noise settings.
method Non-convex SGD optimization for halfspace learning.
result Non-convex SGD achieves misclassification error close to optimal with adversarial noise.
New algorithm for reliable learning of Gaussian halfspaces with improved sample and computational complexity.
problem Learning halfspaces under Gaussian marginals with reliable agnostic model.
method Developed a new algorithm for reliable learning of Gaussian halfspaces with specific sample and computational complexity.
result Achieved a new algorithm with improved sample and computational complexity for reliable learning of Gaussian halfspaces.
A new method uses neural tangent kernel to efficiently compute MMD statistic.
problem Efficiently computing Maximum Mean Discrepancy (MMD) statistic with low memory and computational complexity.
method Identifies a connection between neural tangent kernel (NTK) and MMD to develop a computationally and memory-efficient approach.
result The proposed NTK-MMD statistic is validated through numerical experiments on synthetic and real-world datasets.
Study learning halfspaces with Massart noise under Gaussian distribution, improving previous results.
problem Learning halfspaces with Massart noise under Gaussian distribution, especially when the parameter is 1/2.
method Developed algorithms for general and homogeneous halfspaces with sample and computational complexities.
result Established qualitatively matching lower bounds for the complexities of learning algorithms.
The paper shows how MMD metrizes weak convergence for certain kernels.
problem Characterizing MMD metrizing weak convergence for a wide class of kernels.
method Proving MMD metrizes weak convergence for specific kernels on a locally compact space.
result Corrected prior results and identified new kernels metrizing weak convergence.
A new method for kernel tests without data splitting increases power.
problem Lack of power in kernel-based tests due to data splitting.
method Selective inference framework to learn hyperparameters and test on full sample.
result Empirically larger test power without data splitting, regardless of split proportion.
Study privacy and robustness in learning halfspaces, proving hard trade-offs.
problem Balancing privacy and robustness in learning halfspaces.
method Proves nearly tight bounds on sample complexity for robust private learning of halfspaces.
result Robust and private learning is harder than robust or private learning alone.
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a notion we call maximum weighted loss discrepancy (MWLD), the maximum (weighted) d…
We prove a vertical halfspace theorem for surfaces with constant mean curvature H=1/2, properly immersed in the product space $\h^2\times\re,$ where $\h^2$ is the hyperbolic plane and $\re$ is the set of real numbers. The proof is a geometric application of the classical maximum principle for second order elliptic …
Polynomial-time algorithm for learning halfspaces with Gaussian-distributed data and adversarial noise.
problem Learning halfspaces in the presence of adversarial label noise.
method Iterative soft localization technique enhanced with appropriate testers.
result Output a halfspace with misclassification error $O(\opt)+\eps$.
Gradient descent finds halfspaces with low error for agnostic learning.
problem Agnostic learning of linear halfspaces with convex surrogates.
method Gradient descent on convex surrogates for zero-one loss.
result Gradient descent finds halfspaces with error O(OPT1/2+ε) in poly time and sample complexity. MMD-Flagger detects hallucinations in LLMs by tracking MMD between outputs and temperature-generated counterparts.
problem Detecting hallucinations in large language models.
method Maximum Mean Discrepancy (MMD) to track the difference between model outputs and temperature-generated counterparts.
result MMD-Flagger detects most hallucinations by analyzing the shape of the MMD trajectory.
First proper learning algorithm for Gaussian halfspaces with matching sample and computational complexity.
problem Agnostically learning halfspaces under Gaussian distribution.
method First proper learning algorithm with matching sample and computational complexity.
result First proper learning algorithm for agnostically learning halfspaces under Gaussian distribution with matching sample and computational complexity.
Improved MMD estimator for likelihood-free inference.
problem Computational challenges in estimating MMD for likelihood-free inference.
method Optimally-weighted MMD estimator with improved sample complexity.
result Significantly improved sample complexity for accurate MMD estimation.
Secure SMMD enables data privacy in federated learning.
problem Data privacy in federated learning.
method Homomorphic encryption-based Secure Maximum Mean Discrepancy (SMMD).
result Secure SMMD avoids data leakage and enables effective knowledge transfer.
Study on learning halfspaces under adversarial perturbations, finding computational hardness.
problem Learning halfspaces in the presence of adversarial noise.
method Introduced an efficient learning algorithm and proved a nearly matching computational hardness result.
result The L∞ perturbations case is provably computationally harder than 2≤p<∞. Adversarial training improves robustness of halfspaces in noisy data.
problem Learning robust halfspaces in the presence of label noise.
method Adversarial training with binary cross-entropy or nonconvex sigmoidal loss.
result Adversarial training yields robust halfspaces with improved classification error.
Paper uses statistical depth to create DP estimators for regression.
problem Creating differentially private estimators in high dimensions.
method Uses halfspace and regression depth to analyze maximum influence and construct DP estimators.
result New DP estimators for location and regression show favorable performance.
New method improves source separation using NMF and adversarial learning.
problem Source separation in single channel data.
method Maximum Discrepancy Generative Regularization applied to NMF.
result Improvement in reconstructed signals, especially in weak supervision scenarios.
Proposes TFDF to learn transferable and discriminative features for unsupervised domain adaptation.
problem Difficult to induce supervised classifier without labeled data in unsupervised domain adaptation.
method TFDF optimizes transferability and discriminability by aligning distributions and minimizing class confusion.
result TFDF achieves better performance on real-world datasets compared to existing methods.