Proposes SCR-Apriori for efficient mining of SCR-patterns.
problem Mining high-quality `Set of Contrasting Rules'-pattern (SCR-pattern) efficiently.
method Integrates SCR-pattern structure into Apriori algorithm to prune search space.
result Significantly reduces computational cost compared to state-of-the-art.
Enhances distributed Apriori-like frequent itemsets mining performance.
problem Improving performance of distributed Apriori-like frequent itemsets mining.
method Presented a new distributed approach considering Apriori algorithm's characteristics and distribution aspects.
result The proposed approach significantly enhances performance and achieves good scalability compared to a typical distributed Apriori algorithm.
The paper provides estimates for Kähler metrics with constant scalar curvature.
problem Estimating Kähler metrics with constant scalar curvature.
method Derives apriori estimates for Kähler metrics in terms of a C 0 C^0 C 0 bound. result Higher order derivatives can be estimated in terms of a C 0 C^0 C 0 bound for the Kähler potential. New method for faster TPM from multivariate time series.
problem Mining predictive complex temporal patterns from multivariate time series.
method Fast Temporal Pattern Mining with Extended Vertical Lists.
result Significantly faster performance than previous algorithm.
New geometric approach gives apriori estimate for optimal transport maps.
problem Proving regularity of optimal transport maps under Ma--Trudinger--Wang condition.
method Geometric derivation using pseudo-Riemannian geometry.
result New derivation of C 1 C^1 C 1 interior estimate for optimal maps. This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.
problem Boundedness conditions for Kähler metrics with bounded entropy and scalar curvature.
method Slightly relaxes the boundedness condition on the scalar curvature.
result Apriori estimates and C 3 , α C^{3,α} C 3 , α estimate for the potential of the Kähler metrics under relaxed conditions. It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In addition, we obtain an apriori bound on the curvature of stationary vacuum soluti…
Methodology for learning sparse models using all multiplicative interactions efficiently.
problem Learning high-order feature interactions with fine control.
method Fine Control Kernel framework, combining Fenchel Duality and Apriori algorithm.
result Efficiently solves large sparse learning problems with sparse feature screening rules.
The aim of this paper is to give a proof the Frankel conjecture by using the Kahler Ricci flow alone without assuming apriori the existence of Kahler Einstein metrics. However, there is an essential difference between the real case and the Kahler case. I didn't realize this difference in the calculation of the previous…
We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting curves with boundary to curves without boundary. Our method is new and geometric and…
We consider the mean curvature flow of a closed hypersurface in the complex or quaternionic projective space. Under a suitable pinching assumption on the initial data, we prove apriori estimates on the principal curvatures which imply that the asymptotic profile near a singularity is either strictly convex or cylindric…
Paper refines Chen-Cheng's estimates for Kähler metrics.
problem Uniform boundedness of scalar curvature assumption.
method Replacing uniform boundedness with L p L^p L p -boundedness. result Improved estimates for Kähler metrics under L p L^p L p -boundedness. A parameter-free method clusters data points from multiple subspaces.
problem Subspace clustering with unknown number of clusters and parameters.
method Clusters data points based on angle differences between subspaces; merges clusters until final clustering is obtained.
result Parameter-free approach for clustering data points from multiple subspaces.
System recommends disease treatments based on big data and cloud computing.
problem Inaccurate disease classification and treatment recommendations due to complex symptoms and multi-pathogenesis.
method DPCA for disease-symptom clustering, Apriori for D-D and D-T rules, parallel Apache Spark implementation.
result Effective disease-symptom clustering and accurate treatment recommendations for inexperienced doctors.
This paper connects graph curvature to community structure.
problem Understanding the relationship between network curvature and community formation.
method Defining curvature on networks and analyzing its relation to community structure.
result Apriori bounds on the curvature of intercommunity edges.
We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact n n n -dimensional manifold which has nonnegative Ricci curvature and strictly convex boundary. When n = 3 n=3 n = 3 , this implies apriori area and curvature estimates for these minimal surfaces in terms of the …
Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters r r r is known apriori. In this paper, we propose an approach based on semi-definite relaxations, which does not require…
Universal algorithm minimizes adaptive regret for various convex functions.
problem Minimizing adaptive regret in changing environments for multiple convex functions.
method Borrowing MetaGrad's idea of multiple learning rates and using sleeping experts.
result First universal algorithm for minimizing adaptive regret of convex functions.
It has been shown in \cite{DPSU} that, under some additional assumptions, two simple domains with the same scattering data are equivalent. We show that the simplicity of a region can be read from the metric in the boundary and the scattering data. This lets us extend the results in \cite{DPSU} to regions with the same …
Study on residual Monge-Ampère mass of complex functions with directional Lipschitz continuity.
problem Estimating the residual Monge-Ampère mass of plurisubharmonic functions.
method General decomposition formula under Sasakian structure, L 1 L^{1} L 1 -apriori estimate, upper-bound estimate on residual mass. result Upper-bound estimate on residual mass for uniformly directional Lipschitz continuity confirmed.
The paper proves stability for Möbius transformations in high dimensions.
problem Quantifying how close a map is to a Möbius transformation.
method Local average conformal-isoperimetric deficit controls map deviation.
result Optimal bounds on the deviation of maps from Möbius transformations.
Safe screening rules reduce computation time in logistic regression with ℓ 0 − ℓ 2 \ell_0-\ell_2 ℓ 0 − ℓ 2 regularization.
problem Efficiently solving logistic regression with many features and regularization.
method Screening rules based on Fenchel dual lower bounds of strong conic relaxations.
result A high percentage of features can be safely removed before solving, leading to substantial speed-up.
A new method for faster optimization of noisy functions.
problem Optimizing noisy functions efficiently.
method A universal and adaptive second-order method for convex functions.
result Achieves O ( σ / T ) O(σ/ \sqrt{T}) O ( σ / T ) convergence for stochastic oracles and O ( 1 / T 3 ) O( 1 / T^3) O ( 1/ T 3 ) for deterministic oracles. Paper proves existence of constant scalar curvature Kähler metrics under certain conditions.
problem Existence of constant scalar curvature Kähler metrics.
method Generalized apriori estimates and used automorphism group discreteness, K-energy non-increasing, and properness of K-energy.
result Proves equivalence of non-existence of cscK metric and existence of a destabilized geodesic ray with non-increasing K-energy.
Gaussian processes over graphs enforce specific signal profiles and outperform conventional GPs.
problem Signal processing over graphs with specific profiles.
method Graph Laplacian regularization to enforce desired signal profiles, proving predictive variance advantage.
result Gaussian processes over graphs have strictly smaller predictive variance than conventional GPs.
Safe screening rules reduce ℓ 0 \ell_0 ℓ 0 -regression computation by fixing 76% of variables.
problem Efficiently solving ℓ 0 \ell_0 ℓ 0 -regression problems with large datasets. method Convex relaxation and safe screening rules to eliminate variables.
result 76% of variables can be fixed to their optimal values, reducing computational burden.
This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a general state-space modelling methodology, which allows modelling, estimation and…
Algorithm identifies nearest mode in noisy data.
problem Identifying the point with the minimum k-th nearest neighbor distance in unknown multivariate probability density.
method Sequential learning algorithm using noisy oracle queries to adaptively decide which points to query.
result Upper bounds on query complexity show significant improvement over baselines.
Recursive prediction of graph signals with new nodes added.
problem Predicting graph signals with new nodes added over time.
method Recursive prediction of graph signals using incoming nodes.
result Recursive method results in good prediction performance close to full graph knowledge.
The K-Mean and EM algorithms are popular in clustering and mixture modeling, due to their simplicity and ease of implementation. However, they have several significant limitations. Both coverage to a local optimum of their respective objective functions (ignoring the uncertainty in the model space), require the apriori…
We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only continuous and can vary; the curves are only assumed to have fixed ``topological type'', …
According to a classical result of E.~Calabi any hyperbolic affine hypersphere endowed with its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be described as the level sets of solutions to the "hyperbolic" toric Kähler-Einstein equation e Φ = det D 2 Φ e^Φ = \det D^2 Φ e Φ = det D 2 Φ on proper convex cones. We…
Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H 1 H_1 H 1 . Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Mar…
New algorithm finds k-centers from noisy distance estimates.
problem Finding k-centers in unknown metric spaces with noisy distance queries.
method Active algorithms using UCB, Thompson Sampling, and Track-and-Stop.
result Approximation ratio of two with high probability.
Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.
problem Understanding the relationships between different types of surfaces and their integrable systems.
method Unified view through families of flat connections and parallel sections.
result Complete description of links between different surface types and their dressing transformations.
The paper develops online methods to control familywise error rate in growing hypothesis testing sequences.
problem Controlling familywise error rate in a growing sequence of hypotheses over time.
method Unified algorithmic concepts for offline and online FWER control, including new adaptive online algorithms.
result Substantial gains in power demonstrated and formally proved in a Gaussian sequence model.
Compactness theorem for Riemannian manifolds with volume and curvature bounds.
problem Investigating the regularity of limit spaces of Riemannian manifolds.
method Local volume growth condition, compactness theorem, different convergence notion.
result Compactness theorem for Riemannian manifolds with L p L^p L p curvature bounds and volume growth assumption. MAntRA combines machine learning and Bayesian methods for time-dependent reliability analysis of unknown systems.
problem Time-dependent reliability analysis of systems with unknown governing physics.
method Combines machine learning, Bayesian statistics, and stochastic integration to discover and analyze SDEs from data.
result Demonstrates the effectiveness of MAntRA on three numerical examples, indicating its potential for in-situ and heritage structure analysis.
This paper solves deep learning's edge sensitivity issue by swapping important and irrelevant segments in synthetic data.
problem Edge sensitivity and high computational cost in deep learning classification models.
method Synthetic data with swapped segments to implicitly define receptive fields, preserving label information.
result The method drives networks to early convergence and appropriate solutions, improving person re-identification.
A new method balances model quality and Byzantine robustness in Federated Learning.
problem Byzantine clients sending arbitrary or malicious information.
method Practical weight-truncation-based preprocessing method.
result Empirically demonstrates good balance between model quality and Byzantine robustness.
DVRL uses RL to estimate data value for machine learning tasks.
problem Adaptive learning of data value for machine learning tasks.
method Meta learning framework with reinforcement learning for data value estimation.
result DVRL yields superior data value estimates compared to alternative methods.
Generates confident out-of-distribution samples to improve classifier robustness.
problem Overconfidence in deep learning models on out-of-distribution inputs.
method Uses a GAN to generate out-of-distribution samples that the classifier is confident on, maximizing entropy.
result Shows effectiveness on handwritten characters and natural images datasets.
The paper introduces a method to learn models with built-in explanations.
problem Lack of interpretability in deep learning models.
method Formalizes learning with explanation constraints and provides a learning theoretic framework.
result Models that satisfy these constraints have reduced Rademacher complexities, improving their performance.
This paper introduces a method to find complete and interpretable concept-based explanations for deep neural networks.
problem Lack of complete and interpretable concept-based explanations in deep neural networks.
method Definition of completeness, concept discovery method, and importance score calculation using game-theoretic notions.
result The proposed method finds complete and interpretable concept-based explanations for deep neural networks.
The study examines complete Kähler manifolds with nonnegative Ricci curvature and discovers rigidity properties.
problem Characterizing and understanding properties of complete Kähler manifolds with nonnegative Ricci curvature.
method Analyzes volume growth, scalar curvature, and curvature decay to establish rigidity results.
result Complete Ricci flat Kähler manifolds with Euclidean volume growth are rigid, with unique tangent cones.
Distributed quantization improves classification accuracy with less data.
problem Efficiently classify features from distributed nodes with limited communication.
method Designs tailored quantization schemes for classification, proving NP-hardness and proposing polynomial-time algorithms.
result Tailored quantizers can reduce bit communication by more than a factor of two for the same accuracy.
New RL algorithm gives tighter bounds without domain knowledge.
problem Improving worst-case performance bounds in reinforcement learning.
method Derives algorithm for finite horizon discrete MDPs with analysis yielding state-of-the-art worst-case regret bounds.
result Substantially tighter bounds for environments with small environmental norm, no prior knowledge required.
Study stability of rigid motions and Möbius transformations on spheres, proving new rigidity estimates.
problem Stability of rigid motions and Möbius transformations on spheres.
method Investigates both linear and nonlinear stability aspects of rigid motions and Möbius transformations of S^(n-1) into R^n.
result Optimal rigidity estimates for isometric and conformal maps from S^(n-1) to R^n, including new Korn-type inequalities.