New framework assesses graph-learning datasets for better evaluation.
problem Insufficient evaluation of graph-learning datasets and methods.
method Introduces Rings framework for dataset ablations and proposes performance separability and mode complementarity measures.
result Demonstrates utility of Rings framework for graph-learning dataset evaluation.
Geometric programming approach for traffic equilibrium problems.
problem Optimizing traffic equilibrium in transportation systems.
method Finslerian dynamical model for nonlinear complementarity problems.
result Effective solution for various equilibrium problems in transportation.
Study efficient numerical methods for American basket options.
problem Valuation of American basket options.
method Partial differential complementarity problems (PDCPs) and efficient discretization.
result Approximations of American basket options are close and converge favourably.
Improved Frank-Wolfe algorithm for polytopes converges linearly with dimension dependence on optimal face.
problem Efficiently solving convex minimization problems over polytopes with linear rate.
method Revisiting Frank-Wolfe algorithm with strict complementarity assumption and away-steps.
result Linear convergence rate independent of polytope dimension for optimal face.
New tensor recovery method improves efficiency under strict complementarity.
problem Efficiently recovering low-rank tensors using tensor nuclear norm.
method Developed strict complementarity condition for tensor nuclear norm ball and applied to gradient methods.
result Standard gradient methods achieve linear convergence and nearly linear runtime under strict complementarity.
In a previous paper the second author showed that if M is a pseudomanifold with complementarity other than the 6-vertex real projective plane and the 9-vertex complex projective plane, then M must have dimension ≥6, and - in case of equality - M must have exactly 12 vertices. In this paper we prove that suc…
New method solves subspace optimization problems efficiently.
problem Finding a k-dimensional subspace in high dimensions.
method Local linear convergence of gradient methods under strict complementarity.
result Gradient method converges linearly in high dimensions.
Study explores optimal strategies in games with multiple players and mean-field interactions.
problem Optimal strategies in games with multiple players and mean-field interactions.
method Exploration of three different notions of optimality, including mean-field control solution, mean-field coarse correlated equilibria, and mean-field Nash equilibria.
result Approximation of cooperative and competitive equilibria in large N-player games by mean-field control and mean-field equilibria. Designs algorithms to assist humans without affecting their decisions.
problem Algorithms often fail to improve human decisions.
method Formalizes algorithm design using potential outcomes framework and monotonicity assumption.
result Derives minimax optimal recommendation algorithms for limited data.
This paper studies an environment of simultaneous, separate, first-price auctions for complementary goods. Agents observe private values of each good before making bids, and the complementarity between goods is explicitly incorporated in their utility. For simplicity, a model is presented with two first-price auctions …
In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential complementarity problem. The stability and convergence of the new methods are extensively inv…
Endogenous business cycles explain higher comovement across countries.
problem Standard models struggle to explain high comovement in business cycles across countries.
method Developed a demand-driven reduced-form model with strategic complementarities and international trade linkages.
result Combining endogenous business cycles with exogenous shocks matches empirical comovement levels.
New method uses product embeddings to predict bundle success.
problem Designing effective product bundles in large retail settings.
method Leverage historical purchases and clickstream data to generate product embeddings, then use heuristics for complementarity and substitutability.
result Embeddings-based heuristics predict bundle success, robust across categories and retailers.
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explic…
In this work we present a review of the state of the art of information theoretic feature selection methods. The concepts of feature relevance, redundance and complementarity (synergy) are clearly defined, as well as Markov blanket. The problem of optimal feature selection is defined. A unifying theoretical framework i…
Periodic surfaces have a limited number of bending modes, equal to their membrane modes.
problem Understanding the limitations of bending modes in periodic surfaces.
method Analyzing deformation modes of periodic, piecewise smooth, simply connected surfaces.
result Effective membrane modes and bending modes are orthogonal, limiting the total number of modes to 3.
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
Motivated by advantages of current-mode design, this brief contribution explores the implementation of weight matrices in neuromemristive systems via current-mode memristor crossbar circuits. After deriving theoretical results for the range and distribution of weights in the current-mode design, it is shown that any we…
A new method for analyzing product competition using low-dimensional embeddings.
problem Computational challenges in studying product-level competition for millions of products.
method Product2Vec, a method based on representation learning algorithm Word2Vec.
result The method produces more accurate demand forecasts and price elasticities compared to state-of-the-art models.
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…
Characterizes neutral deformation modes of minimal surfaces.
problem Understanding the energy content of deformation modes of minimal surfaces.
method Analyzes the energy content of stretching, drilling, and bending modes of minimal surfaces.
result All isometries of a minimal surface are globally neutral and give rise to soft elasticity.
Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.
problem Mode collapse in variational inference for multimodal distributions.
method Analyzed annealing strategies for Gaussian mixtures, derived formulas, and tested on neural networks.
result Appropriately chosen annealing schemes can robustly prevent mode collapse.
Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
problem Manual tuning of sparsity parameters in traditional DMD.
method Time-delay embedding and Orthogonal Matching Pursuit.
result Autonomously determines optimally sparse subset of modes.
Geodesics connect model modes in neural network loss landscapes.
problem Connecting modes in neural network loss landscapes.
method Reframed mode connectivity in Information Geometry, hypothesized geodesics as mode-connecting paths, proposed algorithm to approximate geodesics.
result Geodesics achieve mode connectivity in neural networks.
A new, efficient k-modes algorithm improves clustering of categorical data.
problem Clustering categorical data using existing methods like k-means is inefficient. method Developed a novel k-modes algorithm called OTQT, which improves on existing methods. result OTQT finds more accurate clusters per iteration and is faster overall.
Multimodal clustering is an unsupervised technique for mining interesting patterns in n-adic binary relations or n-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n…
EDLP samples flat modes in discrete spaces using entropy.
problem Sampling flat modes in discrete spaces is challenging.
method EDLP uses a continuous auxiliary variable and local entropy to guide sampling.
result EDLP consistently outperforms traditional methods in various tasks.
Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.
Deep learning helps remove secondary B-mode polarization to detect primordial gravitational waves.
problem Removing secondary B-mode polarization from CMB data to detect primordial gravitational waves. method Applied deep learning (ResUNet-CMB) to estimate and remove multiple sources of secondary B-mode polarization. result Deep learning can produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.
A new method for continual learning in GANs learns new modes with limited data.
problem Learning new target modes with limited samples while preserving previously learned ones.
method Mode-affinity score for generative modeling, generator replay, and weighted label generation.
result Gains over state-of-the-art methods, even with fewer training samples.
Empirical study shows GANs overfit and drop modes when training is deterministic.
problem Understanding overfitting and mode drop in GAN training.
method Empirical analysis of GAN training with and without stochasticity.
result GANs overfit and drop modes when training is deterministic.
The paper finds shape modes for vortices in a specific sigma model.
problem Existence of internal modes in CP1 vortices. method Developed a geometric formalism based on the Bogomol'nyi decomposition of the energy functional.
result Proved the existence of at least one shape mode for a general CP1 vortex solution. Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
This paper is inspired from the nice result of Andrew Hassell on the eigenfunctions in the stadium billiard. From a classical paper of V. Arnol'd, we know that quasi-modes are not always close to exact modes. We show that, for almost all Riemannian metrics on closed surfaces with an elliptic generic closed geodesic C, …
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii) a measure of connectivity between clusters, (iii) a technique for choosing the …
New tool detects 'fleeting modes' causing excess risk in financial markets.
problem Detecting portfolios with statistically significant excess risk in financial markets.
method Random Matrix Theory to identify 'fleeting modes' independent of underlying correlation structure.
result Fleeting modes exist in both futures and equity markets, and momentum is a source of excess risk.
Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical an…
Unified model predicts multi-mode failure with multi-sensor data.
problem Independent failure mode and RUL prediction ignores inherent relationship.
method Hierarchical Bayesian framework with Cox model, Gaussian process, and multinomial distributions.
result Robust uncertainty quantification and accurate prediction of multi-mode failure.
Hybrid model for multimodal distributions using diffusion and classification.
problem Sampling from multimodal distributions with correct proportions.
method Divide-and-conquer strategy: identify modes, train classifiers, diffusion models, bridge sampling.
result Framework effectively handles multimodal distributions in high dimensions.
We develop a method for finding the zero modes of the Dirac operator in the presence of BPS monopoles. We use it to find the zero modes in the case of Abelian BPS monopoles in R3.
Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimens…
A new method learns from multi-modal sequences with external memory.
problem Learning new modes in a dynamic environment without prior knowledge.
method Maintains a neural episodic memory with a Dirichlet Process prior to store mode descriptors and transfers knowledge through retrieval.
result Performs continual learning favorably compared to mainstream approaches.
The paper evaluates samplers on multi-modal targets, focusing on mode separation and recovery.
problem Handling multi-modality in sampling.
method Synthetic experimental setting focusing on mode relative importance recovery.
result Illustrates the challenges and potential of samplers in multi-modality.
Improves generative model coverage of underrepresented modes.
problem Generative models miss underrepresented modes in data.
method Leverage score sampling for complete mode coverage.
result Significantly improves mode coverage compared to standard methods.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
New model generates data without mode collapse or mixture.
problem Mode collapse and mode mixture in generative models.
method Inspired by AE-OT, improved sample generation algorithm.
result Free from mode collapse and mixture issues.
Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
Simple mode exploration methods do not improve performance in neural networks.
problem Improving predictive probabilities in neural networks.
method Exploring local regions around diverse solutions using simple methods.
result Simple mode exploration methods do not improve performance.