The paper models the dependence between lifetimes of married couples using copulas.
problem The independence assumption in bivariate lifetime modeling for life insurance products is often violated.
method Copula approach with age difference and gender of the elder partner as arguments of the dependence parameter. Maximum likelihood techniques for parameter estimation.
result The correlation between lifetimes decreases with age difference and is higher when the husband is older.
ExpBERT uses natural language explanations to improve text interpretation.
problem Improving text interpretation for relation extraction tasks.
method Fine-tuning BERT on MultiNLI to interpret natural language explanations.
result ExpBERT matches a BERT baseline but requires less labeled data and improves performance.
We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent EP ideas from (Opper&Winther 05) with covariance decoupling techniques (Wipf&Nag…
Paper predicts turbulent flows using physics-informed deep learning.
problem Predicting turbulent flows from fluid simulations.
method Hybrid approach combining RANS and LES with trainable spectral filters and U-net.
result Significant reduction in prediction error for 60 frames ahead.
Survey article on solving geometric problems with calculus and harmonic analysis.
problem Solving geometric problems using functional calculus and harmonic analysis.
method Combining methods from functional calculus and real-variable harmonic analysis.
result Recent geometric problems have been resolved by these methods.
We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent approximate posterior distributions, and that acts as…
ETM discovers interpretable topics in large vocabularies.
problem Existing topic models fail with large, heavy-tailed vocabularies.
method Generative model combining topic models and word embeddings with variational inference.
result ETM discovers interpretable topics even with large vocabularies.
Spatially-aware machine learning predicts gentrification better than non-spatial models.
problem Predicting gentrification in real estate sales.
method Combining data science, machine learning, and spatial analysis techniques.
result Spatially-conscious machine learning models outperform non-spatial models.
New algorithm for partially observable contexts in finance.
problem Decision making based on partially observable, correlated market information.
method EMKF-Bandit algorithm integrating system identification, filtering, and bandit algorithms.
result Sub-linear regret under conditions on filtering.
The paper explores parabolic regularity in geometric variational analysis.
problem Developing calculus rules and computation formulas for second-order generalized differential constructions.
method Introducing and applying the concept of parabolic regularity to geometric aspects of second-order variational analysis.
result Established new calculus rules and computation formulas for second-order generalized differential constructions.
Retail investors set interest rates for P2P loans based on borrower characteristics.
problem Understanding how individual investors price credit risk in online consumer loan auctions.
method Reverse auction framework, analyzing interest rate variance and borrower characteristics.
result Retail investors exhibit strong predictability in pricing, with gender and marital status influencing interest rates.
N-GCN combines GCNs and random walks for semi-supervised node classification.
problem Semi-supervised node classification on graph-structured data.
method N-GCN trains multiple GCNs over node pairs at different random walk distances, optimizing a classification objective.
result N-GCN outperforms state-of-the-art baselines on challenging node classification tasks.
Study of coupled Sasaki-Einstein and solitons metrics.
problem Existence and properties of coupled Sasaki-Einstein and solitons metrics.
method Isomorphism between Lie algebra and space of coupled basic functions, use of coupled twisted Laplacians, reduction to Kähler-Einstein metrics, existence of toric coupled Sasaki-Einstein metrics.
result Existence and properties of coupled Sasaki-Einstein and solitons metrics, reduction to known cases when applicable.
Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.
problem Understanding when maps on products of spaces can be embedded.
method Uses known results for nonsingular biskew and bilinear maps, studies genericity properties, extends Whitney embedding theorems, and relates to Z/2-coindex of embedding spaces. result Generates strong obstructions to coupled embeddability in terms of combinatorics of triangulations.
UNTIE learns representations of coupled categorical data.
problem Challenges in learning from unlabeled categorical data with complex couplings.
method UNTIE approach for unsupervised representation learning of heterogeneous couplings.
result UNTIE significantly improves categorical data representations on 25 diverse datasets.
Solves modified conjecture for Fano manifolds using Ding stability.
problem Finding Kähler-Einstein metrics on Fano manifolds.
method Interprets Ding semistability and solves modified conjecture.
result Solves modified conjecture for coupled Kähler-Einstein metrics on Fano manifolds.
New algorithm reduces regret in online learning for piecewise continuous functions.
problem Exponential loss in efficiency when moving from classical to adversarial learning.
method Introduces generalized bracketing numbers and Follow-the-Perturbed-Leader algorithm.
result Optimal scaling of optimization oracle calls with average regret.
Paper discusses conditions for deforming coupled Kähler-Einstein metrics.
problem Conditions for deforming coupled Kähler-Einstein metrics.
method Analyzes deformation of coupled Kähler-Einstein metrics on Fano manifolds.
result Necessary and sufficient condition for deformation of coupled Kähler-Einstein metrics.
Develops non-Markovian couplings for sub-Riemannian Brownian motions.
problem Constructing couplings for sub-Riemannian Brownian motions starting from points on the same vertical fiber.
method Uses global isometries to construct maximal couplings, satisfying a reflection principle.
result Estimates coupling time and applies to inequalities for the heat semigroup.
Two new couplings for probability distributions are constructed and analyzed.
problem Constructing optimal couplings for two probability distributions.
method Optimizes constrained Monge-Kantorovich transport problems with supermartingales.
result Two new couplings are identified and characterized.
Numerical observations on martingale couplings are confirmed under certain conditions.
problem Understanding the validity of numerical observations on maximizers and minimizers of martingale couplings.
method Investigation of sufficient conditions and counterexamples for the property to hold.
result The non-decreasing property of martingale couplings is preserved for maximizers under specific conditions.
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
Paper merges GP-LVM and VAE for interpretable latent representations.
problem Learn interpretable latent representations for large data.
method Introduces a novel approximate inference scheme combining GP-LVM and VAE.
result Allows arbitrary capacity of generative bottleneck without losing interpretability.
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and…
Unified analytic account of correlation emergence and Epps effect in coupled limit order books
problem Correlation emergence and Epps effect in coupled limit order books
method Discrete random-walk description of order flow with creation, cancellation, and diffusion, coupled reaction-diffusion equations with moving reaction boundary
result Realized correlations as a function of aggregation time
HyperImpute improves iterative imputation by automatically selecting models and hyperparameters.
problem Imputing missing values in datasets with variable model specifications.
method Generalized iterative imputation framework that adapts and configures models and hyperparameters automatically.
result Demonstrates superior imputation accuracy compared to benchmarks.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
Novel kernels reduce large-scale learning costs.
problem High computational cost in large-scale nonparametric learning.
method Hierarchically compositional kernels using Nyström method and local approximation.
result Significant reduction in training complexities to O(nr) and O(nr2). Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles ov…
Unified framework for coupled tensor completion improves recovery accuracy.
problem Improving recovery accuracy in coupled tensor completion.
method Unified framework using tensor ring (TR) decomposition with shared latent factors and novel optimization model.
result The proposed method achieves superior recovery accuracy on real-world data compared to state-of-the-art methods.
Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.
problem Jointly analyze matrices and tensors with irregular/ragged data.
method Alternating Optimization (AO) and ADMM for fitting PARAFAC2-based CMTF models with various constraints.
result Accurately recovers underlying patterns using various constraints and linear couplings.
Combines causal learning with dynamical systems for practical model identification.
problem Lack of practical, identifiable models for causal inference in dynamical systems.
method Draws connection between causal representation learning and dynamical systems, applying identifiable methods to scalable differentiable solvers.
result Learned explicitly controllable models for trajectory-specific parameters.
Coupled entropy corrects flaws in Tsallis entropy for complex systems.
problem Misinterpretation of generalized temperature and entropy.
method Derived from generalized Pareto and Student's t distributions.
result Provides balanced measure of uncertainty for complex systems.
Statistical physics method analyzes error in learning Ising model couplings.
problem Analyzing error in learning Ising model couplings from independent data.
method Combining replica method and cavity approach for densely connected systems.
result Explicit estimator achieves minimal reconstruction error but requires prior knowledge.
The paper introduces new equations in Kähler geometry and proves their solutions and convexity.
problem Solving equations in Kähler geometry and understanding their geometric implications.
method Using moment map pictures to motivate and prove solutions for the equations.
result The Mabuchi functional for certain equations is shown to be convex.
Flexible framework for CMTF with ADMM for various constraints and couplings.
problem Challenges in data fusion from multiple sources with varying characteristics.
method Flexible algorithmic framework using AO and ADMM for various constraints, loss functions, and couplings.
result Accurate and computationally efficient results for various loss functions, including KL divergence.
Lipschitz regularization improves neural network robustness by coupling weights across layers.
problem Improving neural network robustness under random input uncertainties.
method Regularization of neural networks by their Lipschitz constant, highlighting the coupling effect on weights across layers.
result Lipschitz regularization introduces a tradeoff between robustness and expressiveness, suggesting careful implementation.
Convex norms improve coupled matrix and tensor completion.
problem Efficiently complete coupled matrices and tensors with shared information.
method Proposed convex norms and completion algorithm.
result Excess risk bounds show improved performance compared to uncoupled norms.
Unified Jacobi coupling construction for various geometric settings.
problem Constructing Jacobi structures on associated bundles.
method Extending Sternberg--Weinstein coupling to Jacobi geometry.
result Associated bundles inherit Jacobi structures from base spaces.
Researchers introduce new functionals to measure distance from Kähler-Einstein metrics.
problem Estimating how close a metric is to Kähler-Einstein.
method Introducing Ricci-Calabi and H-functionals, and proving moment weight inequalities and Hessian formulas.
result Established inequalities and formulas to measure distance and conditions for existence of Kähler-Einstein metrics.
Stochastic Schwarz lemma on Kähler manifolds via couplings.
problem Develop a new Schwarz lemma for Kähler manifolds.
method Probabilistic approach using Markovian couplings.
result Improved gradient estimates for harmonic functions.
Formula found for Kähler-Einstein metric existence obstruction.
problem Obtaining Kähler-Einstein metrics on manifolds.
method Residue formula for Futaki-Zhang obstruction.
result Found coupled Kähler-Einstein metrics on a specific toric Fano manifold.
Paper tackles deep learning confounding factors, learns unseen factors.
problem Learning from data with unknown and potentially infinite confounding factors.
method Combines deep generative models with Bayesian non-parametric factor models (Indian Buffet Process).
result Model can learn from data with unknown and potentially infinite confounding factors.
Method to find critical points in vector bundles with fermionic coupling.
problem Finding solutions to energy functionals coupled with fermionic operators.
method Study of critical points of strongly indefinite functionals on vector bundles.
result Existence and multiplicity of solutions for specific equations.
Improved VAE model enhances image accuracy and robustness.
problem Enhancing accuracy and robustness of VAE models.
method Coupled VAE method with generalized entropy function.
result Improved accuracy and robustness of output images.
The paper maps time-series onto networks to reveal hidden joint information.
problem Extract hidden joint information from uncorrelated time-series.
method Discretize time-series amplitudes, map onto networks, measure coupling deviations, and compare with Gaussian distributions.
result Markets may possess joint patterns even if initially uncorrelated.
Unified framework for Brownian motion distances on specific geometric manifolds.
problem Understanding Brownian motion distances on radially isoparametric manifolds.
method Developed a geometric framework and derived drift-window inequalities.
result Unified framework for coadapted Brownian couplings on RIM.
Let (M,g,φ) be a solution to the Ricci flow coupled with the heat equation for a scalar field φ. We show that a complete, κ-noncollapsed solution (M,g,φ) to this coupled Ricci flow with a Type I singularity at time T<∞ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base po…