Austere submanifolds and arid submanifolds constitute respectively two different classes of minimal submanifolds in finite dimensional Riemannian manifolds. In this paper we introduce these two notions into a class of proper Fredholm (PF) submanifolds in Hilbert spaces, discuss their relation and show examples of infin…
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48 results for “PF submanifolds”
A weakly reflective submanifold is a minimal submanifold of a Riemannian manifold which has a certain symmetry at each point. In this paper we introduce this notion into a class of proper Fredholm (PF) submanifolds in Hilbert spaces and show that there exist so many infinite dimensional weakly reflective PF submanifold…
Path group actions induced by sigma-actions and affine Kac-Moody symmetric spaces of group typemath.DG
Extends PF submanifold results and connects Kac-Moody spaces.
problem Computational results and submanifold geometry of PF actions.
method Defines isomorphism between Hilbert spaces, shows equivariance, and uses parallel transport.
result Shows natural isomorphism between Kac-Moody spaces of group type.
On weakly reflective submanifolds in compact isotropy irreducible Riemannian homogeneous spacesmath.DG
Study extends reflective submanifold theory to compact homogeneous spaces.
problem Characterize reflective submanifolds in compact isotropy irreducible spaces.
method Extend previous results to infinite-dimensional Hilbert spaces.
result Inverse image of reflective submanifolds is also reflective.
Differentiable PF via entropy-regularized OT for better inference.
problem Non-differentiability of traditional PF resampling methods.
method Entropy-regularized optimal transport for differentiable resampling.
result Convergent differentiable PF method with improved gradient estimates.
New algorithms solve nonconvex-concave minimax problems without parameter knowledge.
problem Solving nonconvex-concave minimax problems efficiently.
method Three completely parameter-free single-loop algorithms.
result Achieve optimal iteration complexity for nonconvex-concave minimax problems.
Physics-guided neural network improves power flow analysis.
problem Infeasibility of traditional numerical approaches due to outdated or unavailable PF equations.
method Proposes a physics-guided neural network to learn PF mappings from historical data while constraining by physical laws.
result Physics-guided neural network achieves better performance and generalizability than unconstrained data-driven approaches.
This paper uses Karcher's formulation [Kar99] of the O'Neill tensors [O'N66,Gra67] to derive a concise formula for the family of curvature forms obtained by shrinking the fibers of a submersion of semi-Riemannian manifolds by a factor of . The formula clearly shows that as approaches 1, …
Derives PF-ODE for infinite-dimensional functions, improving function generation tasks.
problem Efficient inference in infinite-dimensional diffusion models.
method Derives PF-ODE in infinite-dimensional function spaces.
result Reduces function evaluations while maintaining sample quality.
Paper proposes a new method for efficient Pareto Front modeling.
problem Efficient modeling of Pareto Front (PF) in decision making problems.
method Projection based active Gaussian process regression (P-aGPR) method.
result The proposed method can provide a generative PF model and examine new points efficiently.
Recurrent neural networks (RNNs) have been extraordinarily successful for prediction with sequential data. To tackle highly variable and noisy real-world data, we introduce Particle Filter Recurrent Neural Networks (PF-RNNs), a new RNN family that explicitly models uncertainty in its internal structure: while an RNN re…
SURF steers scalarization weights to uniformly traverse the Pareto front.
problem Non-uniform coverage of the Pareto front when using scalarization weights.
method Geometric analysis and CDF mapping to select weights for uniform coverage.
result SURF converges to uniform Pareto front coverage under provable conditions.
Principal Manifold Flowsstat.ML
PFs and iPFs learn principal manifolds for efficient density estimation.
problem Understanding the geometric structure of normalizing flows.
method Characterize flows using principal manifolds and contours.
result PFs and iPFs can learn principal manifolds and perform density estimation.
Extends RF proximities to all supervised distance-based machine learning contexts.
problem Limited utility of RF proximities in various machine learning tasks.
method Introduces generalized Proximity Forest (PF) model and variant for regression.
result Demonstrates unique advantages over RF and k-nearest neighbors models.
Enhances particle filters with neural augmentation for multi-sub-state tracking.
problem Particle filters struggle with complex or approximated models and low latency requirements.
method Learning Flock (LF) uses a neural network to correct particle weights based on sub-particle relationships.
result LF improves performance, robustness, and latency in radar multi-target tracking.
ATPF combines PF and EnKF for better inference in complex systems.
problem Weight degeneracy in PF and approximation errors in EnKF.
method Adversarial learning to improve posterior matching and incorporate kernel methods for optimization.
result ATPF provides theoretical guarantees and practical advantages over PF and EnKF.
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop an approach to scalable approximate GP regression with finite-data guarantees on th…
We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the ef…
New method for ordinal data improves recommendation systems.
problem Improving recommendation systems with ordinal data.
method Ordinal Non-negative Matrix Factorization (OrdNMF) for ordinal data.
result OrdNMF outperforms existing methods in recommendation experiments.
Particle filtering is a powerful approach to sequential state estimation and finds application in many domains, including robot localization, object tracking, etc. To apply particle filtering in practice, a critical challenge is to construct probabilistic system models, especially for systems with complex dynamics or r…
A new federated multi-armed bandit framework with personalization balances generalization and personalization.
problem Balancing generalization and personalization in federated multi-armed bandits.
method Proposed a Personalized Federated Upper Confidence Bound (PF-UCB) algorithm to achieve a regret.
result PF-UCB achieves an regret regardless of personalization degree and has similar instance dependency to lower bound.
Improved volatility estimation using SV-PF-RNN.
problem Estimating true volatility in the presence of market noise.
method SV-PF-RNN: hybrid neural network and particle filter architecture.
result SV-PF-RNN outperforms basic particle filter.
A new algorithm optimizes local objectives in federated learning with heterogeneous clients.
problem Optimizing local objectives in federated learning with heterogeneous client data.
method Proposes PF-PNE algorithm with double elimination strategy.
result PF-PNE algorithm optimizes local objectives with arbitrary heterogeneity and protects client data confidentiality.
A new method estimates time-varying parameters in earth system models using offline and online data assimilation.
problem Estimating time-varying parameters in complex earth system models.
method Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE-PF)
result HOOPE-PF outperforms existing methods, especially with small ensemble sizes.
Study on the geometry of Cotton gravity field equations.
problem Analyzing the geometry of Cotton gravity field equations.
method Describes the local structure of spatial Riemannian factors and provides sufficient conditions for reduction to -static perfect fluid space-time.
result Provides sufficient conditions for a C--PF to reduce to a -SPFST.
The study characterizes GRW spacetimes with gradient solitons and phantom era.
problem Characterizing generalized Robertson-Walker spacetimes with gradient solitons.
method Examined gradient type Ricci solitons and -quasi Einstein solitons in GRW spacetimes.
result Demonstrated that GRW spacetimes can be Robertson-Walker or phantom era spacetimes under certain conditions.
PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.
problem Locally accelerated CG requires knowledge of smoothness and strong convexity parameters.
method Parameter-Free Locally Accelerated CG (PF-LaCG) algorithm.
result PF-LaCG achieves local acceleration without requiring knowledge of smoothness and strong convexity parameters.
Proposes a continuous flow model to understand and control instability in gradient descent for deep learning.
problem Understanding and controlling the instability of gradient descent in deep learning.
method Introduces the Principal Flow (PF), a continuous time flow that approximates gradient descent dynamics.
result The PF captures divergent and oscillatory behaviors of gradient descent, including escaping local minima and saddle points.
Procedure for determining less discriminatory alternatives in AI audits with limited resources.
problem Difficulty in proving less discriminatory alternatives in AI audits due to resource constraints.
method Closed-form upper bound for loss-fairness Pareto frontier, enabling claimants to fit PFs without training large models.
result A scaling law for loss-fairness Pareto frontiers, allowing claimants to determine if an LDA exists with limited resources.
ePF improves PF for ITS by balancing exploration and exploitation, outperforming baselines.
problem Premature exploitation in PF leads to suboptimal solutions under constrained budgets.
method Integrates Entropic Annealing and Look-ahead Modulation to preserve diversity and evaluate potential.
result Significant improvement in task reward (up to 50% relative) on math benchmarks.
We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom fo…
This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the Kalman filter (KF) and the extended KF (EKF). In contrast with typical methods …
StAD predicts divergence of diffusion and flow models without Jacobian computation.
problem Computing likelihood from diffusion and flow models is computationally expensive.
method Introduces StAD, a distillation method to predict divergence using Langevin-Stein operator.
result StAD predicts divergence with competitive variance and speed compared to existing methods.
Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models.…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in th…
Inverse Particle Filtermath.OC
Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a well-known tool to extract robust topological features, and outputs as \textit{persist…
State space partitioning based on constrained spectral clustering for block particle filteringstat.ML
A new method for state space partitioning in block particle filtering reduces bias and variance.
problem Overcoming the curse of dimensionality in non-linear, non-Gaussian state space estimation.
method Formulates state space partitioning as a clustering problem and uses spectral clustering with constraints.
result The proposed method effectively groups correlated state variables into smaller blocks, reducing bias and variance.
PropFair algorithm ensures fair performance in federated learning.
problem Ensuring fair performance in federated learning for diverse clients.
method PropFair, a novel algorithm based on bargaining games, finds proportionally fair solutions.
result PropFair approximately finds proportional fairness solutions and balances average and worst 10% client performances.
Count data are often used in recommender systems: they are widespread (song play counts, product purchases, clicks on web pages) and can reveal user preference without any explicit rating from the user. Such data are known to be sparse, over-dispersed and bursty, which makes their direct use in recommender systems chal…
Enhanced SMC uses gradients from CRN-PF in Langevin proposals for improved state and parameter estimation.
problem Challenges in high-dimensional parameter spaces for SMC.
method Leveraging gradients from a CRN-PF within a Langevin proposal.
result Higher effective sample size and more accurate parameter estimates.
The time-dependent maximum principle for systems of parabolic equations subject to an avoidance setmath.DG
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Modelscs.LG
VT-DIS improves sampling from Boltzmann distributions with minimal overhead.
problem Bias in Monte Carlo estimates from score-based diffusion models.
method Variance-Tuned Diffusion Importance Sampling (VT-DIS) adapts noise covariance to correct bias.
result VT-DIS achieves effective sample sizes of 80%, 35%, and 3.5% on benchmarks, using less computational budget.
Torsion and fibrationsmath.DG
We study the behaviour of analytic torsion under smooth fibrations. Namely, let F \to E \to^{f} B be a smooth fiber bundle of connected closed oriented smooth manifolds and let be a flat vector bundle over . Assume that and come with Riemannian metrics and comes with a unimodular (not necessarily fla…
SBS uses SVGD to optimize continuous functions globally.
problem Global optimization of continuous Sobolev functions.
method Stein Boltzmann Sampling (SBS) with SVGD.
result SBS and its variants are highly competitive in global optimization.
We describe random walk boundaries (in particular, the Poisson--Furstenberg, or PF-boundary) for a vast family of groups in terms of the hyperbolic boundary of a special free subgroup. We prove that almost all trajectories of the random walk (with respect to an arbitrary nondegenerate measure on the group) converge to …
Paper proposes a new framework for robust multi-modal data fusion under uncertainty.
problem Unexpected modality failures in nonlinear non-Gaussian dynamic processes.
method Dynamic model averaging (DMA) based particle filter (PF) algorithm.
result The proposed solution outperforms state-of-the-art methods in experiments.
This work explores non-negative low-rank matrix factorization based on regularized Poisson models (PF or "Poisson factorization" for short) for recommender systems with implicit-feedback data. The properties of Poisson likelihood allow a shortcut for very fast computations over zero-valued inputs, and oftentimes result…