Fast algorithm solves BVPs in linear time with probabilistic uncertainty.
problem Solving boundary value problems efficiently and accurately.
method Gauss--Markov prior tailored to BVPs, linear-time computation.
result Probabilistic solution with linear time complexity and comparable quality.
The paper shows how to answer future and past questions from high-dimensional time series data.
problem Challenges in answering probabilistic inference questions from high-dimensional time series data.
method Temporal contrastive learning to learn Gaussian representations that enable compact closed-form solutions.
result Representations learned via contrastive learning follow a Gauss-Markov chain, enabling efficient inference and planning.
Solves optimal stopping for Gauss-Markov bridges using time-space transformation.
problem Optimal stopping problem of a Gauss-Markov bridge.
method Time-space transformation approach, Picard iteration algorithm.
result Lipschitz continuity of the optimal stopping boundary and its characterization.
Extended Gauss-Markov theorem for linear estimation with bounded bias.
problem Linear estimation with bounded bias operator.
method Derive optimal estimator formulas for Nuclear and Spectral norms, analyze generalization error.
result Cross-validated Nuclear and Spectral regressors outperform Ridge regression in simulations.
Fenrir uses probabilistic numerics to simplify solving initial value problems.
problem Solving initial value problems in ordinary differential equations.
method Probabilistic numerics and Gauss--Markov regression.
result The method simplifies parameter estimation in ODEs, making it easier and more robust.
New method improves Kalman filtering and smoothing for large state spaces.
problem High computational cost and uncertainty in large-scale Kalman filtering.
method Probabilistic numerical method leveraging GPU acceleration and tunable trade-off.
result Mitigates scaling issues and provides more accurate uncertainty estimates.
Optimal sensor placement minimizes information loss from simulations.
problem Designing efficient sensor networks for spatiotemporal processes.
method Model-based sensor placement criterion with sparse variational inference and Gauss-Markov priors.
result Our method identifies sensor networks that minimize information loss from simulated data.
Enhances machine learning interpretability using category theory.
problem Improving machine learning interpretability and social implementation.
method Develops a categorical framework for structured understanding of supervised learning.
result Introduces the Gauss-Markov Adjunction for clarifying residuals and parameters.
Bayesian approach improves ODE solution accuracy.
problem Improving numerical solutions of ordinary differential equations.
method Bayesian inference with Gaussian filtering and smoothing.
result Maximum a posteriori estimate converges to true solution at polynomial rate.
Runge-Kutta methods are the classic family of solvers for ordinary differential equations (ODEs), and the basis for the state of the art. Like most numerical methods, they return point estimates. We construct a family of probabilistic numerical methods that instead return a Gauss-Markov process defining a probability d…
Fermat-Torricelli points help assess investment risks by smoothing series data.
problem Analyzing investment risks in series with large variance, nonlinear trends, or non-normal distributions.
method Construct Fermat-Torricelli points to reduce random component influence.
result Smoothing series by Fermat-Torricelli points reduces risk assessment errors.
New Hida-Matérn kernels enable flexible process priors and efficient GP inference.
problem Flexible modeling of stationary processes with oscillatory components.
method Introducing a new class of covariance functions (Hida-Matérn kernels) and their state space representations.
result Efficient Gaussian Process inference and improved numerical stability.
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution x and its first q derivatives \emph{a priori} as a Gauss--Markov process X, which is…
Improves deep learning performance on noisy datasets using inverse-variance weighting.
problem Heteroscedastic regression with varying noise levels.
method Batch Inverse-Variance (BIV) loss function for neural networks.
result Significantly improves network performance on noisy datasets compared to other methods.
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…
We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of embedded Hilbert spaces. By inverting this isomorphism and extending continuously, …
Study finds on-chain data can proxy off-chain cryptocurrency pricing.
problem Develop methods to proxy off-chain cryptocurrency pricing using on-chain data.
method Graphical models, mutual information, and ensemble machine learning.
result A significant amount of pricing information is contained in on-chain data, but precise prices are hard to recover except on short time scales.
The study connects monopole chains to Higgs bundles and classifies symmetric chains.
problem Classifying symmetric monopole chains invariant under cyclic actions.
method Formulation of a correspondence between monopole chains and spectral data, using the Nahm transform.
result Classification of symmetric monopole chains of charge k.
New proof of chain duality for simplicial complexes.
problem Proving the existence of chain duality for chain complexes over simplicial complexes.
method Geometric and conceptual treatment of chain duality.
result Fundamental for Ranicki's surgery exact sequence.
Improves multi-label classification with a new network model.
problem Improving multi-label classification accuracy.
method Introduces Classifier Chain Network (CCN) for multi-label classification.
result CCN outperforms benchmark methods in simulations and real data.
Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.
problem Testing identity of reversible Markov chains from a single trajectory.
method Using lumping-congruent Markov embeddings, the problem is simplified to testing symmetric chains over a larger state space.
result Achieves state-of-the-art sample complexity for identity testing.
We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not onl…
We introduce some chain maps between Khovanov complexes. Each of the chain maps commutes with a chain homotopy map and a retraction maps which obtain a Reidemeister invariance of Khovanov homology.
Mack's estimator improves chain ladder prediction for large exposure insurance models.
problem Uncertainty quantification in compound Poisson loss models.
method Large exposure asymptotics applied to Mack's estimator.
result Chain ladder prediction uncertainty can be quantified without model assumptions.
Polynomial invariants classify molecular chains based on their contact arrangements.
problem No established invariants for molecular chains with both hard and soft contacts.
method Developed polynomial invariants for circuit topology of molecular chains.
result Polynomial invariants efficiently classify chains with various contact types.
Unified Morse-Bott-Smale chain complex, resolves well-definedness issue.
problem Well-definedness of Morse-Bott-Smale chain complex.
method Unified five degeneracy relations into a single condition.
result Quasi-isomorphic to Morse-Smale-Witten chain complex, alternative proof of Morse Homology Theorem.
This study aims to improve communication between fragmented blockchain systems in finance.
problem Inefficient and insecure communication in fragmented blockchain systems.
method Analysis of cross-chain interoperability protocols and their properties.
result Comparison and evaluation of cross-chain interoperability protocols.
We analyze a new Markov chain model for better sampling and optimization.
problem Developing a new Markov chain model for improved sampling and optimization.
method We introduce a new class of Ito chains with arbitrary noise and inexact drift/diffusion coefficients, proving a bound in W2-distance. result Our analysis provides improved or first results for various applications like SGLD, sampling, and boosting.
This work improves generalisation bounds using chaining and information theory.
problem Improving generalisation bounds for supervised learning algorithms.
method Developed a theoretical framework linking generalisation bounds to their chained counterparts, derived new bounds using Wasserstein distance.
result Chained generalisation bounds can be tighter than standard bounds, especially for concentrated hypothesis distributions.
The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented C∞-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points…
Study on identifying AMP chain graph models under known and unknown component decompositions.
problem Identifying AMP chain graph models with known and unknown chain component decompositions.
method Analyzes conditions for identifiability of AMP models and proposes algorithms for structure recovery.
result Conditions for DAG identifiability in AMP models extend equal variance criteria for Bayes nets.
No hyperbolic group can have an infinite chain of free subgroups of fixed rank.
problem Infinite ascending chains of free subgroups in hyperbolic groups.
method Proof by contradiction and properties of hyperbolic groups.
result Hyperbolic groups do not contain strictly ascending chains of free quasiconvex subgroups of constant rank.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Proves quaternionic analog of Cartan's theorem and counts arithmetic chains.
problem Understanding transformations of quaternionic hyperbolic spaces.
method Analyzes chain-preserving transformations and arithmetic chains in quaternionic Heisenberg group.
result Proves analog of Cartan's theorem and provides counting and equidistribution results.
The paper provides concentration inequalities for Markov chain variance estimators.
problem Estimating the variance of Markov chains with concentration properties.
method Martingale decomposition method for uniformly geometrically ergodic Markov chains.
result Explicit control of the p-th moment of the OBM estimator difference and dependence on p and mixing time.
A new method simulates a lazy version of a Markov chain for empirical inference.
problem Estimating and testing unknown Markov chains with limited data.
method Simulates an α-lazy version of an unknown Markov chain, making it ergodic.
result The pseudo spectral gap can be applied to non-ergodic Markov chains.
The study provides bounds for geodesic diameter in Euclidean space.
problem Finding bounds for geodesic diameter in Euclidean space.
method Develops a geometric approach using locally rectifiable chains and complete normed commutative group bundles.
result Provides a new method for calculating geodesic diameter bounds.
We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains sequentially to observe their states. The goal of the learner is to sequentially…
In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a ch…
Generic groups satisfy a chain condition for subgroups.
problem Understanding subgroup structures in generic groups.
method Proving for fixed integers m,t,k in generic m-generator t-relator groups. result Generic groups satisfy the Ascending Chain Condition for k-generated subgroups. The study proves stabilizing of ascending chains in specific groups.
problem Stabilization of ascending chains in bounded rank subgroups of 3-manifold groups.
method Reduction to hyperbolic 3-manifolds and use of geometrization.
result Ascending chains in toral relatively hyperbolic groups stabilize.
GNNs improve supply chain analytics with real-world benchmarks.
problem Limited research on applying GNNs to supply chain management.
method Conceptual discussions, detailed formulations, examples, mathematical definitions, and task guidelines.
result GNN-based models outperform other methods by 10-40% in various supply chain tasks.
We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson's group F. The resulting class of groups exhibits a combination of uniformity and diversity. On the one hand, a chain group either has a simple commutator subgroup or the action of the…
Geometrically interprets a duality theorem linking cochain and chain complexes.
problem Understanding a complex duality theorem in geometric terms.
method Introduces a chain isomorphism involving simplicial and cellular complexes.
result Establishes a geometric interpretation of Ranicki duality.
New proof for minimizing tunnel systems in satellite chain links.
problem Minimizing the tunnel number of satellite chain links.
method Proving the tunnel number is minimized for links with a specific number of components and bridge number.
result The result is sharp for satellite chain links over a 2-bridge knot.
Simpler method derived for path geometries on surfaces, characterizing projective path geometries.
problem Characterizing projective path geometries on surfaces.
method Solving the equivalence problem of sub-Riemannian geometry of signature (1,1) on a contact 3-manifold.
result Characterization of projective path geometries in terms of their chains.
In this paper, we deal with the task of building a dynamic ensemble of chain classifiers for multi-label classification. To do so, we proposed two concepts of classifier chains algorithms that are able to change label order of the chain without rebuilding the entire model. Such modes allows anticipating the instance-sp…
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the t…