Defines fiber-wise linear differential operators on vector bundles.
problem No specific problem stated; focuses on definition and equivalence.
method Definition and equivalence of fiber-wise linear differential operators to derivations of line bundles.
result Equivalence of fiber-wise linear differential operators to derivations of line bundles.
This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.
problem Theoretical development of property inheritance for subtensors in tensor train decompositions.
method Theoretical analysis of incoherence and condition number preservation, and tensor train rank preservation through fiber-wise sampling.
result Key tensor properties (incoherence and condition number) can be well preserved to subtensors formed via fiber-wise sampling.
New method for tensor completion from specific mode observations.
problem Recovering multiway data tensors from partial observations.
method Tensor train decomposition for fiber-wise observations.
result Deterministic recovery guarantees for specific observation patterns.
In this paper we extend Witten-Helffer-Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor-Turaev torsi…
In this paper we investigate fiber-wise linear complex Banach sub-Poisson structures defined canonically by the structure of a W*-algebra M. In particular we show that these structures are arranged in the short exact sequence of complex Banach sub-Poisson VB-groupoids with the groupoid of partially invertible elements …
We prove an analogue of Thurston's h-principle for 2-dimensional foliations on manifolds of dimension bigger or equal to 4, in the presence of a fiber-wise non-degenerate 2-form. This helps us understand the flexibility of rank 2 regular Poisson structures on open manifolds with dimension bigger or equal to 4…
Given a Kähler fiber space p:X→Y whose generic fiber is of general type, we prove that the fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on the relative canonical bundle KX/Y of p. We also propose a conjectural generalization of this result for relative twisted Kähler-Eins…
Courant algebroids are a natural generalization of quadratic Lie algebras, appearing in various contexts in mathematical physics. A connection on a Courant algebroid gives an analogue of a covariant derivative compatible with a given fiber-wise metric. Imposing further conditions resembling standard Levi-Civita connect…
Visible Lagrangians in Hitchin systems are studied for pillowcase covers.
problem Visible Lagrangians in Hitchin systems intersecting non-trivially.
method Computation of Fourier-Mukai transforms and study of mirror dual branes.
result Mirror dual branes are closely related to Hausel's toy model.
Study of intersections in Hamiltonian orbits on cotangent bundles.
problem Understanding intersections of projected Hamiltonian orbits in cotangent bundles.
method Generic submersive level set analysis, multi-jet transversality theorem.
result Projected Hamiltonian orbits have discrete intersections, which can be perturbed away under certain conditions.
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably…
We study the duality between M-theory on compact holonomy G2-manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G2-manifolds, called twisted connected sums, which lend themselves to an application of fiber-wise M-theory/Heterotic Duality. For a large class of such G2-man…
Control data constructed for smooth weak deformation retraction of stratified spaces.
problem Construct control data for smooth weak deformation retraction of stratified spaces.
method Show smooth local triviality with conical fibers, construct control data, use fiber-wise scalar multiplications.
result Obtain neighbourhood smooth weak deformation retraction of stratified spaces.
In this paper we define K-theoretic secondary invariants attached to a Lie groupoid G. The K-theory of Cr∗(Gad0) (where Gad0 is the adiabatic deformation G restricted to the interval [0,1)) is the receptacle for K-theoretic secondary invariants. We give a Lie groupoid version of construction given b…
Paper identifies unobserved variables from observable data.
problem Missing variables in empirical studies.
method Function mapping from observables to unobservables based on joint distribution.
result Uniqueness of latent values in each observation.
New framework learns policies for partially observable systems.
problem Learning policies in partially observable dynamical systems.
method Partially Observable Bilinear Actor-Critic framework.
result Algorithm can learn against optimal policies in certain cases.
Efficient RL in partially observable risk-sensitive environments with hindsight observations.
problem Risk-sensitive reinforcement learning in partially observable environments.
method Integrates hindsight observations into POMDP framework, develops novel RL algorithm.
result Achieves polynomial regret with provable efficiency, outperforming existing methods.
Deep learning identifies space objects from uncorrelated observations.
problem Finding small groups of observations of the same space objects from a large set of uncorrelated data.
method Training a deep learning model on a large data set of uncorrelated observations to identify groups of observations likely of the same space objects.
result The model correctly identified 83.1% of observation pairs as belonging to the same space object.
We consider the problem of diagnosis where a set of simple observations are used to infer a potentially complex hidden hypothesis. Finding the optimal subset of observations is intractable in general, thus we focus on the problem of active diagnosis, where the agent selects the next most-informative observation based o…
The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed. We propose ta…
A method uses CG to create efficient channels for ideal observers.
problem Computational intractability of ideal observers for high-dimensional image data.
method Conjugate gradient (CG) method for constructing efficient channels.
result CG-based channels approximate IO and HO performance efficiently.
Extends PD-NJ-ODE to noisy observations and dependent observation times.
problem Predicting continuous-time stochastic processes with irregular and noisy observations.
method Extends PD-NJ-ODE to handle conditional independence and noisy observations.
result Theoretical guarantees and empirical examples for handling noisy observations and dependent observation times.
The paper analyzes the stability of an observer error in a vibrating string system.
problem Stability analysis of observer error in a vibrating string system.
method Abstract Cauchy problem reformulation and application of LaSalle's invariance principle for infinite-dimensional systems.
result The observer error is asymptotically stable.
New algorithm for aggregate inference in HMMs with continuous observations.
problem Inference in large populations with indistinguishable individuals and continuous measurements.
method Continuous observation collective forward-backward algorithm extending existing discrete case algorithm.
result Efficacy demonstrated through numerical experiments.
The paper compares and optimizes estimators for treatment effects with observed confounders and mediators.
problem Estimating treatment effects with observed confounders and mediators.
method Investigates the linear Gaussian causal model, compares and optimizes estimators, and combines datasets.
result An optimal estimator outperforms the backdoor and frontdoor estimators by an unbounded constant factor.
New algorithm improves reinforcement learning from partial observations.
problem Inferior performance of algorithms in real-world reinforcement learning due to partial observability.
method Representation-based approach to POMDPs, leading to a tractable algorithm.
result Empirically demonstrates superior performance with partial observations.
CVRL tackles complex visual observations in reinforcement learning.
problem Complex visual observations in natural environments.
method Contrastive Variational Reinforcement Learning (CVRL) learns a contrastive variational model by maximizing mutual information between latent states and observations.
result CVRL achieves comparable performance with state-of-the-art model-based DRL methods and significantly outperforms them on tasks with complex observations.
A new algorithm CAP learns optimal policies from observational data with confounding bias and missing observations.
problem Offline contextual bandit with confounding bias and missing observations.
method CAP policy learning, forming reward function as solution of integral equation system, building confidence set, and greedily taking action with pessimism.
result Developed an upper bound to the suboptimality of CAP for the offline contextual bandit problem.
We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missi…
New surface observables yield 2-knot invariants in nonabelian theories.
problem Developing new invariants for nonabelian theories.
method Introducing surface observables in BF theory and Yang-Mills theory.
result Surface observables induce new 2-knot invariants and electric fluxes.
Observational learning is a type of learning that occurs as a function of observing, retaining and possibly replicating or imitating the behaviour of another agent. It is a core mechanism appearing in various instances of social learning and has been found to be employed in several intelligent species, including humans…
The paper cleans label noise in supervised classification using Bernoulli sampling.
problem Label noise degrades supervised classifier performance.
method Proposes a label noise cleaning method based on Bernoulli random sampling.
result The method separates clean and noisy observations without prior label information.
New framework for reinforcement learning with sporadic state observations.
problem Partial observability in reinforcement learning.
method Action-Triggered Sporadically Traceable Markov Decision Processes (ATST-MDPs).
result Optimistic algorithm achieving regret bound for episodic learning.
We characterize value functions in partially observable MDPs as semi-algebraic sets.
problem Understanding feasible value functions in partially observable Markov decision processes.
method Characterization of feasible value functions as semi-algebraic sets defined by polynomial inequalities.
result The feasible set of value functions in POMDPs is a semi-algebraic set, not a polytope as in MDPs.
Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown un…
New algorithm infers trajectories from partial observations using optimal transport.
problem Inferring trajectories from partial observations of coupled systems.
method Extends MFL algorithm to latent SDEs using observable state space models and partial observations.
result Experiments show significant outperformance over latent-free baseline.
Study shows observability from a measurable set for Gevrey functions.
problem Determining observability from a subset for Gevrey functions.
method Used measurable sets and inequalities for Gevrey regular functions.
result Established observability estimates from measurable sets for Gevrey functions.
Deep Reinforcement Learning (RL) recently emerged as one of the most competitive approaches for learning in sequential decision making problems with fully observable environments, e.g., computer Go. However, very little work has been done in deep RL to handle partially observable environments. We propose a new architec…
EnCF improves data assimilation for implicit, non-smooth observations.
problem Data assimilation challenges with implicit, many-to-one observations.
method EnCF uses a stochastic controlled flow to update forecast distributions.
result EnCF outperforms Kalman filters for non-Gaussian, implicit observations.
RL struggles with generalization due to implicit partial observability.
problem Generalization in RL is difficult due to implicit partial observability.
method Re-cast RL problem as solving epistemic POMDPs and propose ensemble-based techniques.
result Simple ensemble-based technique achieves significant generalization gains.
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph. We also show that in the undirected case, the learner …
Method estimates observation functions in state-space models without supervision.
problem Unsupervised learning of non-invertible observation functions in nonlinear state-space models.
method Nonparametric generalized moment method using constrained regression.
result Estimates function space of identifiability from state process.
Sig-PCA integrates model outputs and observations to correct model biases.
problem Improving model accuracy and reliability by correcting biases and numerical approximations.
method Sig-PCA framework that combines summary statistics from model outputs with localized observations via a neural network.
result Corrects model outputs to align closely with observational data, preserving essential statistical information.
We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with possibly non locally Lipschitz functions. We characterize the points where this Lip…
This paper uses a generalization of symplectic geometry, known as n-symplectic geometry and developed by Norris, to find observables on three-dimensional manifolds. It will be seen that for the cases considered, the n-symplectic observables are derivable from the symplectic observables of C2. The quantization of…
Helps visually impaired users make better decisions by adjusting their observations.
problem Systematic biases in users' perception and processing of visual information.
method Synthesizes new observations based on true observations to correct user biases.
result Significant improvement in task performance for users with various biases.
A new emulator connects observables directly from data.
problem Constructing fast and accurate surrogate models for robust predictions.
method Introduces Multiparameter Eigenvalue Problem (MEP) emulator trained with Eigenvector Continuation (EC) and Parametric Matrix Model (PMM) data.
result The MEP emulator can make predictions directly from observables to observables.