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…
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48 results for “observed space”
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.
POWSS simplifies Q-value estimation in POMDPs with continuous observations.
problem Lack of theoretical justification for online sampling-based algorithms in POMDPs with continuous observation spaces.
method Developed POWSS, a simplified algorithm that estimates Q-values accurately with high probability and can approach optimality with increased computational power.
result POWSS provides formal theoretical guarantees for Q-value estimation in POMDPs with continuous observations.
This paper tackles efficient clustering of moderate dimensional data from dual observation and attribute spaces.
problem Clustering high-dimensional data, especially when dimensionality is moderate to small.
method Develops an efficient clustering processing pipeline using dual spaces of observations and attributes.
result Established an effective method for clustering in moderate dimensional data.
Unsupervised learning of observation functions in state-space models by nonparametric moment methodsstat.ML
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.
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.
Solves high-dimensional observation learning for control models.
problem Learning dynamics from high-dimensional images is challenging.
method Proposes a Beta DVBF approach to handle latent and observable space discrepancies.
result Demonstrates improved model learning from high-dimensional observations.
Reduces observables on multisymplectic manifolds using Lie algebra actions.
problem Reduction of observables on multisymplectic manifolds with Lie algebra actions.
method Development of a reduction scheme for -algebra of observables.
result Reproduces symplectic observable reduction in specific cases.
Spectral method learns hidden state mapping for RL in rich-observation MDPs.
problem Challenges in RL with large state spaces and hidden low-dimensional structure.
method Spectral decomposition method to learn hidden state to observation state mapping.
result Achieves low regret with weak dependence on observed space dimensionality.
Predictive State Representations (PSRs) are an expressive class of models for controlled stochastic processes. PSRs represent state as a set of predictions of future observable events. Because PSRs are defined entirely in terms of observable data, statistically consistent estimates of PSR parameters can be learned effi…
A new approach predicts next observations without explicit decoding for better control.
problem High-dimensional observations and unknown dynamics in real-world control tasks.
method Proposes a novel information-theoretic LCE approach using predictive coding to develop a decoder-free model.
result The model reliably learns a controllable latent space leading to superior performance.
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.
New method recovers matrix column space with active sampling for better results.
problem Recovering column space of partially observed matrices with limited data.
method Alternating minimization with active sampling strategy.
result Active sampling improves convergence to true column space with higher probability.
Analyzes quantization of flux observables in gauge theories.
problem Lifting Poisson-brackets of flux observables to higher moduli stacks.
method Systematic analysis of canonical quantization and flux quantization laws.
result Topological quantum observables form homology Pontrjagin algebra of loop space.
Efficient RL in large POMDPs with latent determinism and embeddings.
problem Efficient reinforcement learning in large-scale POMDPs with latent states and observations.
method Conditional Hilbert space embeddings, linear optimal -function, deterministic latent transitions, gap assumption.
result Computationally and statistically efficient algorithm for exact optimal policy.
Study bounds expansion coefficient from observable diameter in metric measure spaces.
problem Bound the expansion coefficient from below in terms of the observable diameter.
method Considered concentration of measure phenomenon, connected observable diameter and expansion coefficient, derived upper bound, combined with lower bound to obtain upper bound for observable diameter.
result Obtained upper bound for observable diameter in terms of expansion coefficient.
New RL method tackles rich observation spaces efficiently.
problem Efficient reinforcement learning with rich observations.
method Least Squares Value Elimination by Exploration (LSVEE).
result LSVEE learns near optimal behavior after polynomial episodes.
LD-EnSF speeds up data assimilation with sparse observations.
problem Efficiently assimilate sparse and noisy data into complex dynamical systems.
method LD-EnSF uses latent dynamics networks and history-aware LSTM encoders to process sparse observations without full-space simulations.
result Achieves significant speedups over existing methods while maintaining high accuracy.
Adversarial observations in probabilistic State-Space Models for robust Reinforcement Learningstat.ML
Adversarial attacks on probabilistic state-space models affect latent state and policy decisions.
problem Robust reinforcement learning under adversarial observability.
method Analyzing adversarial attacks on linear probabilistic state-space models.
result Demonstrating the influence of adversarial observations on latent state and policy decisions.
The paper completes matrices from non-uniformly sampled entries, especially when columns are randomly selected and fully observed.
problem Matrix completion from non-uniformly sampled entries, including fully and partially observed columns.
method First, recover the column space from fully observed columns. Then, for each partially observed column, find a vector in the recovered column space with the observed entries. For low-rank matrices, recover them from entries.
result The algorithm can exactly recover a low-rank matrix from merely entries.
This research develops approximation theory for OOMs of infinite-dimensional processes.
problem Developing an approximation theory for OOMs of infinite-dimensional processes.
method Establishing an inner product structure and proving continuity of observable operators.
result A fundamental obstacle in making an infinite-dimensional space of future distributions into a Hilbert space is described.
We tackle linear bandits with partially observable features, achieving sublinear regret.
problem Linear regret due to unobserved features in partially observable linear bandits.
method Feature augmentation with orthogonal basis vectors and a doubly robust estimator.
result Sublinear regret bound of .
Overfitting occurs when RL agents correlate rewards with spurious observation features.
problem Overfitting in reinforcement learning due to correlation with spurious observation features.
method Developed a framework to analyze and design synthetic benchmarks from modified observation spaces.
result Agents can overfit to different observation spaces even if the MDP dynamics are fixed.
Study efficient reinforcement learning for partially observed systems with linear structure.
problem Efficient reinforcement learning for partially observed Markov decision processes with linear structure.
method Proposes OP-TENET algorithm using a Bellman operator with finite memory, adversarial integral equation, and optimistic exploration.
result Achieves ε-optimal policy within O(1/ε^2) episodes with polynomial sample complexity in intrinsic dimension.
Improves active learning efficiency by warping input space based on observed outputs.
problem Insensitivity of Gaussian process uncertainty to actual observations.
method Input warping with learned monotone reparameterization to adjust acquisition function behavior.
result Significantly improved sample efficiency across various benchmarks, especially in non-stationary conditions.
The study finds non-trivial elements in moduli spaces of curvature metrics.
problem Identifying non-trivial elements in moduli spaces of curvature metrics.
method Constructing elements in homotopy groups of moduli spaces of positive curvature metrics.
result Non-trivial elements found in moduli spaces of positive curvature metrics.
Defines simplicity of non-linear mappings using information geometry.
problem Finding a simple yet effective non-linear mapping from latent to observation space.
method Formalizes simplicity through information geometry, independent of empirical data.
result Proves basic properties of the defined simplicity measure.
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
problem Tackles tensor decomposition for unaligned observations.
method Uses functions in RKHS to represent mode with unaligned observations, introduces versatile loss function, proposes optimization algorithm and stochastic gradient method.
result Demonstrates improved tensor decomposition efficiency and effectiveness with synthetic and real data.
Unified framework for singular statistical models using observable charts.
problem Non-identifiability and breakdown of classical asymptotic theory in singular models.
method Invariant framework based on observable charts to define local coordinate systems in model space.
result Observable order provides a lower bound on KL divergence vanishing rate in singular models.
The paper explores the complexities of algorithmic fairness and the assumptions needed for different fairness mechanisms.
problem The lack of a unified understanding of algorithmic fairness across different papers.
method Introducing a mathematical framework that includes the observed space, decision space, and construct space to analyze fairness mechanisms.
result Different fairness mechanisms require different assumptions about the relationship between unobservable variables (construct space) and observable variables (observed space).
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal compactification of a Euclidean vector…
SDIFT generates full-field dynamics from sparse, irregular data.
problem Modeling and reconstructing physical dynamics from sparse, off-grid observations.
method SDIFT uses a functional Tucker model and sequential diffusion for generating full-field evolution from irregular sparse observations.
result Significant improvements in reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.
New method combines variational inference with particle filtering for nonlinear data.
problem Combining variational inference and Monte Carlo sampling for nonlinear data.
method Formulates gradient steepest descent method based on local optimal transport principles, embeds local mappings in RKHS, uses approximations to avoid adjoint evaluation.
result RKHS approximation is highly successful and superior to ensemble approximation for nonlinear observational operators.
Framework classifies partially observed systems using model posterior distributions.
problem Classifying systems with incomplete data.
method Employing posterior distributions over models to account for uncertainty.
result Classifier performance is not affected by model simplicity, provided it captures essential characteristics.
Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric topology, offers great advantage for proximity searching. If we have preprocessed d…
A nonparametric approach for policy learning for POMDPs is proposed. The approach represents distributions over the states, observations, and actions as embeddings in feature spaces, which are reproducing kernel Hilbert spaces. Distributions over states given the observations are obtained by applying the kernel Bayes' …
Symmetric observations don't necessarily imply symmetric causal explanations.
problem Inferring causal models from observed correlations is challenging and computationally intensive.
method An explicit example using a tripartite probability distribution over binary events.
result Symmetries in observations cannot be used to reduce the hypothesis space of causal models.
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.
Optimal observation selection for complex hidden hypotheses.
problem Diagnosis of complex hidden hypotheses using limited observations.
method Active diagnosis through selection of most informative observations based on past results.
result An implication model that predicts future outcomes based on past observations, selecting the most informative next observation.
A new model captures irregularly spaced high-frequency prices and their volatility.
problem Modeling high-frequency prices with irregular spacing and market noise.
method Observation-driven model using Skellam distribution with time-varying volatility and smoothing splines.
result The model provides a good fit to IBM stock data and measures daily realized volatility.
This work formalizes and extends parameter sharing in multi-agent reinforcement learning.
problem Parameter sharing limits multi-agent learning to a single policy, preventing different tasks or action spaces.
method Introduces agent indication and extends parameter sharing to heterogeneous observation and action spaces.
result Proves convergence to optimal policies for parameter sharing in heterogeneous environments.
This paper uses Factored Latent Analysis (FLA) to learn a factorized, segmental representation for observations of tracked objects over time. Factored Latent Analysis is latent class analysis in which the observation space is subdivided and each aspect of the original space is represented by a separate latent class mod…
The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.
In nonlinear state-space models, sequential learning about the hidden state can proceed by particle filtering when the density of the observation conditional on the state is available analytically (e.g. Gordon et al., 1993). This condition need not hold in complex environments, such as the incomplete-information equili…
Paper proposes a new method for learning latent representations for control problems.
problem Learning representations for control algorithms in high-dimensional observation spaces.
method Formulated a loss function (PCC) consisting of prediction, consistency, and curvature terms, derived an amortized variational bound.
result The new variational-PCC learning algorithm leads to superior control performance and more stable training.
New BED method handles online inference for partially observed dynamical systems.
problem Optimizing data collection for partially observable, partially online dynamical systems.
method Derived estimators of expected information gain and its gradient for SSMs, using nested particle filters.
result Successfully handles both partial observability and online inference in realistic models.
FSRM method improves treatment effect estimation from observational data.
problem Estimating treatment effects from observational data with missing counterfactual outcomes and selection bias.
method FSRM method based on deep representation learning and matching, which maps covariate space into a selective, nonlinear, and balanced representation space.
result FSRM method outperforms state-of-the-art methods in estimating treatment effects.
New method extracts dynamics from graph data using DMD in vector-valued spaces.
problem Analyzing nonlinear systems with interdependent observables.
method Formulated Koopman spectral analysis for vector-valued data, developed estimation algorithm.
result Extracts low-dimensional dynamics from graph data.