We investigate the Kaluza-Klein reductions to ten dimensions of the purely gravitational half-BPS M-theory backgrounds: the M-wave and the Kaluza-Klein monopole. We determine the moduli space of smooth (supersymmetric) Kaluza-Klein reductions by classifying the freely-acting spacelike Killing vectors which preserve som…
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48 results for “state space reduction”
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
A method for robust reinforcement learning in large state spaces.
problem Challenges in RL with large state spaces, costly data, and real-world dynamics deviation.
method Distributionally robust Markov decision processes with Gaussian Processes and maximum variance reduction.
result Efficient learning of multi-output nominal transition dynamics with statistical sample complexity bounds.
HashReward improves imitation learning in high-dimensional environments by balancing reward generation and dimensionality reduction.
problem Making policies generalize well in high-dimensional state-action spaces, especially in game playing with raw pixel inputs.
method HashReward uses supervised hashing to balance reward generation and dimensionality reduction.
result HashReward outperforms state-of-the-art methods in high-dimensional environments.
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.
New method shows unitarity in quantization for toric manifolds.
problem Unitarity in quantization commutes with reduction for toric manifolds.
method Generalized coherent state transform (gCST) and geodesic rays of toric Kähler polarizations.
result Quantization commutes unitarily with reduction for the new mixed polarization.
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson manifolds to that for phase spaces of CH systems with external force and control. We g…
Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.
problem High computational complexity of Isomap, especially in eigenvalue decomposition stage.
method Introduces a projection operator to reduce the complexity of the eigenvalue decomposition stage to linear order.
result Reduces Isomap's computational complexity to linear order while preserving structural information.
Paper identifies reductive MDPs, solving them in polynomial time.
problem Computational hardness of general MDPs and tractability of finite-horizon MDPs.
method Defines reductivity, a new class of SSPs, and develops a polynomial-time solution.
result Optimal policies can be found in polynomial time for reductive SSPs and MDPs.
Policy gradient methods have demonstrated success in reinforcement learning tasks that have high-dimensional continuous state and action spaces. However, policy gradient methods are also notoriously sample inefficient. This can be attributed, at least in part, to the high variance in estimating the gradient of the task…
GD-VAEs learn dynamics from observations using geometric and topological information.
problem Learning parsimonious representations of nonlinear dynamics from observations.
method Develops data-driven methods incorporating geometric and topological information using Variational Autoencoders (VAEs).
result GD-VAEs provide methods for learning reduced dimensional representations of nonlinear dynamics.
For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however, focus on a priori state aggregation based on similarities in transition rates, whi…
New method reduces PDE model parameters by 30% with sparsity.
problem Redundant parameters in neural network projections.
method Bregman iterations for sparsity, POD compression, bias propagation.
result 30% fewer parameters with similar accuracy.
A new method for classifying naturally reductive spaces is presented. This method relies on the structure theory of naturally reductive spaces developed in \cite{Storm2018a} and the new construction of naturally reductive spaces in \cite{Storm2018}. We obtain the classification of all naturally reductive spaces in dime…
A new algorithm interprets DR dimensions and selects features.
problem Lack of interpretability in DR algorithms.
method I-KDR algorithm that maps data to a lower dimensional space with interpretable dimensions and feature selection.
result I-KDR provides better interpretations and higher discriminative performance.
Efficient method estimates intrinsic dimension for big data.
problem Estimating intrinsic dimension for large datasets is costly and complex.
method Proposes a matrix-vector product-based approach for efficient intrinsic dimension estimation.
result Demonstrates superior performance compared to state-of-the-art methods.
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A concrete transitive group of isometries is given for the new spaces and also the na…
Normal forms and symplectic reduction for gauge field theory in infinite dimensions.
problem Understanding the structure of moduli spaces in gauge field theory.
method Establishing normal forms for equivariant maps and developing singular symplectic reduction in infinite dimensions.
result The reduced phase space decomposes into smooth manifolds each with a natural symplectic structure.
In the present paper we study naturally reductive homogeneous -metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous -metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler …
Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
We propose the application of a high-speed maximum likelihood clustering algorithm to detect temporal financial market states, using correlation matrices estimated from intraday market microstructure features. We first determine the ex-ante intraday temporal cluster configurations to identify market states, and then st…
New methods for skill rating in sports using state-space models.
problem Improving skill rating in competitive sports.
method State-space models, sequential Monte Carlo, discrete hidden Markov models.
result Advantages of state-space models for time-varying player skills.
Develops a new method for nonlinear dimension reduction using random features.
problem Statistical challenges in generalizing Gaussian process-based latent variable models to non-Gaussian data.
method Random feature latent variable models (RFLVMs) that approximate nonlinear relationships with linear functions of random features.
result RFLVMs produce comparable results to state-of-the-art methods on various data types.
Algebraic treatment of connection reduction over a special disc.
problem Reduction theory for connections over a specific geometric structure.
method Purely algebraic approach for arbitrary groups, with quantitative results.
result New quantitative results in reduction theory.
The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces…
Efficiently simulates slow dynamics of high-dimensional stochastic systems.
problem Simulating high-dimensional stochastic systems with slow dynamics and fast modes.
method Designs an algorithm to estimate an invariant manifold and its dynamics, averaging out fast modes.
result Efficient simulator of effective dynamics on low-dimensional invariant manifold.
Jacobi operators on certain naturally reductive spaces have constant coefficient ODEs.
problem Understanding geometric properties of naturally reductive spaces.
method Analyzing Jacobi operators and their ODEs on these spaces.
result Jacobi operators on these spaces satisfy constant coefficient ODEs.
Machine learning-based applications are increasingly prevalent in IoT devices. The power and storage constraints of these devices make it particularly challenging to run modern neural networks, limiting the number of new applications that can be deployed on an IoT system. A number of compression techniques have been pr…
New findings on Codazzi tensors in homogeneous spaces.
problem Characterizing Codazzi tensor fields in reductive homogeneous spaces.
method Extending results from Lie groups to reductive homogeneous spaces, analyzing the curvature of canonical connections.
result Invariant Codazzi tensor fields on naturally reductive homogeneous spaces are parallel.
Asynchronous Q-learning achieves optimal Q-function estimation with reduced sample complexity.
problem Learning the optimal Q-function in asynchronous Q-learning with limited samples.
method Demonstrates sample complexity bound with variance reduction for -discounted MDPs.
result Sample complexity improved by a factor of and .
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…
New method reduces version space for CNNs, improving active learning performance.
problem Sampling bias in active learning hinders optimal hypothesis finding in neural networks.
method Version space reduction through prior mass reduction and diameter reduction, proposing a new Gibbs-vote disagreement method.
result Diameter-based querying method reduces version space more effectively than prior mass reduction and other methods.
To backpropagate the gradients through stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator that is unbiased, exhibits low variance, and has low computational complexity. Exploiting variable augmentation, REINFORCE, and reparameterization, the ARM estimator achieves adaptive variance reducti…
Improved sample complexity for actor-critic algorithms in MDPs.
problem Achieving optimal policies with limited data in reinforcement learning.
method Single-timescale actor-critic with STORM (STOchastic Recursive Momentum) and a sample buffer.
result Optimal sample complexity of for -optimal policies.
The main result of this paper is that every naturally reductive space can be explicitly constructed from the construction in \cite{Storm2018}. This gives us a general formula for any naturally reductive space and from this we prove reducibility and isomorphism criteria.
Recently, hybrid metaheuristics have become a trend in operations research. A successful example combines the Greedy Randomized Adaptive Search Procedures (GRASP) and data mining techniques, where frequent patterns found in high-quality solutions can lead to an efficient exploration of the search space, along with a si…
A novel method reduces dimensionality for filtering SRNs with observed variables.
problem Challenges in estimating hidden state variables in SRNs with limited observations.
method Filtered Markovian Projection (Filtered MP) for dimensionality reduction in filtering.
result Filtered MP guarantees consistency and superior computational efficiency in high dimensions.
Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to Spin-manifolds. We extend their result to noncompact groups and manifolds. This leads to a result for cocompact actions, and a result for non-cocompact actions for reduction at zero. The r…
SILBO optimizes high-dimensional Bayesian optimization using semi-supervised embedding learning.
problem Bayesian optimization struggles with high-dimensional search spaces.
method SILBO uses semi-supervised dimension reduction to find a low-dimensional space for iterative optimization.
result SILBO outperforms existing methods on high-dimensional Bayesian optimization tasks.
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
Hida-Matérn Kernelstat.ML
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 new algebraic structure emerges from reductive homogeneous spaces.
problem Understanding the algebraic properties of tangent bundles.
method Defined a new algebraic structure based on connections and torsion.
result Post-Lie-Yamaguti algebra is a new algebraic structure related to Lie-Yamaguti algebras.
A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…
Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reductionstat.ML
SQFA learns features maximizing Fisher-Rao distance for better classification.
problem Improving classification accuracy through feature learning.
method SQFA learns linear features maximizing Fisher-Rao distance between class-conditional distributions.
result SQFA-H features achieve the best classification accuracy.
This work tackles large action spaces in RL by binarizing actions.
problem Large action spaces in reinforcement learning cause significant challenges.
method Sequentializing actions and binarizing the action space.
result Binarizing the action space can significantly improve RL algorithms and reduce state space size.
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.