We provide a comprehensive overview and tooling for GP modeling with non-Gaussian likelihoods using state space methods. The state space formulation allows for solving one-dimensional GP models in time and memory complexity. While existing literature has focused on the connection between GP regression …
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48 results for “state-space methods”
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
A new method learns state and proposal dynamics in state-space models using neural networks.
problem Inference in non-linear state-space models.
method StateMixNN method using neural networks for proposal and transition distributions.
result Significantly improved recovery of hidden state, especially in highly non-linear scenarios.
Empirical mode modeling improves state-space analysis of noisy data.
problem Analyzing nonlinear systems with noisy data.
method Combining empirical mode decomposition with empirical dynamic modeling.
result Empirical mode modeling enhances state-space representations in noisy data.
Develops state-space deep Gaussian processes for irregular signals.
problem Solving deep Gaussian process regression problems for irregular signals/functions.
method Represent DGPs as SDEs, solve using state-space filtering and smoothing methods.
result Rich class of priors compatible with irregular signals/functions.
State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.
problem Characterizing state spaces of multifactor approximations of nonnegative Volterra processes.
method Explicit linear transformation of the nonnegative orthant.
result State spaces of multifactor approximations of nonnegative Volterra processes are given by explicit linear transformation of the nonnegative orthant.
Robust state-space radio interferometric imaging using Stochastic Approximation Expectation Maximization
problem Improving state-space radio interferometric imaging in the presence of heavy-tailed noise
method Stochastic Approximation Expectation Maximization
result Significant improvement in reconstruction fidelity and robustness to radio-frequency interference
New method for efficient probabilistic deep state-space models.
problem Efficient inference for probabilistic deep state-space models.
method Deterministic inference algorithm for ProDSSM with neural network weights.
result Superior balance between predictive performance and computational budget.
Generalizes bits back coding for time-series models with latent Markov structures.
problem Efficiently compressing time-series data with latent Markov structures.
method Extends bits back coding to time-series models with latent Markov structures, including HMMs and LGSSMs.
result Effective for small scale models, promising for larger scale settings like video compression.
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.
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 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.
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
A new active learning method for Gaussian process models.
problem Efficiently exploring unbounded state spaces for accurate models.
method Maximizes mutual information with respect to a bounded region using model predictive control.
result Our method yields a better model within the region of interest than entropy-based methods.
Improved state estimation in high-dimensional models using Zig-Zag Sampler.
problem Weight degeneracy in particle filtering methods for high-dimensional state space models.
method Discrete Zig-Zag Sampler applied within the Composite MH Kernel of SMCMC framework.
result Improves estimation accuracy and increases acceptance ratio in high-dimensional state estimation.
State-space models are used in a wide range of time series analysis formulations. Kalman filtering and smoothing are work-horse algorithms in these settings. While classic algorithms assume Gaussian errors to simplify estimation, recent advances use a broader range of optimization formulations to allow outlier-robust e…
State-space models win a forecasting competition for unstable data.
problem Forecasting electricity demand during the post-covid period.
method Adapting state-space models to balance time-series adaptability and machine learning complexity.
result State-space models provide a better compromise between adaptability and accuracy for non-stationary data.
We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning and identification of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome intractable inference distributions via variational inference. Thus, it can handle …
Bayesian model detects altered neural circuits in MCI patients.
problem Detecting altered neural circuits in Mild Cognitive Impairment patients.
method Hierarchical Bayesian recurrent state space model.
result Model discovers latent states predominantly observed in MCI patients.
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.
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…
The method approximates stationary distributions of Markov models by truncating irrelevant states.
problem Computing the stationary distribution of complex Markov models is computationally challenging.
method A state-space lumping scheme that aggregates states in a grid structure, iteratively refining the state-space.
result The method provides a well-justified finite-state projection tailored to the stationary behavior of Markov models.
Several approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a supervised learning problem, have been proposed recently. Finding good policies with such methods requires not only an appropriate classifier, but also reliable e…
A new method for state estimation in state-space models using incomplete data.
problem State estimation in nonlinear state-space models with incomplete observations.
method Statistical analysis of incomplete observations, score function, observed information matrices, EM-gradient-particle filtering.
result Maximum likelihood estimation of state-vector with explicit form of observed information matrix.
Combines pseudo-point and state space approximations for scalable GPs.
problem Handling large numbers of off-the-grid spatial data-points and long time-series.
method Combines pseudo-point approximations for spatial data with state space GP approximations for temporal data.
result Combined approach is more scalable and applicable to a greater range of spatio-temporal problems.
New method for state inference in state-space models with unknown dynamics.
problem State inference in state-space models with computationally expensive and undefined dynamics.
method Estimate state transition dynamics using a multi-output Gaussian process and Bayesian Neural Network as a surrogate model.
result Significant improvement in accuracy for state inference and prediction in non-stationary user models.
This paper examines foreign exchange risk premia from simple univariate regressions to the state-space method. The adjusted traditional regressions properly figure out the existence and time-evolving property of the risk premia. Successively, the state-space estimations overall are quite rationally competent in examini…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived…
D-LinOSS models learn to dissipate energy, improving performance on long-range tasks.
problem Representational limitations of LinOSS models in long-range reasoning.
method Introducing Damped Linear Oscillatory State-Space models (D-LinOSS) that learn to dissipate latent state energy on arbitrary time scales.
result D-LinOSS consistently outperforms previous LinOSS methods on long-range learning tasks, achieving faster convergence and reducing hyperparameter search space.
This paper reviews deep learning methods for state space models.
problem Analyzing temporal dynamics in dynamical systems.
method Selective review of deep neural network approaches for state space models.
result Unified perspective on discrete and continuous time SSMs.
A new method for estimating uncertainty in deep neural networks.
problem Challenges in uncertainty estimation in deep neural networks, especially with increased complexity.
method Decompose tasks into representation learning and state space model for uncertainty estimation.
result The proposed method can estimate predictive distributions on top of existing neural networks.
Paper uses variational inference to estimate nonlinear models.
problem Parameter estimation for nonlinear state-space models.
method Variational inference approach for nonlinear state-space models.
result The method provides robust parameter estimates and outperforms alternatives.
New optimizer G-AdaGrad improves upon AdaGrad for non-convex machine learning problems.
problem Solving non-convex machine learning problems efficiently.
method Proposes a new optimizer G-AdaGrad and analyzes its convergence using state-space models.
result Empirical results show G-AdaGrad performs better than AdaGrad and Adam.
This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.
problem Efficient estimation of free energy in various state spaces.
method Generalized neural transport learning approach for arbitrary state spaces.
result Validation of the proposed method's effectiveness and efficiency in diverse settings.
Long Short-Term Memory (LSTM) is one of the most powerful sequence models. Despite the strong performance, however, it lacks the nice interpretability as in state space models. In this paper, we present a way to combine the best of both worlds by introducing State Space LSTM (SSL) models that generalizes the earlier wo…
A new Fourier model improves ODE prediction.
problem Improving the accuracy of ODE solutions, especially for periodic functions.
method Constructing a Fourier state space model and a hybrid model combining Taylor and Fourier methods.
result The hybrid model can predict ODE solutions more accurately, especially for periodic functions.
Model-based reinforcement learning methods typically learn models for high-dimensional state spaces by aiming to reconstruct and predict the original observations. However, drawing inspiration from model-free reinforcement learning, we propose learning a latent dynamics model directly from rewards. In this work, we int…
KBB algorithm reduces sample complexity for policy evaluation in general state spaces.
problem Policy evaluation in large state spaces with high sample complexity.
method Alternates between fitting Bellman residual and estimating value function via adaptive feature set growth.
result Super-linear convergence rates demonstrated, with reductions in sample complexity.
Deep SSMs use neural networks to identify complex systems.
problem Identifying nonlinear systems with high uncertainty.
method Deep state space models with neural networks.
result Deep SSMs outperform traditional methods on benchmarks.
Divides state space into regions with identical term structure shapes.
problem Classifying term structure shapes in the two-factor Vasicek model.
method Using envelopes and winding numbers to divide and classify the state space.
result Nearly complete classification of parameter space regarding term structure shapes.
Predicts cryptocurrency prices with deep state-space model.
problem Predicting day-ahead crypto-currency prices.
method Proposes a deep state-space model combining state-space formulation and deep neural networks.
result The deep state-space model outperforms state-of-the-art and classical methods in accuracy.
New Q-learning methods improve sample complexity for MDPs with continuous states.
problem Challenges in MDPs with continuous state spaces.
method Two nearest neighbor Q-learning methods with improved sample complexities.
result Minimax optimal sample complexities for offline and online settings.
New method speeds up Gaussian process inference for large datasets.
problem Numerical instability and inefficiency in approximate inference methods for non-Gaussian likelihoods.
method Conjugate-computation variational inference with Kalman recursions.
result Linear-time inference with fast and stable variational inference for state-space GP models.
Symmetries of -foamsmath.GT
Foams have Lie algebra symmetries that simplify web state spaces.
problem Understanding symmetries in foam structures.
method Defined an action of a Lie subalgebra on foams compatible with -foam evaluation.
result Endows -web state spaces with -action.
The paper analyzes variational autoencoders for state space models with risk bounds.
problem Analyzing the risk associated with variational autoencoders for state space models.
method Backward factorization of variational distributions to analyze excess risk, providing oracle inequalities and upper bounds.
result Explicit upper bounds on variational estimation error for state space models under strong mixing assumptions.
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
HyperX uses reward bonuses to enable efficient exploration in meta-learning.
problem Catastrophic failure of meta-learning with sparse rewards.
method HyperX uses novel reward bonuses to explore in approximate hyper-state space.
result HyperX meta-learns better task-exploration and adapts more successfully to new tasks.
We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target statistics. Inference is approximated by the Newton-Raphson algorithm, reduced t…