State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
LS4 models time-series with latent states, outperforming previous methods.
problem Learning sharp transitions in time-series data.
method State space ODE with convolutional representation to bypass hidden states.
result LS4 significantly outperforms previous models in various metrics.
The volume of the quantum mechanical state space over n-dimensional real, complex and quaternionic Hilbert-spaces with respect to the canonical Euclidean measure is computed, and explicit formulas are presented for the expected value of the determinant in the general setting too. The case when the state space is endo…
Structured State-Space Duality connects SSMs to masked attention.
problem Connecting SSMs and attention mechanisms for efficient modeling.
method Formalizing and generalizing SSD from scalar-identity to diagonal state matrices.
result Diagonal SSMs match training complexity lower bounds and support richer dynamics.
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.
Unified treatment of RC in stochastic and deterministic settings.
problem Understanding and generalizing reservoir computing in both deterministic and stochastic contexts.
method Investigation of state-space systems, analysis of fading memory and solution stability, introduction of stochastic echo states.
result Generality of fading memory and solution stability in state-space systems, even without the echo state property.
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.
We address tracking and prediction of multiple moving objects in visual data streams as inference and sampling in a disentangled latent state-space model. By encoding objects separately and including explicit position information in the latent state space, we perform tracking via amortized variational Bayesian inferenc…
New model for insurance states using Markov jump processes with non-countable state space.
problem Modeling insurance states with non-countable state spaces.
method Developed a new Thiele's differential equation for continuous time rehabilitation rates.
result Allows for consistent calculation of reserves in disability insurance.
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space…
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 O(n) time and memory complexity. While existing literature has focused on the connection between GP regression …
Improved state estimation in nonlinear models using amortized backward variational inference.
problem State estimation in general state-space models.
method Amortized backward variational inference with neural network parameters.
result Linear growth of variational approximation error in number of observations.
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.
New RL method handles large state-action spaces with complex models.
problem Complex models and large state-action spaces in reinforcement learning.
method π-KRVI, an optimistic modification of least-squares value iteration using kernel ridge regression.
result First order-optimal regret guarantees under general settings, improving over state of the art.
We prove a conjecture about approximating Gaussian Processes on one dimension.
problem Computational scaling issues with Gaussian Processes on one dimension.
method Developed a new family of state-space models (LEG) to approximate any stationary GP on one dimension.
result Proved that any stationary GP on one dimension can be approximated using the LEG family.
Quantum machine learning classification depends on mutual informations between state and parameter spaces.
problem Generalization in quantum machine learning models.
method Link between quantum machine learning and quantum hypothesis testing, using mutual informations.
result Quantum classifier accuracy and generalization depend on mutual informations between state and parameter spaces.
This primer explains diffusion models in general state spaces.
problem Diffusion models in general state spaces are not well-introduced.
method Develops discrete-time and continuous-time views of diffusion models, deriving Fokker-Planck and master equations.
result Unified understanding of diffusion models across continuous and discrete domains.
New RL method reduces sample complexity for large state-action spaces.
problem Handling large state-action spaces in RL with general Q-functions.
method Nonparametric Q-learning using kernel ridge regression.
result Sample complexity is order optimal with respect to ε and kernel complexity.
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.
Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the sta…
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.
Develops a regression approach for solving MDPs with general state and action spaces.
problem Solving MDPs with large or infinite state and action spaces.
method Regression-based primal-dual martingale approach.
result Tight upper and lower approximations of value functions and optimal policies.
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.
Study proves steady state space hypersurfaces are hyperplanes under certain curvature constraints.
problem Characterizing complete spacelike hypersurfaces in steady state space.
method Extended Omori-Yau's maximum principle.
result Proves complete spacelike hypersurfaces are hyperplanes under specific curvature conditions.
Generative Bayesian Filtering improves inference in complex models without explicit density evaluations.
problem Performing posterior inference in complex nonlinear and non-Gaussian state-space models.
method Generative Bayesian Filtering (GBF) extends GBC to dynamic settings using deep neural networks for recursive posterior inference. Generative-Gibbs sampler bypasses density evaluations for parameter learning.
result GBF significantly outperforms likelihood-free approaches in accuracy and robustness for intractable state-space models.
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.
Paper presents a fast method for estimating hidden states in Bayesian models.
problem Estimating hidden states in Bayesian state space models efficiently.
method Amortized simulation-based inference with pretraining.
result The method achieves sufficient accuracy and fast inference times.
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.
A new method learns complex dynamical systems from data efficiently.
problem Learning complex dynamical systems from large-scale data efficiently.
method Low-rank structured variational autoencoding framework for nonlinear Gaussian state-space models.
result Consistently demonstrates better predictive capabilities compared to other models.
The paper analyzes neural networks for solving high-dimensional Schrödinger eigenvalue problems.
problem Analyzing generalization error of neural networks for high-dimensional Schrödinger eigenvalue problems.
method Proves convergence rate of generalization error independent of dimension d under spectral Barron space assumption. Verifies assumption by proving regularity estimate. result Generalization error rate is independent of dimension d under spectral Barron space assumption. Mamba struggles with long context lengths, but spectrum scaling improves performance.
problem Mamba's performance degrades with increasing context length.
method Spectrum scaling applied to pre-trained Mamba models to improve long-context generalization.
result Spectrum scaling significantly improves performance in long-context settings.
Due to the lack of enough generalization in the state-space, common methods in Reinforcement Learning (RL) suffer from slow learning speed especially in the early learning trials. This paper introduces a model-based method in discrete state-spaces for increasing learning speed in terms of required experience (but not r…
Study on existence of ground states for free energy on hyperbolic space.
problem Existence of ground states for a free energy functional on hyperbolic space.
method Derived HLS-type inequalities on Cartan-Hadamard manifolds to prove existence.
result Established conditions for the existence of ground states on hyperbolic space.
We solve 6-DoF localisation and 3D reconstruction using deep state-space models.
problem 6-DoF localisation and dense 3D reconstruction in spatial environments.
method Approximate Bayesian inference in a deep state-space model combining learning and domain knowledge.
result Near state-of-the-art performance on UAV flight data.
Proposes method to learn state abstractions that generalize across environments.
problem Learning abstractions that generalize in block MDPs.
method Invariant causal prediction to learn model-irrelevant state abstractions (MISA).
result Proves high probability of outputting a state abstraction corresponding to causal feature set for return.
This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optim…
Model-based planning holds great promise for improving both sample efficiency and generalization in reinforcement learning (RL). We show that energy-based models (EBMs) are a promising class of models to use for model-based planning. EBMs naturally support inference of intermediate states given start and goal state dis…
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.
For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vec…
AutoML improves electricity demand forecasting models.
problem Optimizing GAM and state-space model parameters for short-term forecasting.
method Automated online generalized additive model selection using DRAGON package.
result The approach enhances predictive performance of adaptive models.
This paper introduces a new neural ODE model for continuous-time sequence generation.
problem Representing and predicting continuous-time sequences with high accuracy.
method A neural emission model and neural ODE define the latent state evolution, with an Energy-based model for prior distribution.
result The model outperforms existing methods in various tasks, including long-horizon predictions.
We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-siz…
Generates synthetic ECGs conditioned on clinical statements.
problem Privacy issues with sensitive health data.
method Combines diffusion models and structured state space models.
result SSSD-ECG outperforms GAN-based competitors in synthetic data quality.
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.
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.
We derive, for the square operator of Yau, an analogue of the Omori-Yau maximum principle for the Laplacian. We then apply it to obtain nonexistence results concerning complete spacelike hypersurfaces with constant higher order mean curvature in the Steady State space.
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.
New method learns state embeddings from demonstrations for improved reinforcement learning.
problem Difficult relationship between observed state and useful policy actions in dynamic problems.
method Variational framework for learning state embeddings that optimize trajectory linearity.
result Learning embedding spaces improves policy gradient reinforcement learning performance.