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.
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.
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 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.
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space mod…
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.
Stanza models complex time series with balance between traditional and deep learning approaches.
problem Capturing long-term structure in non-stationary time series.
method Nonlinear, non-stationary state space model.
result Achieves forecasting accuracy competitive with deep LSTMs, especially for multi-step ahead forecasting.
Structured state space models improve ECG classification and reveal new insights.
problem Improving ECG analysis through deep learning.
method Applying structured state space models to capture long-term dependencies in ECG data.
result SSMs lead to significant improvements in ECG classification over current state-of-the-art.
New model preserves symmetry in multivariate time series, improving performance.
problem Implicit ordering in MTS models violates inherent exchangeability.
method Permutation-equivariant 2D state space model with canonical architecture.
result Eliminates sequential dependency chains and simplifies stability analysis.
This work studies learning dynamics in SSMs, linking them to deep linear networks.
problem Lack of theoretical understanding of SSMs, especially in deep state spaces.
method Analyzes learning dynamics of linear SSMs, focusing on frequency domain, and establishes links to deep linear networks.
result Analytical solutions for SSM learning dynamics under mild assumptions, linking to deep linear networks.
Implements SSSD for missing value imputation and forecasting in time series data.
problem Missing values in time series data.
method Structured state space models combined with conditional diffusion models.
result SSSD outperforms state-of-the-art methods on various data sets and missingness scenarios.
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…
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.
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 glN-foam evaluation. result Endows glN-web state spaces with sl2-action. 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.
We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the kernel space. The kernel space contains a set of meta states which are desired …
New method improves deep learning model robustness and accuracy for long sequences.
problem Challenges in learning long-range sequence tasks using state-space models.
method Proposes a perturb-then-diagonalize (PTD) methodology to address ill-posed diagonalization problems in SSMs.
result Demonstrates improved robustness and accuracy of S5-PTD model on Long-Range Arena benchmark.
In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are particularly challenging in such nonstationary environments. In this paper, we study c…
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.
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.
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.
Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.
problem Challenges in understanding discrete diffusion models on combinatorial state spaces.
method Established convergence bounds for three discrete diffusion models using Euler approximations.
result Optimal non-asymptotic convergence guarantees for discrete diffusion models without boundedness assumptions.
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The c…
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.
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 explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a general state-space modelling methodology, which allows modelling, estimation and…
The paper stabilizes PD term structures under forecast uncertainty using a Kalman filter with an anchored observation model.
problem Stable estimation of lifetime PDs under forecast uncertainty.
method Reformulated in state-space framework, introduced an anchored observation model.
result Asymptotic stochastic stability of error dynamics, leading to smoother projections.
MambaStock predicts stock prices with high accuracy using a state space model.
problem Inaccurate stock price predictions due to nonlinearity in stock market data.
method Mamba-based state space model with selection mechanism and scan module.
result MambaStock outperforms previous methods in stock price prediction accuracy.
The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force mo…
Algorithm estimates human decision-making in high-dimensional states with finite-time guarantees.
problem Estimating optimal policies and measures of fit in dynamic decision models with high-dimensional state spaces.
method Single-loop estimation algorithm with stochastic gradient steps for reward maximization.
result Algorithm converges to a stationary solution with finite-time guarantees and approximates maximum likelihood sublinearly.
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.
Bayesian approach optimizes in-context learning for state space models.
problem Optimizing in-context learning for state space models.
method Bayesian optimal sequential prediction over latent sequence tasks.
result Bayesian optimal predictor converges to posterior predictive mean.
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.
IBPF algorithm tackles high-dimensional parameter learning for complex systems.
problem Learning high-dimensional parameters in complex, partially observed, and nonlinear systems.
method Iterated Block Particle Filter (IBPF) for graphical state space models.
result IBPF algorithm consistently beats the curse of dimensionality across various experiments.
Improves state space models' resistance to noise.
problem State space models' initialization assumes noise-free data, which is often violated.
method Uncertainty-aware initialization for state space models, reformulating HiPPO with measurement noise.
result Improves model resistance to noise at training and inference time.
New PG samplers improve inference in coupled state-space models.
problem Bayesian inference from multiple time series with shared parameters.
method Marginalized Particle Gibbs samplers for coupled state-space models.
result Improved parameter inference through shared information.
In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of the forward price dynamics in the approximation models and derive the rate of c…
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.
Our article considers a Gaussian variational approximation of the posterior density in a high-dimensional state space model. The variational parameters to be optimized are the mean vector and the covariance matrix of the approximation. The number of parameters in the covariance matrix grows as the square of the number …
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.
SSMs can be poisoned with clean labels, leading to generalization failure.
problem The implicit bias of SSMs can be manipulated by including special training examples with clean labels.
method Formal proof and empirical demonstration of the phenomenon.
result SSMs can fail to generalize even with clean labels, due to the inclusion of special training examples.
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and corresponding Gaussian Process kernels are derived. Experimen- tal results demonstrat…
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 …
Combines deep state space models with diffusion models for better forecasting and capturing latent dynamics
problem Forecasting and capturing latent dynamics in time series
method DDSSM: Diffusion-driven state space model
result Empirically outperforms state-of-the-art deep SSM
Mamba Hawkes Process improves modeling of event sequences with long-term dependencies.
problem Modeling mutual inhibition and nonlinearity in asynchronous event sequences.
method Introduces Mamba Hawkes Process using Mamba state space architecture.
result MHP outperforms existing models across various datasets.
SPECTRA improves probabilistic energy forecasting by separating trends and uncertainties.
problem Interacting uncertainties from renewable intermittency, demand flexibility, market volatility, and weather impact probabilistic forecasts.
method Adaptive state-space exogenous context and temporal-frequency resolution architecture.
result Achieved best CRPS in 14 out of 18 settings, reducing CRPS by 5.74% and upper-tail quantile risk by 7.27%.
EBMs trained on discrete data using heat equations on graph structures.
problem Training EBMs on discrete or mixed data.
method Heat equations on graph structures for data perturbation.
result Efficacy demonstrated in various applications.
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