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…
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48 results for “State-space prior”
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…
We forecast S&P 500 excess returns using a flexible Bayesian econometric state space model with non-Gaussian features at several levels. More precisely, we control for overparameterization via novel global-local shrinkage priors on the state innovation variances as well as the time-invariant part of the state space mod…
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibi…
Improved DSSMs for easier interpretable latent variables.
problem Complex and hard-to-interpret latent variables in DSSMs.
method Simplified predictive decoder and shrinkage priors.
result Interpretable latent variables improve forecasting performance.
New methods combine MALA and mGRAD for scalable Bayesian inference in high-dimensional state-space models.
problem Bayesian inference in high-dimensional state-space models with limited scalability.
method Combines gradient-based MALA and prior-informed mGRAD for scalable inference.
result Extends classical MCMC methods to handle multiple time steps and particles.
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.
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.
Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…
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.
A DRL framework optimizes portfolios using a LFSS module for feature extraction.
problem Optimizing dynamic portfolios in financial markets.
method Deep Reinforcement Learning with a Latent Feature State Space module.
result The proposed DRL framework outperforms benchmarks in portfolio optimization.
A probabilistic framework for online test-time adaptation
problem Adapting models to new data under distributional shift
method State-space modelling architecture
result Characterizing parameter learning, time evolution, prior tuning, and prediction
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.
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.
Paper introduces OMD for ordered state transitions in SSMs.
problem Modeling ordered latent states in dynamic systems.
method Ordered Matrix Dirichlet (OMD) prior over ordered stochastic matrices.
result OMD models recover interpretable ordered latent structure without sacrificing predictive performance.
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gauss…
One of the key challenges in applying reinforcement learning to real-life problems is that the amount of train-and-error required to learn a good policy increases drastically as the task becomes complex. One potential solution to this problem is to combine reinforcement learning with automated symbol planning and utili…
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.
New GP model tackles physics constraints efficiently.
problem Lack of efficient, physics-informed models for complex systems.
method Physics-informed variational state-space Gaussian process.
result Efficient spatio-temporal modeling with improved performance.
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.
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…
Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Spacecs.LG
Unified framework for convergence of discrete diffusion models without state space size dependence.
problem Fundamental limitations in existing convergence theory for discrete diffusion models, especially under singular priors and large vocabularies.
method Unified adjoint-equation-based framework that establishes dimension-free convergence guarantees in any integral probability metric (IPM).
result First dimension-free convergence bounds applicable to both masked and uniform priors, free of state space size .
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.
The class of chain event graph models is a generalisation of the class of discrete Bayesian networks, retaining most of the structural advantages of the Bayesian network for model interrogation, propagation and learning, while more naturally encoding asymmetric state spaces and the order in which events happen. In this…
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.
Develops VAEs for learning complex physical systems from data.
problem Learning low-dimensional representations of nonlinear physical systems.
method Variational Autoencoders with manifold latent spaces.
result Effective in learning nonlinear Burgers equation and constrained mechanical systems.
New method samples Jeffreys prior for objective Bayesian inference.
problem Sampling from Jeffreys prior is challenging.
method Metropolis-Adjusted Langevin Algorithm
result Samples can be directly used in Bayesian methods.
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors, depending on the dimension of the models and the cardinalities of their sample sp…
FunBaT extends Tucker decomposition to handle continuous-indexed tensor data.
problem Handling continuous-indexed tensor data that doesn't fit traditional Tucker decomposition.
method FunBaT treats continuous-indexed data as interactions between a core tensor and a group of latent functions modeled by Gaussian processes (GP). It converts each GP into a state-space prior and uses advanced message-passing techniques for scalable inference.
result FunBaT effectively handles real-world data with continuous indexes, demonstrating its advantage in synthetic and real-world applications.
Goal-conditioned policies are used in order to break down complex reinforcement learning (RL) problems by using subgoals, which can be defined either in state space or in a latent feature space. This can increase the efficiency of learning by using a curriculum, and also enables simultaneous learning and generalization…
Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to …
Non asymptotic estimation lower bounds for LTI state space models with Cramér-Rao and van Treesmath.ST
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in a model and represents uncertainty in model parameters by maintaining a probability distribution over them. This paper presents Monte Carlo BRL (MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a finite set of hypotheses…
Local PCA detects intrinsic parameterization of complex thermo-chemical state-spaces.
problem Detecting intrinsic parameterization of complex thermo-chemical state-spaces.
method Local PCA applied to local clusters of data.
result Local PCA finds meaningful parameterization linked to local stoichiometry, reaction progress, and soot formation processes.
dynestyx: A library for probabilistic programming of dynamical systems
problem integrating state-space models into probabilistic programming languages
method a unified interface for specifying priors and performing inference
result principled uncertainty quantification for state and parameters
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
problem Prohibitive computational and parametric complexity in high-dimensional, non-stationary dynamical systems.
method ETGPSSM integrates a single shared GP with input-dependent normalizing flows for scalable and flexible modeling.
result ETGPSSM outperforms existing models in computational efficiency and accuracy.
Paper proposes a recursive GPSSM for efficient online learning.
problem Efficient online learning for dynamical models with limited prior information.
method Recursive Gaussian Process State-Space Model with adaptive capabilities for domains and hyperparameters.
result Superior accuracy, computational efficiency, and adaptability compared to state-of-the-art methods.
A central challenge in reinforcement learning is discovering effective policies for tasks where rewards are sparsely distributed. We postulate that in the absence of useful reward signals, an effective exploration strategy should seek out {\it decision states}. These states lie at critical junctions in the state space …
Unified approach to Bayesian inference with guarantees on covariance matrices.
problem Approximate Bayesian inference with PSD guarantees.
method Bayes-Newton methods extending Newton's method for optimisation.
result Novel algorithms with PSD covariance matrices.
GP-PSRL achieves sublinear regret for continuous control with unbounded state space.
problem Analyzing regret bounds for GP-PSRL in continuous control with unbounded state space.
method Recursive application of Borell-Tsirelson-Ibragimov-Sudakov inequality and chaining method.
result Sublinear regret bound of for GP-PSRL.
We extend the Deep Image Prior (DIP) framework to one-dimensional signals. DIP is using a randomly initialized convolutional neural network (CNN) to solve linear inverse problems by optimizing over weights to fit the observed measurements. Our main finding is that properly tuned one-dimensional convolutional architectu…
Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is …
Method infers MJPs from noisy observations without prior training.
problem Inference of MJPs from noisy and sparse observations is challenging.
method Broad probability distribution, synthetic dataset, and neural network model.
result Zero-shot inference of MJPs across different state spaces.
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 State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricingq-fin.CP
In this article we investigate a state-space representation of the Lee-Carter model which is a benchmark stochastic mortality model for forecasting age-specific death rates. Existing relevant literature focuses mainly on mortality forecasting or pricing of longevity derivatives, while the full implications and methods …
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
A new method for estimating adversarial strategies in nonlinear systems.
problem Inferring an intelligent adversarial agent's strategy in highly nonlinear systems.
method Formulated inverse cognition as a nonlinear Gaussian state-space model and developed an inverse UKF (IUKF) system.
result The estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.
Study agnostic RL in large state spaces with weak function approximation.
problem Statistical intractability of agnostic policy learning in various environments.
method Investigates agnostic policy learning with different forms of environment access.
result Agnostic policy learning remains statistically intractable with certain forms of environment access.