A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
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…
A novel multi-resolution Gaussian process model for efficient time traversal.
Active learning selects inputs for GPSSM to learn latent states.
Develops state-space deep Gaussian processes for irregular signals.
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…
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 …
The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the variational sparse approximation which relies on inducing points and 2) the state-space…
A new model detects anomalies in time series data efficiently.
New method speeds up Gaussian process inference for large datasets.
A new active learning method for Gaussian process models.
ETGPSSM efficiently models high-dimensional, non-stationary systems with reduced complexity.
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 …
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dy…
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…
We prove a conjecture about approximating Gaussian Processes on one dimension.
New GP model tackles physics constraints efficiently.
A method for robust reinforcement learning in large state spaces.
New Hida-Matérn kernels enable flexible process priors and efficient GP inference.
Paper proposes a recursive GPSSM for efficient online learning.
We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using …
The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS …
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…
Enhances Gaussian process models for handling variable error variances and multiple responses.
New method for efficient Bayesian inference in GPSSMs.
We extend Neural Processes (NPs) to sequential data through Recurrent NPs or RNPs, a family of conditional state space models. RNPs model the state space with Neural Processes. Given time series observed on fast real-world time scales but containing slow long-term variabilities, RNPs may derive appropriate slow latent …
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…
Combines pseudo-point and state space approximations for scalable GPs.
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
New method for state inference in state-space models with unknown dynamics.
Improved Gaussian Process model for predicting trajectories without independence assumption errors.
Gaussian processes help in modeling complex, nonlinear relationships in signal processing.
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model inside a particle filter framework. Model updating is done at measurement sample …
Bayesian filtering approach identifies nonlinear restoring forces in dynamic systems.
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficientl…
A new framework using kernel packets overcomes limitations of state space models for multi-dimensional data.
Efficient Reinforcement Learning usually takes advantage of demonstration or good exploration strategy. By applying posterior sampling in model-free RL under the hypothesis of GP, we propose Gaussian Process Posterior Sampling Reinforcement Learning(GPPSTD) algorithm in continuous state space, giving theoretical justif…
Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.
Study uses a bivariate model to price crude oil futures.
The paper introduces a new pairs trading model using nonlinear and non-Gaussian state-space models.
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the system states and the transition function. We exploit Markov structure in the true…
Unified approach to Bayesian inference with guarantees on covariance matrices.
The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in…
Bayesian approach for learning spatiotemporal systems from noisy data.
Robust state-space radio interferometric imaging using Stochastic Approximation Expectation Maximization
We propose a method to optimise the parameters of a policy which will be used to safely perform a given task in a data-efficient manner. We train a Gaussian process model to capture the system dynamics, based on the PILCO framework. Our model has useful analytic properties, which allow closed form computation of error …
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…