New algorithms cluster non-stationary time series data.
problem Clustering time series generated by piecewise stationary processes.
method Proposed a natural formulation and introduced a notion of consistency for clustering.
result Simple, efficient algorithms that work without additional assumptions.
Study finds sample size needed for non-stationary model selection.
problem Accurately selecting graphical models from non-stationary data.
method Analyzed a specific model selection method for non-stationary Gaussian processes.
result Derived a sufficient condition for sample size based on non-stationary data.
In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and non-renewal. We give t…
Study on fake stationary Volterra Heston model for non-stationary processes.
problem Non-stationary nature of true Volterra equations.
method Weak notion of stationarity (fake stationary regime) for inhomogeneous affine Stochastic Volterra equations.
result Existence of limiting distributions in the long run, which may depend on initial state.
New method clusters stationary stochastic processes using covariance-based dissimilarity.
problem Clustering wide-sense stationary ergodic stochastic processes.
method Covariance-based dissimilarity measure with consistent algorithms for offline and online clustering.
result Asymptotically consistent algorithms for efficient clustering.
New kernels model non-stationary data efficiently.
problem Efficiently modeling non-stationary data with Gaussian processes.
method Model spectral density as a mixture of frequency surfaces, solve generalised Fourier transform.
result Derives efficient inference methods for non-stationary kernels.
Flexible non-stationary modeling of spatial outcomes using a mixed-stationary Gaussian process.
problem Limited flexibility in non-stationary models and computational intractability.
method Developed a non-stationary Gaussian process with individually set stationarity parameters at each location, using a non-parametric mixture model to reduce parameters and incorporate spatial correlation.
result Improved prediction efficiency through spatially correlated components in the mixture model.
Efficient GP framework for scalable non-stationary processes.
problem Heavy memory and computational requirements in Gaussian process regression for large data sets.
method Exploits structure in the kernel matrix, uses multiple sets of non-equidistant inducing points, and employs Toeplitz and Kronecker structure for efficient inference.
result Demonstrated scalability on numerical examples and large biomedical datasets.
Extends Gaussian Processes for multi-modal, non-stationary data.
problem Modeling non-stationary multi-modal processes.
method Adds a latent variable to modulate covariance over training data.
result Shows improved modeling of multi-modal and non-stationary processes.
Bayesian Optimization uses Deep Gaussian Processes for non-stationary functions.
problem Optimizing expensive non-stationary functions with classic Gaussian Processes.
method Deep Gaussian Processes as surrogate models for capturing non-stationarity.
result The proposed algorithm outperforms state-of-the-art methods on analytical and aerospace design problems.
Develops a deep non-stationary kernel for non-stationary spatio-temporal point processes.
problem Capturing non-stationary dependencies in point process data.
method Approximates the influence kernel with a novel low-rank decomposition and introduces a log-barrier penalty to maintain non-negativity.
result Demonstrates superior performance and computational efficiency compared to state-of-the-art methods.
Study optimal transport for stationary processes, estimating joinings and costs.
problem Optimal transport for stationary stochastic processes.
method Introduced estimators for optimal joinings and costs, established consistency and error rates.
result Consistent estimators of optimal joinings and costs under mild and stronger mixing assumptions.
Unified review of methods for inferring non-stationary process parameters.
problem Inferring parameters of non-stationary processes without a known model.
method Unified review and categorization of algorithms for Parameter Inference from a Non-stationary Unknown Process (PINUP).
result Simple statistical features can perform well on non-stationary systems, highlighting gaps in existing methods.
Paper proposes a method to remove faults from time-series data using non-stationary Gaussian processes.
problem Fault removal in time-series data with non-stationary Gaussian processes.
method Two non-parametric Gaussian process models for physical phenomenon and fault. Markov Region Link kernel for non-stationary processes.
result Successfully removed drift and bias errors in faulty sensor data and EOG artifact corrupted EEG signals.
The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of bivariate point processes characterized by the intensities as a general class of piecewise deterministic Markov processes. The BDCP describes a rich dynamic structure where the system is under the influence of both external and internal factors model…
Paper introduces a neural network-based non-stationary influence kernel for complex event data.
problem Modeling complex, non-stationary, and dependent discrete event data.
method Neural Spectral Marked Point Processes (NSMPP) with a versatile non-stationary influence kernel.
result NSMPP outperforms state-of-the-art models on synthetic and real data.
This work explores variably scaled kernels to improve non-stationary Gaussian processes.
problem Limited ability of stationary kernels to represent heterogeneous correlation structures.
method Introduces variably scaled kernels to modify correlation structures explicitly.
result Improved reconstruction accuracy and better uncertainty estimates for non-stationary data.
New method for non-stationary GPR using HMC for gradient-based inference.
problem Modeling input-dependent dynamics in non-stationary GPR.
method Gradient-based inference with Hamiltonian Monte Carlo (HMC).
result Non-stationary GPR outperforms stationary models in gene expression modeling.
Study approximates risk process with non-stationary claims using Hawkes process.
problem Approximating risk process with non-stationary claims.
method Gaussian approximation and functional central limit theorem.
result Established diffusion approximation for ruin probability.
The paper studies convergence of kernel autocovariance operators for stationary processes.
problem Estimating autocovariance operators of stationary processes on Polish spaces.
method Investigates convergence of empirical estimates of autocovariance operators under various conditions.
result Provides consistency results for kernel PCA and spectral analysis methods.
New definition of joint stationarity improves process recovery over graphs.
problem Regression tasks with high-dimensional multivariate processes dependent on graph topology.
method Introduces joint stationarity, a new definition that reduces estimation variance and complexity.
result One reliably learns covariance structure from a single realization and solves MMSE problems nearly linearly in time.
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.
This paper shows how to use SS models for non-stationary Gaussian processes.
problem Efficient computation of Gaussian process inferences for large datasets.
method Develops state space representation for non-stationary Gaussian processes.
result Non-stationary kernels can be mapped to state space models.
Flexible GP model improves wind power prediction accuracy.
problem Accurate probabilistic prediction of wind power for grid stability.
method Heteroscedastic non-stationary Gaussian process with generalised spectral mixture kernel.
result The proposed model outperforms conventional GP models in wind power prediction.
Proposes LSGP for better graph signal representation.
problem Local variations in graph process characteristics.
method Locally stationary graph process (LSGP) model.
result LSGP provides accurate signal representations.
New kernel HMK improves Gaussian process expressiveness and supports harmonizable covariances.
problem Improving the expressiveness of Gaussian processes with non-stationary kernels.
method Proposed harmonizable mixture kernel (HMK) and variational Fourier features.
result HMK interpolates between local patterns and offers robust kernel learning.
Neural non-stationary spectral kernels improve performance on benchmark datasets.
problem Learning and discovering complex patterns in data.
method Generalized spectral mixture kernels with input-dependent functions modeled as Gaussian processes and hyperparameter functions as neural networks.
result Neural non-stationary spectral kernels achieve the best performance on benchmark datasets.
The paper analyzes learning schemes for various stationary stochastic processes.
problem Analyzing learning schemes with different stationary stochastic processes.
method Unified treatment of various mixing processes using generalized Bernstein-type inequality.
result Sharp oracle inequalities and convergence rates for learning schemes.
Inter-domain Deep Gaussian Processes improve inference for non-stationary data.
problem Inference limitations in Gaussian processes for non-stationary data.
method Combines inter-domain and deep Gaussian processes for scalable approximate inference.
result Outperforms inter-domain shallow GPs and conventional DGPs on non-stationary data.
Algorithm simulates complex-valued Gaussian processes efficiently.
problem Simulating noncircular or improper complex-valued stationary Gaussian processes.
method Circulant embedding method for multivariate Gaussian processes.
result Exact simulation possible except for negative eigenvalues.
Model separates overall uncertainty into aleatoric and epistemic components for active learning.
problem Active learning with uncertainty quantification.
method Non-stationary Heteroscedastic Gaussian process model.
result Model separates overall uncertainty into aleatoric and epistemic components.
Study on Volterra Cox-Ingersoll-Ross process, proving asymptotic independence and ergodicity.
problem Analyzing the Volterra Cox-Ingersoll-Ross process and its properties.
method Fine asymptotic analysis of Volterra Riccati equation, affine transformation formula.
result Proves asymptotic independence and ergodicity of the process.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
problem Effects of stochastic resetting on geometric Brownian motion.
method Analysis of geometric Brownian motion under stochastic resetting.
result Resetting makes geometric Brownian motion stationary but non-ergodic.
Researchers use Gaussian processes with non-stationary kernels to model precipitation patterns in the Upper Indus Basin.
problem Uncertainty in precipitation patterns in the Upper Indus Basin, Himalayas.
method Proposes Gaussian processes with structured non-stationary kernels to model precipitation patterns, accounting for spatial variation with a latent Gaussian process.
result The proposed model adapts to varying precipitation patterns across distinct topography and outperforms stationary models in ablation experiments.
The paper extends NSGPs with L1-regularization for sparsity and solves the resulting R-NSGP regression problem.
problem Sparsity in non-stationary temporal data.
method Developed an ADMM-based method for solving the regularized NSGP regression problem.
result The proposed methods induce sparsity in the parameters of NSGPs.
Estimates stationary distribution from batch transitions without access to the underlying process.
problem Estimating stationary distribution from batch transitions without access to the underlying process.
method Proposes a consistent estimator based on a correction ratio function and variational power method (VPM).
result VPM provides significantly better estimates across various problems.
Introduces a new stationary GE-process for gold price analysis.
problem Analyzing gold price data with a flexible stationary process.
method Developed a new stationary GE-process with three parameters. Analyzed synthetic and real gold price data.
result Maximum likelihood estimators can be obtained for the unknown parameters.
Strong stability of ergodic iterations proven without ergodic driving sequence.
problem Ensuring strong stability of ergodic iterations under non-ergodic driving sequences.
method Revisiting processes driven by stationary ergodic sequences, proving strong stability under mild conditions on recursive maps.
result Strong stability of iterations proven without ergodic driving sequence.
Consistent estimation of constrained autoregressive processes.
problem Estimating autoregressive processes with coefficients constrained to an ellipsoid.
method Use of constrained and penalized estimators under different norms.
result Provide consistency results for estimation of constrained autoregressive processes.
Solves online resource allocation problems with budget constraints.
problem Maximizing revenue for e-commerce platforms under budget constraints.
method Integrated online optimization and learning algorithm for non-stationary Poisson processes.
result Effective and efficient solutions for constrained resource allocation problems.
Develops Hilbert space for stationary ergodic processes to identify signals in noise.
problem Identifying meaningful signals in noisy data.
method Non-standard generalizations of probability vectors to form a Hilbert space.
result Identifies meaningful angles between data streams and sources under noise.
A new kernel improves Gaussian process performance for non-stationary data.
problem Poor prediction and uncertainty quantification with standard GPs.
method Study and comparison of non-stationary kernels, propose a new combined kernel.
result A new kernel outperforms existing stationary and non-stationary kernels.
The paper develops a stationary-distribution theory for Random Forest ensemble size selection.
problem Determining the optimal number of trees in Random Forests.
method Modeling the ensemble size as a birth-death Markov chain and deriving its stationary distribution.
result The stationary ensemble size B∗ scales as O(ε−2) as ε↓0. New covariance function improves climate model accuracy.
problem Non-stationary and non-uniform spatial data in climate modeling.
method Intrinsic non-stationary covariance function for Gaussian process regression.
result Improved regression estimates for relative sea level changes.
The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
We study the existence of a unique stationary distribution and ergodicity for a 2-dimensional affine process. The first coordinate is supposed to be a so-called alpha-root process with α\in(1,2]. The existence of a unique stationary distribution for the affine process is proved in case of α\in(1,2]; further, in case of…
New rule universally consistent for online learning with non-ergodic data.
problem Online learning with non-ergodic data processes.
method Developed an online learning rule for processes on (X,Y) pairs.
result Generalizes past results to non-ergodic processes on (X,Y).