The chapter compares Gaussian process models for stochastic simulators with varying noise.
problem Modeling stochastic simulators with varying noise.
method Various Gaussian process models are compared, including input varying noise variance, non-Gaussian noise, and quantile modeling.
result Sequential design procedures are adapted for these models.
Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes. However, a large class of problems comprises underlying temporal dependency structures in a sequence of stochastic processes that Neural Processes (NP) do not e…
Unified framework connects reinforcement learning and optimal control.
problem Sequential decision-making across different communities.
method Unified modeling framework based on optimizing policies.
result Unified framework includes four universal policy classes.
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting. Our algorithm is applicable to both finite hidden Markov models and hierarchical D…
Stochastic gradient descent approximates Gaussian process posteriors efficiently.
problem Efficiently sampling from Gaussian process posteriors with limited computational resources.
method Developed stochastic gradient optimization objectives for sampling from Gaussian process posteriors.
result Stochastic gradient descent produces accurate predictive distributions, even in non-convergent cases.
RANP improves neural processes for sequential data.
problem Capturing temporal order and recurrent structure from sequential data.
method Incorporated ANP into a recurrent neural network.
result RANP outperforms NPs and LSTMs in 1D regression and autonomous-driving tasks.
We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic volatility and unknown stock appreciation rate. The volatility parameter is driven by an external economic factor modeled as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use the dynami…
We solve a broad class of sequential decision-making problems with partially observed states.
problem Sequential decision-making under uncertainty with partially observed states.
method Modeling as a partially observed Markov decision process (POMDP) and separating state and modulation process.
result The approach allows for specialized approximate solution procedures.
Algorithm solves job acceptance problem with random arrivals and values.
problem Decision-making under random job arrivals and values with limited acceptance.
method Proposes Non-Parametric Sequential Allocation (NPSA) algorithm.
result Expected reward converges to optimality as sample size increases.
PASOA optimizes Bayesian design by improving SMC samplers and EIG.
problem Sequential design optimization for accurate parameter inference.
method Sequential optimization using contrastive estimation, SMC samplers, and tempering.
result PASOA optimizes design and inference with improved consistency.
This work introduces a new model for complex stochastic processes.
problem Difficulties in representing non-stationary distributions with conventional models.
method Recurrent Autoregressive Flows using normalizing flows with recurrent neural connections.
result Demonstrates the effectiveness of the proposed model through experiments.
Adaptive batching improves Gaussian process surrogates for noisy level set estimation.
problem Learning the level set of noisy simulator responses.
method Developed four novel adaptive batching schemes for Gaussian process metamodels.
result Adaptive batching brings significant computational speed-ups with minimal loss of modeling fidelity.
This paper speeds up iterative GP inference with warm starting.
problem Improving scalability of Gaussian process inference.
method Warm starting sequential posteriors using known solutions.
result Significant speed-ups and improved Bayesian optimisation performance.
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong theoretical results from stochastic analysis. Signatures capture sequential struc…
Self-balancing sampler improves sampling efficiency and unpredictability.
problem Efficient and unpredictable sampling in various applications.
method Adaptive biasing of sampling probabilities to achieve faster convergence and unpredictability.
result Self-balancing sampler converges at O(n−1) rate, outperforming IID sampling. We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood estimation, we explore the associated risk bound. Further, we consider the superposition o…
Optimal sequential testing for Markovian data with lower and upper bounds.
problem Sequential hypothesis testing for Markovian data.
method Non-asymptotic lower bounds and optimal test design.
result Optimal test matches lower bound asymptotically.
Model change points in time-series data with neural SDEs and variational autoencoders.
problem Modeling change points in time-series data with neural stochastic differential equations.
method Proposes a novel model formulation and training procedure based on the variational autoencoder framework, alternating between updating neural SDE parameters and change points.
result Demonstrates the expressive power of the proposed model in modeling both classical parametric SDEs and real datasets with distribution shifts.
Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing linear learners using SG…
Warm-start strategies speed up GP inference by 19x.
problem Efficient sequential inference in Gaussian processes.
method Three warm-start strategies exploiting smaller linear systems.
result Warm-starting achieves up to 19x speed-up in convergence.
We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic samplers, in particular with heavy-tailed simulation noise and low signal-to-no…
Efficient methods for answering complex probabilistic queries in sequential data.
problem Complex probabilistic queries in sequential data.
method Broad class of novel approximation techniques for marginalization in sequential models.
result Efficient techniques for answering long-range probabilistic queries.
The paper tests hypotheses on two Lévy process-driven streams of observations.
problem Testing hypotheses on two Lévy process-driven streams of observations.
method Infinitesimal generators and super/sub-solutions are used to compute bounds and analyze the model.
result Bounds for infinitesimal generators are computed in terms of super/sub-solutions.
This study models target trajectories using stochastic processes for efficient tracking.
problem Efficiently modeling and predicting target trajectories in continuous time.
method Decomposes trajectory modeling into deterministic and stochastic components using Gaussian or Student's-t processes. result Demonstrates superior performance in tracking maneuvering targets compared to existing methods.
The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not efficiently capture the setting where the set of available decisions (actions) at each time step is stochastic. Recently, the stochastic action set Markov decision process (SAS-MDP) formulation has b…
Online VSMC efficiently learns SSM parameters in streaming data.
problem Parameter learning and latent state inference in state-space models.
method Combines particle methods and variational inference for online learning.
result Online VSMC achieves efficient, entirely on-the-fly parameter estimation and particle proposal adaptation.
The paper uses Bayesian methods to infer hidden processes with unknown parameters.
problem Estimating hidden processes from noisy observations with unknown parameters.
method Variational Bayesian inference with autoregressive moving average (ARMA) and vector autoregressive (VAR) models, combined with sequential Monte Carlo (SMC) and importance sampling resampling (SISR).
result The proposed inference method accurately estimates hidden states from non-linear noisy observations.
We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem for an auxiliary observation process. The solution can be approximated efficiently…
Combines Bézier curves with Gaussian processes for better sequential data modeling.
problem Limited expressiveness of MDNs in probabilistic modeling of sequential data.
method Integrates Gaussian processes with probabilistic Bézier curves for full Bayesian inference.
result Improves expressiveness of MDNs by enabling full Bayesian inference.
Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L) Lemma, the Restricted Isometry Property (RIP), randomized sketching algorithms, …
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is controlled by a shared global latent process and a private local latent process…
Enhances interpolation paths in latent space using particle filters.
problem Generating meaningful interpolations between data points in latent space.
method Introduces a discriminator network to guide particle filter sampling of interpolation paths.
result Improved variability and stronger drift towards high data density areas.
Generative adversarial network for probabilistic forecasting of random systems.
problem Forecasting random dynamical systems without distributional assumptions.
method Recurrent neural network and generative adversarial network (GAN) with regularization based on maximum mean discrepancy (MMD).
result The proposed model successfully forecasts complex stochastic processes with multiple-step predictions.
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with t…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility models that uses opening and closing prices along with the minimum and maximum p…
Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
Extends GP models for sequential data, scalable and robust.
problem Handling sequential input-output observations in multi-task settings.
method Variational inference with sparse approximations and recursive GP priors.
result Tractable continual learning with KL divergences and recursive reconstruction.
Signature kernel handles sequential data with theoretical and practical advantages.
problem Handling sequential data efficiently and accurately.
method Positive definite kernel based on stochastic analysis with efficient computation.
result Strong empirical performance and theoretical guarantees.
We develop a probabilistic framework for sequential random projection.
problem Challenges of sequential decision-making under uncertainty.
method Novel construction of a stopped process and method of mixtures.
result Achieved a non-asymptotic probability bound for random projection.
A training-free method for conditional sampling using flow matching.
problem Weight degeneracy in high-dimensional importance sampling.
method Sequential Monte Carlo with resampling and stochastic flow.
result Significantly outperforms existing methods on MNIST and CIFAR-10.
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.
A new method uses ABC-SMC to infer hybrid models in bioprocesses with limited data.
problem Inference of hybrid models in bioprocesses with limited real data and high uncertainties.
method Approximate Bayesian Computation with Sequential Monte Carlo (ABC-SMC) and linear Gaussian dynamic Bayesian network (LG-DBN) for posterior distribution approximation.
result The method accelerates hybrid model inference and supports process monitoring and robust control.
New SMC samplers improve stochastic optimisation efficiency.
problem Optimizing functions with intractable gradients in machine learning and statistics.
method Sequential Monte Carlo (SMC) samplers for stochastic optimisation.
result Significant computational gains achieved with SMC approximations.
Gaussian processes help in modeling complex, nonlinear relationships in signal processing.
problem Modeling complex, nonlinear relationships in signal processing.
method Sequential inference for Gaussian processes.
result Gaussian processes enable efficient and accurate modeling of complex relationships.
This paper shows how to combine optimal tests into log-optimal processes.
problem How to combine optimal sequential tests into log-optimal processes.
method Using a new class of WAIT e-processes, the paper aggregates asymptotically optimal sequential tests into asymptotically log-optimal processes.
result It is possible to aggregate asymptotically optimal sequential tests into asymptotically log-optimal e-processes.
In recent years, active subspace methods (ASMs) have become a popular means of performing subspace sensitivity analysis on black-box functions. Naively applied, however, ASMs require gradient evaluations of the target function. In the event of noisy, expensive, or stochastic simulators, evaluating gradients via finite …
Dynamic probabilistic forecasts guide optimal decisions in uncertain processes.
problem Optimal decision making in processes influenced by uncertain random factors.
method Stochastic models for probabilistic forecast evolution, calibrated from ensemble forecasts.
result Optimal decision strategies determined using dynamic probabilistic forecasts.
New method solves optimization problems with stochastic objectives and constraints.
problem Optimization problems with stochastic objectives and deterministic constraints.
method Trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method.
result Global almost-sure convergence to first-order stationary points under standard assumptions.