VISA improves inference efficiency for complex models.
problem Efficient approximate inference in computationally intensive models.
method Sequential sample-average approximations within a trust region.
result VISA achieves comparable accuracy with computational savings.
Simulation-based inference methods can produce unreliable posterior approximations.
problem Reliability of simulation-based inference methods for scientific use cases.
method Benchmarked algorithms including Neural Posterior Estimation, Neural Ratio Estimation, Sequential Neural Likelihood, and Approximate Bayesian Computation.
result Ensembling posterior surrogates provides more reliable approximations.
Study approximates unknown function levels with queries.
problem Approximating unknown function levels through sequential queries.
method Introduce Bisect and Approximate algorithms to reduce to local function approximation.
result Rate-optimal sample complexity guarantees for H{ö}lder functions.
Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo (NSMC), a methodology that generalises the SMC framework by requiring only approxi…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors…
New algorithm for clustering data streams with no substitutions.
problem Clustering sequential data with no point substitution.
method Careful risk estimation, linear bin division, multiscale center selection.
result First constant approximation algorithm for random-order k-median clustering.
Bayesian framework for sequential learning tasks with low-rank approximations.
problem Balancing knowledge retention and adaptability in sequential neural networks.
method Bayesian framework with diagonal plus low-rank approximations of the precision matrix.
result Unlocking capabilities to encode task relationships and incorporate prior knowledge from later tasks.
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.
SFSVI uses Gaussian mixtures to approximate neural network outputs for continual learning.
problem Learning new tasks without forgetting old ones in neural networks.
method Sequential function-space variational inference with Gaussian mixture approximation.
result Gaussian mixture SFSVI outperforms other methods in continual learning.
Diffusion Transformer captures spatial-temporal dependencies in sequential data.
problem Capturing rich spatial and temporal dependencies in sequential data.
method Established theoretical guarantees for diffusion transformers learning Gaussian process data.
result Spatial-temporal dependencies are captured within attention layers of diffusion transformers.
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formul…
SigGPDE scales sparse Gaussian processes for sequential data.
problem Predicting and quantifying uncertainty in sequential data.
method Sparse variational inference framework for Gaussian Processes, leveraging GP signature kernel gradients as PDE solutions.
result Significant computational gains and state-of-the-art performance on large sequential datasets.
Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior…
New bounds for SMC show its advantage over MCMC in multimodal distributions.
problem Estimating expectations under multimodal distributions with slow global mixing.
method Proves finite sample complexities for SMC with local mixing times, addressing bias through sequential resampling.
result SMC provides fully polynomial time approximation for multimodal problems.
Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.
problem Efficiently implementing Gaussian process acquisition functions for expensive simulations.
method Proposed a truncated eigenbasis representation for closed-form evaluation of IMSE acquisition function.
result Significantly lower prediction error and reduced computation time compared to benchmarks.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
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.
Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in failure-prone and adversarial environments, sensors get attacked, data get deleted, and a…
New method improves generative model performance by fully conditioning variational posteriors.
problem Inaccurate inference due to partial conditioning of variational posteriors in sequential LVMs.
method Introduces fully-conditioned approximate posteriors to improve generative model performance.
result Improves generative modelling and multi-step prediction performance.
Diffusion approximations optimize sequential experimentation for uncertain parameters.
problem Maximizing reward from unknown parameter Θ with delayed action.
method Bayesian sequential experimentation framework, dynamic programming, diffusion asymptotics.
result Derives diffusion approximation for optimal experimentation strategy.
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.
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample (cross-)moments; it allows to obtain a "sequentialized" version of any static kernel. The…
New method uses SoS densities and α-divergences for efficient sequential transport maps.
problem Efficiently generating samples from approximated densities.
method Sequential transport maps using Sum-of-Squares (SoS) densities and α-divergences.
result Convex optimization problems with efficient semidefinite programming solutions.
We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We describe a procedure for constructing and learning a structured neural network whic…
A universal framework for constructing confidence sets using sequential likelihood mixing.
problem Constructing reliable confidence sets for realizable likelihood functions.
method Sequential likelihood mixing, integrating Bayesian inference and regret inequalities.
result Establishes fundamental connections and provable coverage guarantees for various inference techniques.
vsOED optimizes experiment design with reinforcement learning for Bayesian models.
problem Optimizing the sequence of experiments in Bayesian models for efficient data collection.
method Reinforcement learning with variational posterior approximations to optimize design policy.
result vsOED achieves superior sample efficiency compared to existing methods.
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve Markov chain Monte Carlo sampling with limited applicability to large data sets. W…
The paper proposes using path signatures for better inference in time series data.
problem Simulation models with time series data often lack tractable likelihood functions.
method Approximate Bayesian Computation with path signatures to handle sequential data.
result Theoretical guarantees on the resultant posteriors for Bayesian parameter inference.
A new method for efficient inference in sequential latent-variable models.
problem Computational challenges in integrating subject-specific random effects.
method Anchored variational inference framework to approximate posterior distributions.
result The method achieves accurate estimation with significant computational gains.
Efficient algorithms identify true hypothesis from many options with minimal actions.
problem Identifying true hypothesis from a large set of options with minimal actions.
method Greedy approximation algorithms for active sequential hypothesis testing.
result First approximation guarantees for ASHT, independent of the number of hypotheses.
LSBI approximates likelihood with linear functions for cosmological parameter estimation.
problem Estimating cosmological parameters from complex data.
method Sequential Linear Simulation-based Inference (LSBI) using Gaussian approximations.
result LSBI achieves convergence after 4-5 rounds of simulations, comparable to neural methods.
SNPLA uses normalizing flows for efficient inference in implicit models.
problem Efficient inference in implicit models with complex likelihood and posterior learning.
method Sequential Neural Posterior and Likelihood Approximation (SNPLA) algorithm using normalizing flows.
result SNPLA achieves competitive performance with faster posterior draws compared to MCMC methods.
A new method for online VI in SSMs using asymptotic contrast.
problem Lack of functionality for streaming data in standard VI methods for SSMs.
method Propose maximising an IWAE-type variational lower bound on the asymptotic contrast function using stochastic approximation.
result OSIWAE allows for online learning of model parameters and latent states.
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general, these expectations cannot be calculated analytically, and one way to approximat…
A new method for Bayesian inference using diffusion models.
problem Bayesian inference in simulator-based models.
method Score-based diffusion models trained with a sequential training procedure.
result Comparable or superior performance compared to existing methods.
Enhances SMC² with Hessian info for more efficient posterior approximation.
problem Improving accuracy and efficiency in Bayesian inference.
method Integrates second-order information (Hessian) into SMC²'s proposal distribution.
result Second-order proposals lead to more accurate posterior approximations and better step-size selection.
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings, produce output samples drawn from a distribution that may be far from the target …
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information availab…
This Chapter, "ABC Samplers", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and algorithms used to sample from the ABC approximation to the posterior distribution, including methods based on rejection/importance sampling, MCMC and sequential Monte Carlo.
New methods optimize experiment selection for sequential data, improving model accuracy.
problem Optimizing experiment selection for sequential data in multidimensional cases.
method Adopting greedy experiment selection methods for maximum likelihood estimation.
result Proposed methods produce consistent and asymptotically normal estimators.
New method for evaluating sequential recommendations with lower variance.
problem Evaluating good sequences of music, video, news, and e-commerce recommendations.
method Proposes a new counterfactual estimator for sequential reward interactions with lower variance and asymptotic unbiasedness.
result Our method outperforms existing methods in bias and data efficiency for sequential track recommendations.
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
A new Fusion method combines multiple distributions efficiently.
problem Combining multiple distributions for big data or privacy.
method Recursive divide-and-conquer Monte Carlo approach.
result A robust Fusion method for many sub-posteriors.
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.
OMLE combines optimism and MLE for efficient sequential decision making.
problem Efficiently solving sequential decision making problems, especially in partially observable settings.
method Combines optimism for exploration and maximum likelihood estimation for model learning.
result OMLE learns near-optimal policies for a wide range of sequential decision making problems.
New method for MCMC models without perfect or sequential samplers.
problem Bayesian inference for complex models with intractable terms.
method Utilizes tractable independence model to construct unbiased estimates.
result Scalable method for high-dimensional models.
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.
Approximate inference in probabilistic graphical models (PGMs) can be grouped into deterministic methods and Monte-Carlo-based methods. The former can often provide accurate and rapid inferences, but are typically associated with biases that are hard to quantify. The latter enjoy asymptotic consistency, but can suffer …