The paper uses persistent homology to estimate recurrence times in multi-variate time series.
problem Estimating recurrence times in multi-variate time series with different cyclic behaviors.
method Persistent homology framework with three specialized methods.
result Validated methods on real-world data, including a new benchmark dataset.
Extends tracking guarantees for time-varying variational inequalities.
problem Tracking solutions of time-varying variational inequalities.
method Extends existing results to sublinear solution paths and periodic problems.
result Discrete dynamical systems of periodic time-varying VI can exhibit chaotic behavior or converge to the solution.
Variational Prediction simplifies Bayesian inference without test time costs.
problem Bayesian inference's computational costs and posterior predictive distribution marginalization.
method Variational Prediction learns a variational approximation to the posterior predictive distribution using a variational bound.
result Directly learns a variational approximation to the posterior predictive distribution without test time marginalization costs.
New clustering algorithm for time series data using RNN and variational Bayes.
problem Lack of generative model-based clustering methods for time series data.
method Recurrent Neural Network (RNN) with variational Bayes method.
result Robustness against phase shift, amplitude, and signal length variations.
Continuous latent time series models are prevalent in Bayesian modeling; examples include the Kalman filter, dynamic collaborative filtering, or dynamic topic models. These models often benefit from structured, non mean field variational approximations that capture correlations between time steps. Black box variational…
Two popular classes of methods for approximate inference are Markov chain Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run for a long enough time, while variational inference tends to give better approximations at shorter time horizons. However, the amount of time needed for MCMC to exceed…
Bayes-CATSI uses variational Bayesian deep learning for medical time series data imputation.
problem Missing values in medical time series data.
method Bayes-CATSI integrates variational inference for uncertainty quantification and context-aware imputation.
result Bayes-CATSI outperforms CATSI by 9.57% in imputation performance.
DualVDT improves time-series forecasting with a novel dual reparametrized structure.
problem Time-series forecasting with improved performance and analytical rigor.
method Dual reparametrized variational mechanisms on VAE, latent score based generative model, reverse time stochastic differential equation, variational ancestral sampling, KL divergence reduction.
result Advanced performance in time-series forecasting with reduced KL divergence.
Gaussian process variational autoencoders improve disentanglement in time series data.
problem Learning disentangled representations from multivariate time series data.
method Model each latent channel with a Gaussian process prior and a structured variational distribution to capture temporal dependencies.
result Competitive performance on benchmark and real-world medical time series data.
New algorithm for continuous-time switching systems using variational inference.
problem Inference in time-series data with continuous-time switching systems.
method Developed a variational inference algorithm combining Gaussian process approximation and posterior inference for Markov jump processes.
result Bayesian latent state estimates and point estimates of unknown parameters for arbitrary points on the real axis.
CLPF models continuous time-series data with improved representational power and variational approximations.
problem Fitting continuous time-series data with existing models faces challenges in representational power and variational quality.
method CLPF uses a time-dependent normalizing flow driven by a stochastic differential equation to decode continuous latent processes into continuous observables. Maximum likelihood optimization is achieved through a novel variational posterior process.
result CLPF outperforms state-of-the-art baselines on synthetic and real-world time-series data.
VCoTTA uses variational Bayesian methods to adapt models under continuous domain shifts.
problem Error accumulation in continual test-time adaptation.
method VCoTTA employs variational Bayesian techniques to update a Bayesian Neural Network (BNN) during testing, combining priors from source and teacher models.
result VCoTTA effectively mitigates error accumulation in CTTA, as shown by experimental results on three datasets.
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future…
We consider variation of energy of the light-like particle in Riemann space-time, find lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance with principles of the calculus of variations in mechanics. This method is shown to not lea…
Research into time series classification has tended to focus on the case of series of uniform length. However, it is common for real-world time series data to have unequal lengths. Differing time series lengths may arise from a number of fundamentally different mechanisms. In this work, we identify and evaluate two cla…
New model predicts energy prices volatility by smoothing time variation and persistence.
problem Separate study of volatility's time variation and persistence.
method Dynamic persistence model that allows shocks with heterogeneous persistence to vary smoothly over time.
result Significantly improves volatility forecasts over state-of-the-art models.
VHVM models financial time series with varying volatility.
problem Modeling heteroscedastic behavior in multivariate financial time series.
method Variational autoencoder and recurrent neural network for capturing relationships and temporal dynamics.
result VHVM outperforms GARCH and SV models on FX datasets.
New method speeds up Gaussian process inference for large datasets.
problem Numerical instability and inefficiency in approximate inference methods for non-Gaussian likelihoods.
method Conjugate-computation variational inference with Kalman recursions.
result Linear-time inference with fast and stable variational inference for state-space GP models.
Improves scalability and efficiency of mixture models in black-box variational inference.
problem Scaling mixture models in black-box variational inference leads to high parameter and time costs.
method Introduces MISVAE for amortized mixture parameter space and new ELBO estimators.
result Achieves superior estimation performance with fewer parameters and shorter inference time.
A new method scales Gaussian process variational autoencoders to handle high-dimensional time series.
problem Scalability issue in Gaussian process variational autoencoders (GPVAEs).
method Introducing Markovian GPs and using Kalman filtering and smoothing for linear time training.
result MGPVAE outperforms existing approaches in various tasks with high scalability.
Improved state estimation in nonlinear models using amortized backward variational inference.
problem State estimation in general state-space models.
method Amortized backward variational inference with neural network parameters.
result Linear growth of variational approximation error in number of observations.
Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.
problem Estimating posterior densities in probabilistic models.
method Variational formulation of particle flow, Fisher-Rao gradient flow, Gaussian and Gaussian mixture approximations.
result Gaussian and Gaussian mixture approximations of Fisher-Rao particle flow reduce to Exact Daum and Huang particle flow under linear Gaussian assumptions.
This paper models time-series data with a mixture of Markov chains, automatically determining the number of components.
problem Tackles the inability of common Markov state modeling frameworks to discern heterogeneities in complex data.
method Uses a mixture of Markov chains and variational expectation-maximization algorithm for automatic component selection.
result Achieves performance consistent with theoretically optimal error scaling, identifying meaningful heterogeneities in various data sets.
This paper examines challenges and solutions for solving variational inequalities.
problem Stability issues in solving variational inequalities, especially in multi-objective scenarios.
method Continuous-time analysis to understand and improve stability of algorithms.
result Understanding continuous-time dynamics can help in designing more stable algorithms for variational inequalities.
Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulat…
Paper introduces COBRA variations for multivariate time series forecasting.
problem Multivariate time series forecasting challenges.
method Innovative COBRA variations, data preprocessing, Bayesian optimisation vs. grid search.
result Proposed methodologies outperform state-of-the-art models.
A new method infers neural trajectories in real-time, improving experimental design.
problem Real-time inference of neural trajectories for immediate feedback.
method Exponential family variational Kalman filter (eVKF) for online learning.
result eVKF achieves competitive performance on synthetic and real-world data.
VSI model predicts survival distributions efficiently.
problem Predicting time-to-event distributions in clinical applications.
method Variational framework for non-parametric distribution estimation.
result Improved performance over competing solutions.
We review three algorithms for Latent Dirichlet Allocation (LDA). Two of them are variational inference algorithms: Variational Bayesian inference and Online Variational Bayesian inference and one is Markov Chain Monte Carlo (MCMC) algorithm -- Collapsed Gibbs sampling. We compare their time complexity and performance.…
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
Develops a variational method for ultrametric phylogenetic trees.
problem Accurate and efficient approximation of posterior distributions over trees in Bayesian phylogenetics.
method Variational Bayesian approach based on coalescent times of a single-linkage clustering.
result Achieves competitive accuracy with significantly fewer gradient evaluations.
Proposes a model for multi-horizon probabilistic forecasting of time series influenced by asynchronous events.
problem Forecasting time series influenced by asynchronous events is challenging.
method Introduces Variational Synergetic Multi-Horizon Network (VSMHN), a deep conditional generative model combining deep point processes and variational recurrent neural networks.
result Produces accurate, sharp, and realistic probabilistic forecasts.
Derives optimal control conditions using calculus of variations.
problem Optimizing Markov control in stochastic control problems.
method Calculus of variations approach to derive necessary conditions.
result Solves the Merton portfolio optimization problem.
A new model captures variability in time series data.
problem Capturing high variability in time series data.
method Temporal latent variables and dynamic weight modifications.
result Demonstrated efficacy on various sequential data.
Warm starts improve variational quantum algorithms by avoiding barren plateaus.
problem Barren plateaus in variational quantum algorithms limit scaling.
method Exploring warm starts in iterative variational methods for quantum circuits.
result Warm starts can lead to substantial gradients in small regions, suggesting trainability.
A new model integrates LSTM and copulas for high-dimensional financial data.
problem Modeling high-dimensional dependencies across financial markets.
method Variational LSTM with regular vine copulas.
result Outperforms benchmarks in cross-market portfolio forecasting.
We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trad…
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
A distributed framework for reducing high-dimensional matrix-variate time series data.
problem Reducing dimensionality of high-dimensional, heterogeneous matrix-variate time series data.
method Data partitioning, distributed two-dimensional tensor PCA, aggregation, final PCA, factor matrix computation.
result Preserves latent matrix structure, improves computational efficiency and information utilization.
Time-variant value function transfer method for RL.
problem Transfer learning with time-variant task distributions.
method Variational approach leveraging temporal structure.
result The proposed method outperforms time-invariant approach in experiments.
We derive asymptotic expansions for option data to detect infinite variation volatility.
problem Detecting infinite variation volatility in high-frequency option data.
method Nonparametric higher-order asymptotic expansions for small-time changes of characteristic functions of Itô semimartingales.
result Evidence of infinite variation volatility in high-frequency option data.
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic splines, are well captured by genetic programming in the form of dynamical equations. …
New method models longitudinal data using variational inference and normalizing flows.
problem Handling high-dimensional longitudinal data with time dependency.
method Variational inference with normalizing flows for latent variables.
result The method achieves better likelihood estimates and more reliable missing data imputation.
The paper studies curves in Riemannian manifolds using total variation flow.
problem Analyzing the evolution of curves in Riemannian manifolds using total variation.
method Defining and proving the existence of strong solutions to the flow equations, showing variational equality, and proving convergence.
result Strong solutions converge to a constant map in finite time for non-positive sectional curvature.
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational posterior. However, existing methods on implicit posteriors still face challenges of…
Proposes a new VAE framework for anomaly detection in time series data.
problem Data scarcity leads to latent holes and discontinuous regions in latent space, causing non-robust reconstructions.
method Combines VAEs with self-supervised learning to address data scarcity and improve anomaly detection.
result Improves robustness of anomaly detection in time series data by addressing latent holes and discontinuities.
Paper establishes lower bounds for non-stationary kernelized bandits.
problem Optimizing functions with noisy observations in non-stationary scenarios.
method Develops algorithm-independent lower bounds for time-varying functions under total variation constraints.
result First algorithm-independent lower bounds for time-varying kernelized bandits.
We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vi…