Optimizes Gaussian process hyperparameters using Bayesian autoregression.
problem Optimizing hyperparameters for Matérn kernel temporal Gaussian processes.
method Recursive Bayesian estimation for autoregressive parameters.
result Outperforms traditional optimization methods in runtime and accuracy.
Bayesian method estimates Kronecker graphical models from autoregressive processes.
problem Estimating Kronecker graphical models from autoregressive Gaussian processes.
method Bayesian approach to estimate Kronecker graphical models.
result Effectiveness demonstrated through numerical experiments and real-world data application.
We develop methods to estimate lag and parameters for multiple stable autoregressive processes.
problem Estimating lag and parameters for multiple stable autoregressive processes with unknown lag.
method Use convex programming to simultaneously select lag and estimate parameters across multiple processes.
result The estimated process is stable, and forecasting errors can outperform known rates.
Study improves dividend discount model using VAR process.
problem Improving dividend discount models for better predictions.
method Introduced a Gordon growth model based on Vector Autoregressive Process (VAR).
result Two Propositions related to the new model.
Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings o…
New method for identifying autoregressive systems on manifolds.
problem Identifying autoregressive systems on Stiefel and Grassmann manifolds.
method Defining parameters as orthogonal group elements, averaging over observations, conjugate gradient descent on manifolds.
result System parameters can be estimated efficiently using the proposed algorithm.
Model nonstationary spatial processes using normalizing flows.
problem Difficult selection of spatial warping functions.
method Neural autoregressive flows (NAFs) for complex, high-dimensional warpings.
result NAFs model has greater representational capacity than other spatial process models.
EventFlow forecasts event sequences without autoregression, improving accuracy.
problem Forecasting errors in autoregressive models for event sequences.
method EventFlow uses flow matching to learn joint distributions over event times directly.
result EventFlow reduces forecast error by 20%-53% compared to baselines.
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the estimation of such processes using constrained and penalized estimators. As an applica…
A new online learning setting for autoregressive processes with sublinear regret.
problem Sequential decision-making with temporal dependence in autoregressive processes.
method Autoregressive Bandits (ARBs) and AutoRegressive Upper Confidence Bound (AR-UCB) algorithm.
result Sublinear regret of order $\widetilde{\mathcal{O}} \left( \frac{(k+1)^{3/2}\sqrt{nT}}{(1-Γ)^2}
ight)$ for optimal policy.
Develops probabilistic forecasting for Sea Level Anomalies using Conformal Prediction on functional time series.
problem Forecasting and uncertainty quantification for Sea Level Anomalies.
method Functional data analysis, Conformal Prediction, Functional Autoregressive Processes.
result Proposed method provides accurate probabilistic predictions and uncertainty quantification for Sea Level Anomalies.
We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood …
Efficiently combines autoregressive and set-based models for joint distributions.
problem Joint distributions over multiple predictions from set-based models.
method Causal autoregressive buffer that caches context and captures dependencies.
result Up to 20x faster joint sampling and density evaluation, up to 7x lower memory usage.
Novel F2NARX model improves surrogate modeling for stochastic dynamical systems.
problem Challenges in constructing accurate and efficient surrogate models for stochastic dynamical systems.
method Function-on-Function Nonlinear AutoRegressive model with eXogenous inputs (F2NARX) combining PCA and Gaussian process regression.
result F2NARX outperforms state-of-the-art NARX models in efficiency and accuracy.
Latent Block-Diffusion Temporal Point Processes (LBDTPP) is a semi-autoregressive framework for generating asynchronous event sequences.
problem Generating asynchronous event sequences
method Latent Block-Diffusion Temporal Point Processes
result Outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks
The paper provides a finite-sample deviation bound for stable autoregressive processes.
problem Deviation bounds for least squares estimators in Gaussian AR(n) processes.
method Utilizes martingale concentration inequalities and tail-bound for χ² distributed variables.
result Problem-dependent finite-time bound on the deviation probability of AR(n) process parameters.
Autoregressive sequence models achieve state-of-the-art performance in domains like machine translation. However, due to the autoregressive factorization nature, these models suffer from heavy latency during inference. Recently, non-autoregressive sequence models were proposed to reduce the inference time. However, the…
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic n…
Modified asymmetric hidden Markov models for time series with autoregressive components.
problem Dynamic relationships between variables in time series data.
method Introducing an asymmetric autoregressive component to recent asymmetric hidden Markov models.
result The model can choose the optimal autoregressive order for better likelihood.
In this article, we first propose the modified Hannan-Rissanen Method for estimating the parameters of the autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical character…
This paper presents the R package GAS for the analysis of time series under the Generalized Autoregressive Score (GAS) framework of Creal et al. (2013) and Harvey (2013). The distinctive feature of the GAS approach is the use of the score function as the driver of time-variation in the parameters of nonlinear models. T…
We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability a…
ARCNPs improve CNPs by autoregressively modeling dependencies.
problem CNPs struggle with modeling dependencies in predictions.
method Autoregressive deployment of factorized Gaussian CNPs.
result ARCNPs significantly outperform non-AR CNPs in various tasks.
Paper proposes a self-supervised method to denoise autoregressive signals with heavy-tailed noise.
problem Denoising autoregressive signals corrupted by heavy-tailed noise.
method Self-supervised learning approach without requiring full noise distribution knowledge.
result Strong denoising performance compared to baseline methods, especially for impulsive noise.
This paper proposes an autoregressive (AR) model for sequences of graphs, which generalises traditional AR models. A first novelty consists in formalising the AR model for a very general family of graphs, characterised by a variable topology, and attributes associated with nodes and edges. A graph neural network (GNN) …
Alternative sampling method for autoregressive models using Langevin dynamics.
problem Efficiently sampling from autoregressive models.
method Initialize sequences with white noise and follow Langevin dynamics on global log-likelihood.
result Parallelizes and generalizes sampling process for autoregressive models.
Proposes a non-autoregressive Transformer for time series forecasting.
problem Autoregressive errors and spatial-temporal dependencies in time series forecasting.
method Introduces a Non-Autoregressive Transformer with a learned temporal influence map.
result Demonstrates state-of-the-art performance on time series forecasting datasets.
We consider the Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedasticity process, denoted by FIEGARCH(p,d,q), introduced by Bollerslev and Mikkelsen (1996). We present a simulated study regarding the estimation of the risk measure VaRp on FIEGARCH processes. We consider the distr…
This paper explores how Transformers predict next tokens in autoregressive tasks.
problem Understanding the success of Transformers in autoregressive learning.
method Trained a Transformer on a next-token prediction task, focusing on commuting orthogonal matrices.
result Trained Transformers can be seen as implementing gradient descent for a specific objective function.
A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressi…
Improved language generation with faster sampling speed.
problem Speed and coherence issues in autoregressive language models.
method Introduces Neural Flow Diffusion Models (NFDM) for discrete state spaces.
result Substantially reduces likelihood gap with autoregressive models.
A new method for separating mixed signals in space and time.
problem Nonlinear and nonstationary spatio-temporal data challenges.
method Identifiable autoregressive variational autoencoder.
result The method outperforms existing techniques in blind source separation and spatio-temporal prediction.
DiAMoNDBack models protein backmapping from coarse-grained Cα traces.
problem Restoring all-atom details from coarse-grained protein representations.
method Autoregressive denoising diffusion model for residue-by-residue backmapping.
result Achieves state-of-the-art reconstruction performance in diverse applications.
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.
New method for identifying graph shift operators using vertex-time autoregressive models.
problem Identifying graph shift operators from graph signals.
method Online optimization using vertex-time autoregressive model and stochastic gradient projection.
result Successful recovery of graph shift operators from graph signals.
Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregr…
Non-autoregressive translation (NAT) models remove the dependence on previous target tokens and generate all target tokens in parallel, resulting in significant inference speedup but at the cost of inferior translation accuracy compared to autoregressive translation (AT) models. Considering that AT models have higher a…
Discriminator guidance improves autoregressive diffusion models for generating molecular graphs.
problem Improving the accuracy of autoregressive diffusion models for generating molecular graphs.
method Deriving ways to use a discriminator with a pretrained generative model in the discrete case, including optimal and sub-optimal scenarios.
result Using a discriminator can correct pretrained models and improve exact sampling from the data distribution.
Linear attention in Transformers can be interpreted as dynamic VAR models.
problem Misalignment between Transformers and autoregressive forecasting objectives.
method Interpreting linear attention as VAR, rearranging MLP, attention, and flow.
result SAMoVAR improves performance, interpretability, and efficiency.
Thermalizer stabilizes autoregressive models for long-term predictions in chaotic systems.
problem Long-term predictions in chaotic spatiotemporal systems are unreliable due to trajectory divergence.
method Diffusion models are used to implicitly estimate the score of an invariant measure, which stabilizes autoregressive emulators by applying denoising during inference.
result Thermalization extends the time horizon of stable predictions by an order of magnitude in chaotic systems.
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series eco…
New framework IIA identifies innovations in general nonlinear vector autoregressive processes.
problem Limited generality of NVAR models due to additive innovation assumption.
method Independent Innovation Analysis (IIA) framework, assuming mutual independence and modulation by an auxiliary variable.
result Guarantees identifiability of innovations with arbitrary nonlinearities, up to permutation and component-wise invertible nonlinearities.
The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows for the innovations to be contemporaneously correlated. We overcome the lack of …
Transformers learn a mesa-optimizer to implement in-context learning.
problem Understanding the convergence of autoregressive training to a mesa-optimizer.
method Investigated a one-layer linear causal self-attention model autoregressively trained by gradient flow.
result Proved that autoregressive training converges to a gradient descent step for an OLS problem, validating the mesa-optimizer hypothesis.
We introduce a novel multivariate random process producing Bernoulli outputs per dimension, that can possibly formalize binary interactions in various graphical structures and can be used to model opinion dynamics, epidemics, financial and biological time series data, etc. We call this a Bernoulli Autoregressive Proces…
New GLS estimator handles high-dimensional data with autocorrelated errors.
problem High-dimensional regressions with autocorrelated errors.
method LASSO regression, autoregressive model fitting, and whitening.
result The method outperforms unadjusted LASSO in estimating errors driven by autoregressive processes.
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.
problem Efficiently sampling lattice field theories with computational challenges.
method Integrates locality into autoregressive conditional normalizing flows.
result Autocorrelation times improved by orders of magnitude for φ4 theory on a 2D lattice.