Related papers: A tutorial on reproducing a predefined autocovaria…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…
Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression…
Autoregressive (AR) models, common in sequence generation, are limited in many biological tasks such as de novo peptide sequencing and protein modeling by their unidirectional nature, failing to capture crucial global bidirectional token…
Existing autoregressive (AR) image generative models use a token-by-token generation schema. That is, they predict a per-token probability distribution and sample the next token from that distribution. The main challenge is how to model the…
Generative models in Autonomous Driving (AD) enable diverse scene creation, yet existing methods fall short by only capturing a limited range of modalities, restricting the capability of generating controllable scenes for comprehensive…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…
A causal vector autoregressive (CVAR) model is introduced for weakly stationary multivariate processes, combining a recursive directed graphical model for the contemporaneous components and a vector autoregressive model longitudinally.…
This paper introduces a new parsimonious structure for mixture of autoregressive models. the weighting coefficients are determined through latent random variables, following a hidden Markov model. We propose a dynamic programming algorithm…
Autocovariance of the error term in a time series model plays a key role in the estimation and inference for the model that it belongs to. Typically, some arbitrary parametric structure is assumed upon the error to simplify the estimation,…
This study introduces a novel spatial autoregressive model in which the dependent variable is a function that may exhibit functional autocorrelation with the outcome functions of nearby units. This model can be characterized as a…
Isotonic regression is a nonparametric approach for fitting monotonic models to data that has been widely studied from both theoretical and practical perspectives. However, this approach encounters computational and statistical overfitting…
Conditional visual generation has witnessed remarkable progress with the advent of diffusion models (DMs), especially in tasks like control-to-image generation. However, challenges such as expensive computational cost, high inference…
Prediction of trajectories such as that of pedestrians is crucial to the performance of autonomous agents. While previous works have leveraged conditional generative models like GANs and VAEs for learning the likely future trajectories,…
Symmetries of the auto-cumulant function (the generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using theory of group…
This paper presents Diffusion via Autoregressive models (D-AR), a new paradigm recasting the image diffusion process as a vanilla autoregressive procedure in the standard next-token-prediction fashion. We start by designing the tokenizer…
The paper proposes an identification procedure for autoregressive gaussian stationary stochastic processes wherein the manifest (or observed) variables are mostly related through a limited number of latent (or hidden) variables. The method…
This article studies estimation of a stationary autocovariance structure in the presence of an unknown number of mean shifts. Here, a Yule-Walker moment estimator for the autoregressive parameters in a dependent time series contaminated by…
This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance…