Related papers: A Generalization and Extension of an Autoregressiv…
The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…
Diffusion language models enable any-order generation and bidirectional conditioning, offering appealing flexibility for tasks such as infilling, rewriting, and self-correction. However, their formulation-predicting one part of a sequence…
Contemporary time series analysis has seen more and more tensor type data, from many fields. For example, stocks can be grouped according to Size, Book-to-Market ratio, and Operating Profitability, leading to a 3-way tensor observation at…
We construct an autoregressive model with random coefficients that has a stationary distribution after proper normalization. This limit distribution is found to be stable.
In this paper, we study the derivations, central extensions and the automorphisms of the infinite-dimensional Lie algebra W which appeared in [8] and Dong-Zhang's recent work [22] on the classification of some simple vertex operator…
To predict the next token, autoregressive models ordinarily examine the past. Could they also benefit from also examining hypothetical futures? We consider a novel Transformer-based autoregressive architecture that estimates the next-token…
In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general…
A time series is a sequence of observations taken sequentially in time. The autoregressive integrated moving average is a class of the model more used for times series data. However, this class of model has two critical limitations. It fits…
In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is…
Large language models (LLMs) based on transformer architectures are typically described through collections of architectural components and training procedures, obscuring their underlying computational structure. This review article…
Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions. We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an…
We propose a model for hierarchical structured data as an extension to the stochastic temporal convolutional network. The proposed model combines an autoregressive model with a hierarchical variational autoencoder and downsampling to…
We apply concepts of majorization theory to derive new insights in the field of extremal dependence structures. In particular, we consider the Rearrangement Algorithm by Puccetti and Rueschendorf, where majorization arguments yield a…
This paper provides an ablation-based analysis of latent autoregression in GP-VAE models, building upon our previous work introducing the architecture. Language models typically rely on an autoregressive factorization over tokens. In…
We consider first order expansions of convex penalized estimators in high-dimensional regression problems with random designs. Our setting includes linear regression and logistic regression as special cases. For a given penalty function $h$…