Related papers: Long-memory process and aggregation of AR(1) stoch…
Motivated by the modeling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a…
In the application of autoregressive models the order of the model is often estimated using either a sequence of likelihood ratio tests, a likelihood based information criterion, or a residual based test. The properties of such procedures…
Image AutoRegressive (IAR) models have achieved state-of-the-art performance in speed and quality of generated images. However, they also raise concerns about memorization of their training data and its implications for privacy. This work…
A statistical inference for random coefficient first-order autoregressive model $[RCAR(1)]$ was investigated by P.M. ROBINSON (1978) in which the coefficients varying over individuals. In this paper we attempt to generalize this result to…
Large language models (LLMs) demonstrate remarkable reasoning capabilities, yet their performance often deteriorates sharply in long-horizon tasks, exhibiting systematic breakdown beyond certain scales. Conventional explanations primarily…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special…
We propose an Embedding Network Autoregressive Model for multivariate networked longitudinal data. We assume the network is generated from a latent variable model, and these unobserved variables are included in a structural peer effect…
In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are…
A quantity of interest to characterise continuous-valued stochastic processes is the differential entropy rate. The rate of convergence of many properties of LRD processes is slower than might be expected, based on the intuition for…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
In the autoregressive process of first order AR(1), a homogeneous correlated time series $u_t$ is recursively constructed as $u_t = q\; u_{t-1} + \sigma \;\epsilon_t$, using random Gaussian deviates $\epsilon_t$ and fixed values for the…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
$L_1$ regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, $L_1$ regularization typically selects…
Online reinforcement learning agents are currently able to process an increasing amount of data by converting it into a higher order value functions. This expansion of the information collected from the environment increases the agent's…
We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the…
We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the…
Traditional studies of memory for meaningful narratives focus on specific stories and their semantic structures but do not address common quantitative features of recall across different narratives. We introduce a statistical ensemble of…
We propose a stochastic process driven by the memory effect with novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of…
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This…