Related papers: Phasetype distributions, autoregressive processes …
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
In this work, we employ autoregressive models developed in financial engineering for modeling of forest dynamics. Autoregressive models have some theoretical advantage over currently employed forest modeling approaches such as Markov chains…
We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis,…
The optimal (`equilibrium') macroscopic properties of an economy with $N$ industries endowed with different technologies, $P$ commodities and one consumer are derived in the limit $N\to\infty$ with $n=N/P$ fixed using the replica method.…
We propose a novel recursive system identification algorithm for linear autoregressive systems with skewed innovations. The algorithm is based on the variational Bayes approximation of the model with a multivariate normal prior for the…
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at…
We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show…
Overshoot is a novel, momentum-based stochastic gradient descent optimization method designed to enhance performance beyond standard and Nesterov's momentum. In conventional momentum methods, gradients from previous steps are aggregated…
The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which system's outputs are contaminated by possibly large…
We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal observations of such time series…
Generalized autoregressive score (GAS) models are a class of observation-driven time series models that employ the score to dynamically update time-varying parameters of the underlying probability distribution. GAS models have been…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
We consider the problem of finding confidence intervals for the risk of forecasting the future of a stationary, ergodic stochastic process, using a model estimated from the past of the process. We show that a bootstrap procedure provides…
The problem of sums of independent, identically distributed random variables with stretched-exponential tails exhibits a dynamical phase transition and has recently reemerged in the context of active transport and condensation phenomena. We…
In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion…
The growing interest for high dimensional and functional data analysis led in the last decade to an important research developing a consequent amount of techniques. Parallelized algorithms, which consist in distributing and treat the data…
In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…