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Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
An important assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of "no change-point" is stationary. This…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…
A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in…
We study subsampling estimators for the limit variance \[ \sigma^2=Var(X_1)+2 \sum_{k=2}^\infty Cov(X_1,X_k) \] of partial sums of a stationary stochastic process $(X_k)_{k\geq 1}$. We establish $L_2$-consistency of a non-overlapping block…
In many real-world applications, continuous machine learning (ML) systems are crucial but prone to data drift, a phenomenon where discrepancies between historical training data and future test data lead to significant performance…
Segmentation of moving objects in dynamic scenes is a key process in scene understanding for navigation tasks. Classical cameras suffer from motion blur in such scenarios rendering them effete. On the contrary, event cameras, because of…
Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…
We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of…
Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…
Changepoint models typically assume the data within each segment are independent and identically distributed conditional on some parameters which change across segments. This construction may be inadequate when data are subject to local…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We study numerical methods for the nonlinear partial differential equation that governs the motion of level sets by affine curvature. We show that standard finite difference schemes are nonlinearly unstable. We build convergent finite…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
Since the work of Page in the 1950s, the problem of detecting an abrupt change in the distribution of stochastic processes has received a great deal of attention. In particular, a deep connection has been established between Lorden's…
Moving object segmentation based on LiDAR is a crucial and challenging task for autonomous driving and mobile robotics. Most approaches explore spatio-temporal information from LiDAR sequences to predict moving objects in the current frame.…
In preliminary analysis of control charts, one may encounter multiple shifts and/or outliers especially with a large number of observations. The following paper addresses this problem. A statistical model for detecting and estimating…