Related papers: The Onsager--Machlup functional for data assimilat…
Recently, continual learning has received a lot of attention. One of the significant problems is the occurrence of \emph{concept drift}, which consists of changing probabilistic characteristics of the incoming data. In the case of the…
The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…
The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing. Based on strong invariance principles, we analyse data…
This paper considers the problem of minimizing the time average of a stochastic process subject to time average constraints on other processes. A canonical example is minimizing average power in a data network subject to multi-user…
Real-world data deviating from the independent and identically distributed (i.i.d.) assumption of in-distribution training data poses security threats to deep networks, thus advancing out-of-distribution (OOD) detection algorithms.…
Autocorrelations in MCMC chains increase the variance of the estimators they produce. We propose the occlusion process to mitigate this problem. It is a process that sits upon an existing MCMC sampler, and occasionally replaces its samples…
Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…
A method, recently advanced as the conformable Euler method, a general method for the finite difference discretization of fractional initial value problems for fractions in (0, 1], is shown to be valid only for the integer derivative. The…
We present a theoretical framework for M-FISHER, a method for sequential distribution shift detection and stable adaptation in streaming data. For detection, we construct an exponential martingale from non-conformity scores and apply…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…
Walk on stars (WoSt) has shown its power in being applied to Monte Carlo methods for solving partial differential equations, but the sampling techniques in WoSt are not satisfactory, leading to high variance. We propose a guiding-based…
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…
We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.…
Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly…
Weak drift of an infinitely divisible distribution $\mu$ on $\mathbb{R}^d$ is defined by analogy with weak mean; properties and applications of weak drift are given. When $\mu$ has no Gaussian part, the weak drift of $\mu$ equals the minus…
Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and…
We introduce a new approach for decoupling trends (drift) and changepoints (shifts) in time series. Our locally adaptive model-based approach for robustly decoupling combines Bayesian trend filtering and machine learning based…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…