Related papers: A quickest detection problem with false negatives
Concept drift refers to the change of data distributions over time. While drift poses a challenge for learning models, requiring their continual adaption, it is also relevant in system monitoring to detect malfunctions, system failures, and…
The problem of quickest detection of a change in distribution is considered under the assumption that the pre-change distribution is known, and the post-change distribution is only known to belong to a family of distributions…
We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…
We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete…
This paper deals with the problems of consistence and strong consistence of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. A central limit theorem for…
We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
Consider the optimal stopping problem of a one-dimensional diffusion with positive discount. Based on Dynkin's characterization of the value as the minimal excessive majorant of the reward and considering its Riesz representation, we give…
Uncertain changes in data streams present challenges for machine learning models to dynamically adapt and uphold performance in real-time. Particularly, classification boundary change, also known as real concept drift, is the major cause of…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
Brownian motion with known positive drift is sampled in stages until it crosses a positive boundary $a$. A family of multistage samplers that control the expected overshoot over the boundary by varying the stage size at each stage is shown…
We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…
We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be…
In this article we consider a Brownian motion with drift of the form \[dS_t=\mu_t dt+dB_t\qquadfor t\ge0,\] with a specific nontrivial $(\mu_t)_{t\geq0}$, predictable with respect to $\mathbb{F}^B$, the natural filtration of the Brownian…
The problem of detecting a single anomalous process among multiple independent processes is considered. Under a constraint on the number of processes that can be probed simultaneously, the decision maker should decide which processes to…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
We consider a linear stochastic differential equation with stochastic drift and multiplicative noise. We study the problem of approximating its solution with the process that solves the equation where the possibly stochastic drift is…
We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well know that there exists a critical drift which separates those processes which die out almost surely and those which survive with positive…
We consider the problem of optimally stopping a general one-dimensional stochastic differential equation (SDE) with generalised drift over an infinite time horizon. First, we derive a complete characterisation of the solution to this…
We utilize neural network embeddings to detect data drift by formulating the drift detection within an appropriate sequential decision framework. This enables control of the false alarm rate although the statistical tests are repeatedly…