Related papers: Stability of Optimal Filter Higher-Order Derivativ…
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are…
In many applications, a state-space model depends on a parameter which needs to be inferred from a data set. Quite often, it is necessary to perform the parameter inference online. In the maximum likelihood approach, this can be done using…
The problem of stability of the optimal filter is revisited. The optimal filter (or filtering process) is the conditional probability of the current state of some stochastic process (the signal process), given both present and past values…
We consider a hidden Markov model with multiplicative noise emerging from studies of software reliability. We show the stability of the optimal filter with respect to general initial conditions in the total variation- and $L^p$-norm and…
Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity,…
Weighted finite-state machines are a fundamental building block of NLP systems. They have withstood the test of time -- from their early use in noisy channel models in the 1990s up to modern-day neurally parameterized conditional random…
This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished…
A stable filter has the property that it asymptotically `forgets' initial perturbations. As a result of this property, it is possible to construct approximations of such filters whose errors remain small in time, in other words…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in $V$-norm, path-wise along almost all observation sequences. In contrast to previous works, our results allow for unbounded…
When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on…
Can stochastic gradient methods track a moving target? We study the problem of tracking multidimensional time-varying parameters under noisy observations and possible model misspecification. Gradient-based filters update the time-varying…
The utilization of online stochastic algorithms is popular in large-scale learning settings due to their ability to compute updates on the fly, without the need to store and process data in large batches. When a constant step-size is used,…
Differentiation filters can be made proper by composition with a first-order low-pass filter at a desired bandwidth, resulting in a "dirty derivative." A stable closed-loop system that relies on output derivatives remains stable when the…
We are interested in the optimal filter in a continuous time setting. We want to show that the optimal filter is stable with respect to its initial condition. We reduce the problem to a discrete time setting and apply truncation techniques…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
We develop an online gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…