相关论文: Stochastic Formulation of Causal Digital Twin: Kal…

In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…

Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal…

We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require…

Many state estimation and control algorithms require knowledge of how probability distributions propagate through dynamical systems. However, despite hybrid dynamical systems becoming increasingly important in many fields, there has been…

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear…

Since the innovation of the ubiquitous Kalman filter more than five decades back it is well known that to obtain the best possible estimates the tuning of its statistics $X_0$, $P_0$, $\Theta$, $R$ and $Q$ namely initial state and…

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic…

State estimation of dynamical systems in real-time is a fundamental task in signal processing. For systems that are well-represented by a fully known linear Gaussian state space (SS) model, the celebrated Kalman filter (KF) is a low…

A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an…

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…

One major drawback of state-of-the-art artificial intelligence is its lack of explainability. One approach to solve the problem is taking causality into account. Causal mechanisms can be described by structural causal models. In this work,…

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…

We consider the problem of distributed Kalman filtering for sensor networks in the case there are constraints in data transmission and there is model uncertainty. More precisely, we propose two distributed filtering strategies with…

It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where…

Kalman smoothers reconstruct the state of a dynamical system starting from noisy output samples. While the classical estimator relies on quadratic penalization of process deviations and measurement errors, extensions that exploit Piecewise…

The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…

Simultaneous Localization and Mapping (SLAM) algorithms perform visual-inertial estimation via filtering or batch optimization methods. Empirical evidence suggests that filtering algorithms are computationally faster, while optimization…

A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent…

Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…