相关论文: On Statistical Methods of Parameter Estimation for…

This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by…

We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…

We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we…

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…

Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation,…

Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…

A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…

In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…

This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…

We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…

In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes the lower bound of its marginalized log-likelihood. Then,…

This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the…

Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…

Recurrence entropy $(\cal S)$ is a novel time series complexity quantifier based on recurrence microstates. Here we show that $\mathsf{max}(\cal S)$ is a \textit{parameter-free} quantifier of time correlation of stochastic and chaotic…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to…

This paper proposes methods of predicting dynamic time series (including non-stationary ones) based on a linguistic approach, namely, the study of occurrences and repetition of so-called N-grams. This approach is used in computational…

Clinical decision requires reasoning in the presence of imperfect data. DTs are a well-known decision support tool, owing to their interpretability, fundamental in safety-critical contexts such as medical diagnosis. However, learning DTs…