Related papers: Sensitivity, robustness and identifiability in sto…
Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…
The Fisher information matrix can be used to characterize the local geometry of the parameter space of neural networks. It elucidates insightful theories and useful tools to understand and optimize neural networks. Given its high…
We advocate a numerically reliable and accurate approach for practical parameter identifiability analysis: Applying column subset selection (CSS) to the sensitivity matrix, instead of computing an eigenvalue decomposition of the Fischer…
We propose a numerical technique for parameter inference in Markov models of biological processes. Based on time-series data of a process we estimate the kinetic rate constants by maximizing the likelihood of the data. The computation of…
Sensitivity analysis of biochemical reactions aims at quantifying the dependence of the reaction dynamics on the reaction rates. The computation of the parameter sensitivities, however, poses many computational challenges when taking…
The Fisher matrix formalism has in recent times become the standard method for predicting the precision with which various cosmological parameters can be extracted from future data. This approach is fast, and generally returns accurate…
We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for…
A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
The Quantum Fisher Information Matrix (QFIM) plays a crucial role in quantum optimization algorithms such as Variational Quantum Imaginary Time Evolution and Quantum Natural Gradient Descent. However, computing the full QFIM incurs a…
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
We study the problem of parameter estimation in time series stemming from general stochastic processes, where the outcomes may exhibit arbitrary temporal correlations. In particular, we address the question of how much Fisher information is…
This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for…
Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables,…
We investigate the quantum parameter estimation in circuit quantum electrodynamics via dispersive measurement. Based on the Metropolis Hastings (MH) algorithm and the Markov chain Monte Carlo (MCMC) integration, a new algorithm is proposed…
The Fisher matrix approach (Fisher 1935) allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a…
The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…