Related papers: Automatic estimation of attractor invariants

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…

This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…

A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…

Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness. The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in…

We study instrumental variable regression in data rich environments. The goal is to estimate a linear model from many noisy covariates and many noisy instruments. Our key assumption is that true covariates and true instruments are…

We introduce an algorithm to locate contours of functions that are expensive to evaluate. The problem of locating contours arises in many applications, including classification, constrained optimization, and performance analysis of…

We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…

Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties…

This paper studies the multi-task high-dimensional linear regression models where the noise among different tasks is correlated, in the moderately high dimensional regime where sample size $n$ and dimension $p$ are of the same order. Our…

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

We investigate the problem of estimating a given real symmetric signal matrix $\textbf{C}$ from a noisy observation matrix $\textbf{M}$ in the limit of large dimension. We consider the case where the noisy measurement $\textbf{M}$ comes…

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal…

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down…

In this paper, adaptive estimation based on noisy quantized observations is studied. A low complexity adaptive algorithm using a quantizer with adjustable input gain and offset is presented. Three possible scalar models for the parameter to…

The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…

A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…

Numerical studies of quantum field theories usually rely upon an accurate determination of stochastically estimated correlation functions in order to extract information about the spectrum of the theory and matrix elements of operators. The…