Related papers: High Dimensional Geometry and Limitations in Syste…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
This paper introduces a novel direct approach to system identification of dynamic networks with missing data based on maximum likelihood estimation. Dynamic networks generally present a singular probability density function, which poses a…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
Learning governing dynamics from data is a common goal across the sciences, yet it is only well-posed when the underlying mechanisms are identifiable. In practice, many data-driven methods implicitly assume identifiability; when this…
A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify in high dimensional systems. The results show that the method is suitable for discriminating stochastic from…
Small noise can induce rare transitions between metastable states, which can be characterized by Maximum Likelihood Paths (MLPs). Nongradient systems contrast gradient systems in that MLP does not have to cross the separatrix at a saddle…
Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
In our companion work \cite{Stojnicl1RegPosasymldp} we revisited random under-determined linear systems with sparse solutions. The main emphasis was on the performance analysis of the $\ell_1$ heuristic in the so-called asymptotic regime,…
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…
We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS \citep{sheffet2017differentially}, they are…
In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their…
We derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI…
Light Detection and Ranging (LiDAR) is an essential sensor technology for autonomous driving as it can capture high-resolution 3D data. As 3D object detection systems (OD) can interpret such point cloud data, they play a key role in the…
We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…
The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function…
We give near-tight lower bounds for the sparsity required in several dimensionality reducing linear maps. First, consider the JL lemma which states that for any set of n vectors in R there is a matrix A in R^{m x d} with m = O(eps^{-2}log…