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In recent years, the mathematical limits and algorithmic bounds for probabilistic group testing have become increasingly well-understood, with exact asymptotic thresholds now being known in general scaling regimes for the noiseless setting.…
The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential…
Randomized smoothing has achieved great success for certified robustness against adversarial perturbations. Given any arbitrary classifier, randomized smoothing can guarantee the classifier's prediction over the perturbed input with…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to…
We consider nonlinear stochastic systems that arise in path planning and control of mobile robots. As is typical of almost all nonlinear stochastic systems, the optimally solving problem is intractable. We provide a design approach which…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of…
Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…
We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
We have shown how the intrinsic properties of a noise process can set an upper bound for the time derivative of entropy in a nonequilibrium system. The interplay of dissipation and the properties of noise processes driving the dynamical…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
This paper develops a unified finite-time theory for the ordinary least squares estimation of possibly unstable and even slightly explosive vector autoregressive models under linear restrictions, with the applicable region $\rho(A)\leq…
Influence of weak uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of a passive transverse vector field advected by an incompressible turbulent flow is investigated by means of the field…
This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using…
Given measurements of a linear time-invariant system, the McMillan degree is the dimension of the smallest such system that reproduces these observed dynamics. Using impulse response measurements where the system has been started in some…
Regression discontinuity designs assess causal effects in settings where treatment is determined by whether an observed running variable crosses a pre-specified threshold. Here we propose a new approach to identification, estimation, and…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…