Related papers: PAC-Bayesian-Like Error Bound for a Class of Linea…

In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for…

In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems,…

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a…

This paper presents a PAC-Bayes framework for learning controllers for unknown stochastic linear discrete-time systems, where the system parameters are drawn from a fixed but unknown distribution. We derive a data-dependent high probability…

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory…

One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured…

In this paper, we derive a PAC-Bayes bound on the generalisation gap, in a supervised time-series setting for a special class of discrete-time non-linear dynamical systems. This class includes stable recurrent neural networks (RNN), and the…

We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution…

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…

The identification of Linear Time-Varying (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t,…

We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…

Neural Stochastic Differential Equations model a dynamical environment with neural nets assigned to their drift and diffusion terms. The high expressive power of their nonlinearity comes at the expense of instability in the identification…

Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and…

In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical…

In this paper, an attack-resilient estimation algorithm is presented for linear discrete-time stochastic systems with state and input constraints. It is shown that the state estimation errors of the proposed estimation algorithm are…

We consider the problem of learning Neural Ordinary Differential Equations (neural ODEs) within the context of Linear Parameter-Varying (LPV) systems in continuous-time. LPV systems contain bilinear systems which are known to be universal…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

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…

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…

One of the defining properties of deep learning is that models are chosen to have many more parameters than available training data. In light of this capacity for overfitting, it is remarkable that simple algorithms like SGD reliably return…