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Gaussian Processes (GPs) are state-of-the-art tools for regression. Inference of GP hyperparameters is typically done by maximizing the marginal log-likelihood (ML). If the data truly follows the GP model, using the ML approach is optimal and computationally efficient. Unfortunately very often this is not case and suboptimal results are obtained in terms of prediction error. Alternative procedures...
Sign-Perturbed Sums (SPS) is a recently developed finite sample system identification method that can build exact confidence regions for linear regression problems under mild statistical assumptions. The regions are well-shaped, e.g., they are centred around the least-squares (LS) estimate, star-convex and strongly consistent. One of the main assumptions of SPS is that the distribution of the noise...
Repetitive Scenario Design (RSD) is a randomized approach to robust design based on iterating two phases: a standard scenario design phase that uses N scenarios (design samples), followed by randomized feasibility phase that uses No test samples on the scenario solution. We give a full and exact probabilistic characterization of the number of iterations required by the RSD approach for returning a...
The problem of achieving a good trade-off in Stochastic Model Predictive Control between the competing goals of improving the average performance and reducing conservativeness, while still guaranteeing recursive feasibility and low computational complexity, is addressed. We propose a novel, less restrictive scheme, which is based on considering stability and recursive feasibility separately. Through...
A probabilistic analytic center cutting plane method with multiple cuts is proposed for a class of robust feasibility problems which is to find a solution satisfying a set of parameter dependent convex constraints for all possible parameter values. In particular, a new update rule is presented for constructing a smaller polytope which contains the intersection among a previous polytope and half spaces...
In this paper, we address finite-horizon control for a stochastic linear system subject to constraints on the control and state variables. A control design methodology is proposed where the appropriate trade-off between the minimization of the control cost (performance) and the satisfaction of the state constraints (safety) can be decided by introducing appropriate chance-constrained problems depending...
In this paper, we propose a novel randomized approach to Stochastic Model Predictive Control (SMPC) for a linear system affected by a disturbance with unbounded support. As it is common in this setup, we focus on the case where the input/state of the system are subject to probabilistic constraints, i.e., the constraints have to be satisfied for all the disturbance realizations but for a set having...
In many applications it is necessary to determine whether an observation from an incoming high-volume data stream matches expectations or is anomalous. A common method for performing this task is to use an Exponentially Weighted Moving Average (EWMA), which smooths out the minor variations of the data stream. While EWMA is efficient at processing high-rate streams, it can be very volatile to abrupt...
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