The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is base...
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ISBN:
(纸本)9781713872344
The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of Paley-Wiener reproducing kernel Hilbert spaces. The starting point of the paper is a recently developed algorithm to which we propose three types of improvements. First, we relax the assumptions on the noises by replacing the symmetricity assumption with a weaker distributional invariance principle. Then, we propose a more efficient way to estimate the norm of the target function, and finally we enhance the construction of the confidence bands by tightening the constraints of the underlying convex optimization problems. The refinements are also illustrated through numerical experiments.
In this letter we consider multi-agent coalitional games with uncertain value functions for which we establish distribution-free guarantees on the probability of allocation stability, i.e., agents do not have incentiv...
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In this letter we consider multi-agent coalitional games with uncertain value functions for which we establish distribution-free guarantees on the probability of allocation stability, i.e., agents do not have incentives to defect from the grand coalition to form subcoalitions for unseen realizations of the uncertain parameter. In case the set of stable allocations, the so called core of the game, is empty, we propose a randomized relaxation of the core. We then show that those allocations that belong to this relaxed set can be accompanied by stability guarantees in a probably approximately correct fashion. Finally, numerical experiments corroborate our theoretical findings.
We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems generated by a possibly inexact quantification of some parameters in the s...
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We provide out-of-sample certificates on the controlled invariance property of a given set with respect to a class of black-box linear systems generated by a possibly inexact quantification of some parameters in the state-space matrices. By exploiting a set of realizations of those undetermined parameters, verifying the controlled invariance property of the given set amounts to a linear program, whose feasibility allows us to establish an a-posteriori probabilistic certificate on the controlled invariance property of such a set with respect to the unknown linear time-invariant dynamics. We apply this framework to the control of a networked system with unknown weighted graph.
The Twin-in-the-Loop (TiL) framework for vehicle dynamics control has been recently introduced with the goal of simplifying the end-of-line-tuning phase and enhancing the controller performance. In TiL schemes, high-f...
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The Twin-in-the-Loop (TiL) framework for vehicle dynamics control has been recently introduced with the goal of simplifying the end-of-line-tuning phase and enhancing the controller performance. In TiL schemes, high-fidelity vehicle models are run on-board to compute the nominal control action, while a simple closed-loop compensator takes the model-mismatch into account. In this paper, we discuss the robustness properties of the TiL approach to uncertain working conditions. In particular, we show that, due to the model-free nature of the compensator tuning, randomized tools represent an effective way to guarantee a certain level of robustness to different operating conditions with reasonable confidence levels. Simulation results illustrate the effectiveness of the proposed approach within a braking control case study.
In this letter we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classific...
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In this letter we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines both the Bayes optimal classifier and the misclassification probabilities. A resampling based framework is presented and combined with consistent point estimators of the conditional kernel mean map, in order to construct distribution-free hypothesis tests. These tests are introduced in a flexible manner allowing us to control the exact probability of type I error for any sample size. We also prove that both proposed techniques are consistent under weak statistical assumptions, i.e., the type II error probabilities pointwise converge to zero.
This paper proposes a new class of randomized algorithms to incrementally compute the Google PageRank of a large-scale number of webpages. First, we reformulate the PageRank computation as a least squares (LS) problem...
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ISBN:
(纸本)9781479978878
This paper proposes a new class of randomized algorithms to incrementally compute the Google PageRank of a large-scale number of webpages. First, we reformulate the PageRank computation as a least squares (LS) problem. Motivated by a random surfer model, the LS problem is solved in a randomized incremental way. Specifically, when visiting a page, the surfer incrementally updates an estimate of the PageRank by using the information from those pages connected by hyperlinks. Then, the surfer either randomly selects an outgoing link of the current page and moves to the page pointed by this link, or interrupts its search and jumps to an arbitrary page. Subsequently, the PageRank estimate is updated again. The transition between pages is naturally modeled as a Markov process. Under an ergodicity property, we prove the convergence of the proposed algorithm to the PageRank in both the almost sure and L~P sense. A comparison with a classical PageRank algorithm is discussed as well.
This letter addresses the current stress policy design in the Dual-Active-Bridge (DAB) converters with the randomized computation approach. First, a hybrid automaton approach is applied to model the dynamics of the DA...
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This letter addresses the current stress policy design in the Dual-Active-Bridge (DAB) converters with the randomized computation approach. First, a hybrid automaton approach is applied to model the dynamics of the DAB converter. Then the optimal feedback policy of a quadruple-phase-shift is obtained via solving a peak current minimization problem with DAB converter dynamics and transferred power constraints. A randomized optimization approach is applied to solve the problem. The proposed control scheme is validated by numerical simulation and compared with the traditional double-phase-shift and triple-phase-shift policies. The simulation results verify that the proposed quadruple-phase-shift method has better performance regarding the current stress.
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in ...
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This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and multi-rollout setting. In both instances, the number of samples required in order to obtain acceptable estimates can produce optimization problems with an intractably large number of decision variables for a second-order algorithm. We show that a randomized and distributed Newton algorithm based on Hessian-sketching can produce epsilon-optimal solutions and converges geometrically. Moreover, the algorithm is trivially parallelizable. Our results hold for a variety of sketching matrices and we illustrate the theory with numerical examples.
In this letter, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic...
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In this letter, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the absolute value of the prediction error. The proposed scheme is based on a probabilistic scaling methodology in which the number of required randomized samples is independent of the complexity of the prediction model. The methodology is extended to address the case in which the probabilistic uncertain quantification is required to be valid for every member of a finite family of predictors. We illustrate the results of the paper by means of a numerical example.
In this paper, we study the "decoding" problem for discrete-time, stochastic hybrid systems with linear dynamics in each mode. Given an output trace of the system, the decoding problem seeks to construct a s...
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ISBN:
(纸本)9781450391962
In this paper, we study the "decoding" problem for discrete-time, stochastic hybrid systems with linear dynamics in each mode. Given an output trace of the system, the decoding problem seeks to construct a sequence of modes and states that yield a trace "as close as possible" to the original output trace. The decoding problem generalizes the state estimation problem, and is applicable to hybrid systems with non-determinism. The decoding problem is NP-complete, and can be reduced to solving a mixed-integer linear program (MILP). In this paper, we decompose the decoding problem into two parts: (a) finding a sequence of discrete modes and transitions;and (b) finding corresponding continuous states for the mode/transition sequence. In particular, once a sequence of modes/transitions is fixed, the problem of "filling in" the continuous states is performed by a linear programming problem. In order to support the decomposition, we "cover" the set of all possible mode/transition sequences by a finite subset. We use well-known probabilistic arguments to justify a choice of cover with high confidence and design randomized algorithms for finding such covers. Our approach is demonstrated on a series of benchmarks, wherein we observe that relatively tiny fraction of the possible mode/transition sequences can be used as a cover. Furthermore, we show that the resulting linear programs can be solved rapidly by exploiting the tree structure of the set cover.
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