In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: We consider linear models for stochastic dynamics. To any such model can be as-<lb>sociated a network (namely a directed graph) describing which degrees of freedom<lb>interact under the dynamics. We tackle the problem of learning such a network<lb>from observation of the system trajectory over a time interval T .<lb>We analyze the l1-regularized least squares algorithm and, in the setting in which<lb>the underlying network is sparse, we prove performance guarantees that are uni-<lb>form in the sampling rate as long as this is sufficiently high. This result substan-<lb>tiates the notion of a well defined ‘time complexity’ for the network inference<lb>problem. keywords: Gaussian processes, model selection and structure learning, graphical models, sparsity<lb>and feature selection.

Output: Learning Networks of Stochastic Differential Equations


Input: Consider Input: As a general and thus popular model for autonomous systems, partially observable Markov decision process (POMDP) can capture uncertainties from different sources like sensing noises, actuation errors, and uncertain environments. However, its comprehensiveness makes the planning and control in POMDP difficult. Traditional POMDP planning problems target to find the optimal policy to maximize the expectation of accumulated rewards. But for safety critical applications, guarantees of system performance described by formal specifications are desired, which motivates us to consider formal methods to synthesize supervisor for POMDP. With system specifications given by Probabilistic Computation Tree Logic (PCTL), we propose a supervisory control framework with a type of deterministic finite automata (DFA), za-DFA, as the controller form. While the existing work mainly relies on optimization techniques to learn fixed-size finite state controllers (FSCs), we develop an L∗ learning based algorithm to determine both space and transitions of za-DFA. Membership queries and different oracles for conjectures are defined. The learning algorithm is sound and complete. An example is given in detailed steps to illustrate the supervisor synthesis algorithm.

Output: Supervisor Synthesis of POMDP based on Automata Learning


Input: Consider Input: Advances in sensing technologies and the growth of the internet have resulted in an explosion in the size of modern datasets, while storage and processing power continue to lag behind. This motivates the need for algorithms that are efficient, both in terms of the number of measurements needed and running time. To combat the challenges associated with large datasets, we propose a general framework for active hierarchical clustering that repeatedly runs an off-the-shelf clustering algorithm on small subsets of the data and comes with guarantees on performance, measurement complexity and runtime complexity. We instantiate this framework with a simple spectral clustering algorithm and provide concrete results on its performance, showing that, under some assumptions, this algorithm recovers all clusters of size Ω(log n) using O(n log n) similarities and runs in O(n log n) time for a dataset of n objects. Through extensive experimentation we also demonstrate that this framework is practically alluring.


Output: Efficient Active Algorithms for Hierarchical Clustering