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.

Q: Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure. The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks. We introduce the directed super-structure as a natural generalization of its undirected counterpart. Our results apply to several variants of score-based Bayesian network structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian network structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth, and in linear time if in addition the super-structure has bounded maximum degree. Furthermore, we show that if the directed super-structure is acyclic, then exact Bayesian network structure learning can be carried out in quadratic time. We complement these positive results with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform polynomial time tractability (subject to a complexity-theoretic assumption). Similarly, exact Bayesian network structure learning remains NP-hard for "almost acyclic" directed super-structures. Furthermore, we show that the restrictions remain essential if we do not search for a globally optimal network but aim to improve a given network by means of at most k arc additions, arc deletions, or arc reversals (k-neighborhood local search).

A: Parameterized Complexity Results for Exact Bayesian Network Structure Learning
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Q: Online media offers opportunities to marketers to deliver brand messages to a large audience. Advertising technology platforms enables the advertisers to find the proper group of audiences and deliver ad impressions to them in real time. The recent growth of the real time bidding has posed a significant challenge on monitoring such a complicated system. With so many components we need a reliable system that detects the possible changes in the system and alerts the engineering team. In this paper we describe the mechanism that we invented for recovering the representative metrics and detecting the change in their behavior. We show that this mechanism is able to detect the possible problems in time by describing some incident cases.

A: Finding Needle in a Million Metrics: Anomaly Detection in a Large-scale Computational Advertising Platform
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Q: We propose an online convex optimization algorithm (RESCALEDEXP) that achieves<lb>optimal regret in the unconstrained setting without prior knowledge of any bounds<lb>on the loss functions. We prove a lower bound showing an exponential sep-<lb>aration between the regret of existing algorithms that require a known bound<lb>on the loss functions and any algorithm that does not require such knowledge.<lb>RESCALEDEXP matches this lower bound asymptotically in the number of itera-<lb>tions. RESCALEDEXP is naturally hyperparameter-free and we demonstrate empir-<lb>ically that it matches prior optimization algorithms that require hyperparameter<lb>optimization. 1 Online Convex Optimization Online Convex Optimization (OCO) [1, 2] provides an elegant framework for modeling noisy,<lb>antagonistic or changing environments. The problem can be stated formally with the help of the<lb>following definitions:<lb>Convex Set: A setW is convex ifW is contained in some real vector space and tw+(1 t)w W<lb>for all w,w W and t [0, 1].<lb>Convex Function: f :W R is a convex function if f(tw + (1 t)w) tf(w) + (1 t)f(w)<lb>for all w,w W and t [0, 1]. An OCO problem is a game of repeated rounds in which on round t a learner first chooses an element<lb>wt in some convex space W , then receives a convex loss function 't, and suffers loss 't(wt). The<lb>regret of the learner with respect to some other u W is defined by

A:
Online Convex Optimization with Unconstrained Domains and Losses
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