Near-Optimal Sensor Placements in Gaussian Processes: Theory, Efficient Algorithms and Empirical Studies

By Andreas Krause, Amarjeet Singh, Carlos Guestrin. 2008

548 citations recorded by the source corpus.

Citations in the corpus

• Active learning of inverse models with intrinsically motivated goal exploration in robots (2013, neutral): “logistic regression [27], support vector machines [28], gaussian processes [29, 30, 31].”
• Non-monotone submodular maximization under matroid and knapsack constraints (2009, neutral): “It is also well known that ln det A[S] is submodular on [n], but ln det A[S] is not even approximately monotone (see [ 30, Section 8.2 ]): For example, for”
• Guarantees for Greedy Maximization of Non-submodular Functions with Applications (2017, unknown): “However, for many applications, including experimental design and sparse Gaussian processes (Lawrence et al., 2003), F ( S ) is in general not submodular (Krause et al., 2008) and the above guarantee does not hold.”
• Submodular Function Maximization (2014, unknown): “Krause et al. (2008c) develop Saturate , an algorithm that is guaranteed to efficiently obtain a set S such that f min ( S ) ≥ OPT k , and | S | ≤ 1 + max v ln i f i ( { v } ) k .”
• Robust Submodular Observation Selection (2008, unknown): “…objective functions, for example, the marginal variance at one location, or the information gain for a fixed set of parameters (Das and Kempe, 2008; Krause et al., 2007b; Krause and Guestrin, 2005; Guestrin et al., 2005), satisfy submodularity , an intuitive diminishing returns property: Adding a…”
• Machine Learning in Wireless Sensor Networks: Algorithms, Strategies, and Applications (2014, unknown): “[103] provided an optimized solution to sensor placement in applications with spatially correlated data such as”
• Learning photographic global tonal adjustment with a database of input/output image pairs (2011, unknown): “We ran sensor selection [11] to select S using the described covariance matrix.”
• Distributed Gaussian Processes (2015, unknown): “…including geostatistics (Cressie, 1993), optimisation (Jones et al., 1998; Brochu et al., 2009), data visualisation (Lawrence, 2005), robotics and reinforcement learning (Deisenroth et al., 2015), spatio-temporal mod-MPD acknowledges the support of an Imperial College Junior Research Fellowship.”
• Gaussian process dynamic programming (2009, unknown): “Similar ideas have been proposed for instance by Murray-Smith and Sbarbaro (2002) and Krause et al. (2008).”
• On Submodularity and Controllability in Complex Dynamical Networks (2014, unknown): “It occurs often in applications [2], [20], [22] (though is underexplored in systems and control theory); is preserved under various operations, allowing design flexibility; is supported by an elegant and practically useful mathematical theory; and there are efficient methods for minimizing and appro”
• Online Submodular Maximization with Preemption (2015, unknown): “In machine learning, submodular maximization has been used for document summarization [46, 47], sensor placement [41, 42, 44], and information gathering [43].”