In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampled set of linear projections of the composite signal. In this paper, we propose using the Dantzig selector model incorporating an overcomplete dictionary to separate a noisy undersampled collection of composite signals, and present an algorithm to efficiently solve the model. The Dantzig selector is a statistical approach to finding a solution to a noisy linear regression problem by minimizing the $\ell_1$ norm of candidate coefficient vectors while constraining the scope of the residuals. If the underlying coefficient vector is sparse, then the Dantzig selector performs well in the recovery and separation of the unknown composite signal. In the following, we propose a proximity operator based algorithm to recover and separate unknown noisy undersampled composite signals through the Dantzig selector. We present numerical simulations comparing the proposed algorithm with the competing Alternating Direction Method, and the proposed algorithm is found to be faster, while producing similar quality results. Additionally, we demonstrate the utility of the proposed algorithm in several experiments by applying it in various domain applications including the recovery of complex-valued coefficient vectors, the removal of impulse noise from smooth signals, and the separation and classification of a composition of handwritten digits.

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We also show an analogous result for the more general random dot product graph model.

Learning sparse combinations is a frequent theme in machine learning. In this paper, we study its associated optimization problem in the distributed setting where the elements to be combined are not centrally located but spread over a network. We address the key challenges of balancing communication costs and optimization errors. To this end, we propose a distributed Frank-Wolfe (dFW) algorithm. We obtain theoretical guarantees on the optimization error $\epsilon$ and communication cost that do not depend on the total number of combining elements. We further show that the communication cost of dFW is optimal by deriving a lower-bound on the communication cost required to construct an $\epsilon$-approximate solution. We validate our theoretical analysis with empirical studies on synthetic and real-world data, which demonstrate that dFW outperforms both baselines and competing methods. We also study the performance of dFW when the conditions of our analysis are relaxed, and show that dFW is fairly robust.

Directed graphs have asymmetric connections, yet the current graph clustering methodologies cannot identify the potentially global structure of these asymmetries. We give a spectral algorithm called di-sim that builds on a dual measure of similarity that correspond to how a node (i) sends and (ii) receives edges. Using di-sim, we analyze the global asymmetries in the networks of Enron emails, political blogs, and the c elegans neural connectome. In each example, a small subset of nodes have persistent asymmetries; these nodes send edges with one cluster, but receive edges with another cluster. Previous approaches would have assigned these asymmetric nodes to only one cluster, failing to identify their sending/receiving asymmetries. Regularization and "projection" are two steps of di-sim that are essential for spectral clustering algorithms to work in practice. The theoretical results show that these steps make the algorithm weakly consistent under the degree corrected Stochastic co-Blockmodel, a model that generalizes the Stochastic Blockmodel to allow for both (i) degree heterogeneity and (ii) the global asymmetries that we intend to detect. The theoretical results make no assumptions on the smallest degree nodes. Instead, the theorem requires that the average degree grows sufficiently fast and that the weak consistency only applies to the subset of the nodes with sufficiently large leverage scores. The results results also apply to bipartite graphs.

This article describes the DSN scheduling wngine (DSE) component of a new scheduling system being deployed for NASA's deep space network. The DSE provides core automation functionality for scheduling the network, including the interpretation of scheduling requirements expressed by users, their elaboration into tracking passes, and the resolution of conflicts and constraint violations. It has been integrated with a web application which provides DSE functionality to all DSN users through a standard web browser, as part of a peer-to-peer schedule negotiation process for the entire network. The system has been deployed operationally and is in routine use, and is in the process of being extended to support long-range planning and forecasting, and near-real-time scheduling.

The challenging timeline for DARPA's Orbital Express mission demanded a flexible, responsive, and (above all) safe approach to mission planning. Mission planning for space is challenging because of the mixture of goals and constraints. These technologies had a significant impact on the success of the Orbital Express mission. Finally, we formulated a technique for converting procedural information to declarative information by transforming procedures into models of hierarchical task networks (HTNs).

The challenging timeline for DARPA’s Orbital Express mission demanded a flexible, responsive, and (above all) safe approach to mission planning. Mission planning for space is challenging because of the mixture of goals and constraints. Every space mission tries to squeeze all of the capacity possible out of the spacecraft. For Orbital Express, this means performing as many experiments as possible, while still keeping the spacecraft safe. Keeping the spacecraft safe can be very challenging because we need to maintain the correct thermal environment (or batteries might freeze), we need to avoid pointing cameras and sensitive sensors at the sun, we need to keep the spacecraft batteries charged, and we need to keep the two spacecraft from colliding... made more difficult as only one of the spacecraft had thrusters. Because the mission was a technology demonstration, pertinent planning information was learned during actual mission execution. For example, we didn’t know for certain how long it would take to transfer propellant from one spacecraft to the other, although this was a primary mission goal. The only way to find out was to perform the task and monitor how long it actually took. This information led to amendments to procedures, which led to changes in the mission plan. In general, we used the ASPEN planner scheduler to generate and validate the mission plans. ASPEN is a planning system that allows us to enter all of the spacecraft constraints, the resources, the communications windows, and our objectives. ASPEN then could automatically plan our day. We enhanced ASPEN to enable it to reason about uncertainty. We also developed a model generator that would read the text of a procedure and translate it into an ASPEN model. Note that a model is the input to ASPEN that describes constraints, resources, and activities. These technologies had a significant impact on the success of the Orbital Express mission. Finally, we formulated a technique for converting procedural information to declarative information by transforming procedures into models of hierarchical task networks (HTNs). The impact of this effort on the mission was a significant reduction in (1) the execution time of the mission, (2) the daily staff required to produce plans, and (3) planning errors. Not a single miss-configured command was sent during operations.

We are pleased to introduce the space application issue articles in this issue of AI Magazine. The exploration of space is a testament to human curiosity and the desire to understand the universe that we inhabit. As many space agencies around the world design and deploy missions, it is apparent that there is a need for intelligent, exploring systems that can make decisions on their own in remote, potentially hostile environments. At the same time, the monetary cost of operating missions, combined with the growing complexity of the instruments and vehicles being deployed, make it apparent that substantial improvements can be made by the judicious use of automation in mission operations.

This article describes the DSN scheduling wngine (DSE) component of a new scheduling system being deployed for NASA's deep space network. The DSE provides core automation functionality for scheduling the network, including the interpretation of scheduling requirements expressed by users, their elaboration into tracking passes, and the resolution of conflicts and constraint violations. The DSE incorporates both systematic search and repair-based algorithms, used for different phases and purposes in the overall system. It has been integrated with a web application which provides DSE functionality to all DSN users through a standard web browser, as part of a peer-to-peer schedule negotiation process for the entire network. The system has been deployed operationally and is in routine use, and is in the process of being extended to support long-range planning and forecasting, and near-real-time scheduling.

We study consistency of learning algorithms for a multi-class performance metric that is a non-decomposable function of the confusion matrix of a classifier and cannot be expressed as a sum of losses on individual data points; examples of such performance metrics include the macro F-measure popular in information retrieval and the G-mean metric used in class-imbalanced problems. While there has been much work in recent years in understanding the consistency properties of learning algorithms for `binary' non-decomposable metrics, little is known either about the form of the optimal classifier for a general multi-class non-decomposable metric, or about how these learning algorithms generalize to the multi-class case. In this paper, we provide a unified framework for analysing a multi-class non-decomposable performance metric, where the problem of finding the optimal classifier for the performance metric is viewed as an optimization problem over the space of all confusion matrices achievable under the given distribution. Using this framework, we show that (under a continuous distribution) the optimal classifier for a multi-class performance metric can be obtained as the solution of a cost-sensitive classification problem, thus generalizing several previous results on specific binary non-decomposable metrics. We then design a consistent learning algorithm for concave multi-class performance metrics that proceeds via a sequence of cost-sensitive classification problems, and can be seen as applying the conditional gradient (CG) optimization method over the space of feasible confusion matrices. To our knowledge, this is the first efficient learning algorithm (whose running time is polynomial in the number of classes) that is consistent for a large family of multi-class non-decomposable metrics. Our consistency proof uses a novel technique based on the convergence analysis of the CG method.