On June 6, 2015, Kalief Browder took his own life at his home, in the Bronx. He was twenty-two years old. He had been released from Rikers Island two years earlier, ending an ordeal that had begun on a spring night in 2010, when he had been arrested for robbery, at sixteen. He spent the next three years in jail trying to prove his innocence, and, for about two of those years, he was held in solitary confinement, where he attempted suicide several times. The charges against him were eventually dropped.

We introduce an algorithm for long distance path planning in complex marine environments. The available free space in marine environments changes over time as a result of tides, environmental restrictions, and weather. As a result of these considerations, the free space region in marine environments needs to be dynamically generated and updated. The approach presented in this paper demonstrates that it is feasible to compute optimal paths using A* search on visibility graphs defined over quadtrees. Our algorithm exploits quadtree data structures for efficiently computing tangent edges in visibility graphs. We have developed an admissible heuristic that accounts for large islands while estimating the cost-to-go and provides a better lower bound than the Euclidean distance-based heuristic. During the search over visibility graphs, the branching factor of A* can be large due to the large size of the region. We introduce the idea of focusing the search by limiting the child nodes to be in certain regions of the workspace. Our results show that focusing the search significantly improves the computational efficiency without any noticeable degradation in path quality. We have also developed a method to estimate bounds on how far the computed path can be from the optimal path when methods for focusing the search are utilized for speeding up the computation.

The GEO-Stationary Coastal and Air Pollution Events (GEO-CAPE) mission plans to put a visible spectrum imaging instrument on a satellite in geo-stationary orbit to perform ocean color remote sensing. Two different instrument designs, Filter Radiometer (FR) and COastal Ecosystems Dynamic Imager (COEDI), with different shape for the imaged area and image acquisition time, are being evaluated. Scheduling observations for either instrument requires optimizing science objectives in the presence of predicted cloud cover and available daylight. We model this scheduling problem as both Mixed Integer Linear Program (MILP) and Constraint Programming (CP) problems, and compare these two formulations for FR and COEDI using real cloudiness data collected at different times throughout the year. Our results show that MILP is the more suitable technique, and the schedule quality metric shows FR is the preferred design. We have reported our results to the GEO-CAPE mission team to assist them making an informed decision for the next step in formulating this mission.

This paper describes a novel encoding for sequential numeric planning into the problem of determining the satisfiability of a logical theory T. We introduce a novel technique, orthogonal to existing work aiming at producing more succinct encodings that enables the theory solver to roll up an unbounded yet finite number of instances of an action into a single plan step, greatly reducing the horizon at which T models valid plans. The technique is then extended to deal with problems featuring disjunctive global constraints, in which the state space becomes a non-convex n dimensional polytope. In order to empirically evaluate the encoding, we build a planner, SPRINGROLL, around a state–of–the–art off– the–shelf SMT solver. Experiments on a diverse set of domains are finally reported, and results show the generality and efficiency of the approach.

Hierarchical Task Network (HTN) planning is a formalism that can express constraints which cannot easily be expressed by classical (non-hierarchical) planning approaches. It enables reasoning about procedural structures and domain-specific search control knowledge. Yet the cornucopia of modern heuristic search techniques remains largely unincorporated in current HTN planners, in part because it is not clear how to estimate the goal distance for a partially-ordered task network. When using SHOP2-style progression, a task network of yet unprocessed tasks is maintained during search. In the general case it can grow arbitrarily large. However, many — if not most — existing HTN domains have a certain structure (called tail-recursive) where the network's size is bounded. We show how this bound can be calculated and exploited to automatically translate tail-recursive HTN problems into non-hierarchical STRIPS representations, which allows using both hierarchical structures and classical planning heuristics. In principle, the approach can also be applied to non-tail-recursive HTNs by incrementally increasing the bound. We give three translations with different advantages and present the results of an empirical evaluation with several HTN domains that are translated to PDDL and solved by two current classical planning systems. Our results show that we can automatically find practical bounds for solving partially-ordered HTN problems. We also show that classical planners perform similarly with our automatic translations versus a previous hand-bounded HTN translation which is restricted to totally-ordered problems.

We introduce three novel semi-parametric extensions of probabilistic canonical correlation analysis with identifiability guarantees. We consider moment matching techniques for estimation in these models. For that, by drawing explicit links between the new models and a discrete version of independent component analysis (DICA), we first extend the DICA cumulant tensors to the new discrete version of CCA. By further using a close connection with independent component analysis, we introduce generalized covariance matrices, which can replace the cumulant tensors in the moment matching framework, and, therefore, improve sample complexity and simplify derivations and algorithms significantly. As the tensor power method or orthogonal joint diagonalization are not applicable in the new setting, we use non-orthogonal joint diagonalization techniques for matching the cumu-lants. We demonstrate performance of the proposed models and estimation techniques on experiments with both synthetic and real datasets.

We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij} \sim P$ if $i, j$ are both in the community and $A_{ij} \sim Q$ otherwise, for two known probability distributions $P$ and $Q$. We identify a sufficient condition and a necessary condition for the success of SDP for the general model. For both the Bernoulli case ($P={{\rm Bern}}(p)$ and $Q={{\rm Bern}}(q)$ with $p>q$) and the Gaussian case ($P=\mathcal{N}(\mu,1)$ and $Q=\mathcal{N}(0,1)$ with $\mu>0$), which correspond to the problem of planted dense subgraph recovery and submatrix localization respectively, the general results lead to the following findings: (1) If $K=\omega( n /\log n)$, SDP attains the information-theoretic recovery limits with sharp constants; (2) If $K=\Theta(n/\log n)$, SDP is order-wise optimal, but strictly suboptimal by a constant factor; (3) If $K=o(n/\log n)$ and $K \to \infty$, SDP is order-wise suboptimal. The same critical scaling for $K$ is found to hold, up to constant factors, for the performance of SDP on the stochastic block model of $n$ vertices partitioned into multiple communities of equal size $K$. A key ingredient in the proof of the necessary condition is a construction of a primal feasible solution based on random perturbation of the true cluster matrix.

In this paper, we explore degrees of freedom in deep sigmoidal neural networks. We show that the degrees of freedom in these models is related to the expected optimism, which is the expected difference between test error and training error. We provide an efficient Monte-Carlo method to estimate the degrees of freedom for multi-class classification methods. We show degrees of freedom are lower than the parameter count in a simple XOR network. We extend these results to neural nets trained on synthetic and real data, and investigate impact of network's architecture and different regularization choices. The degrees of freedom in deep networks are dramatically smaller than the number of parameters, in some real datasets several orders of magnitude. Further, we observe that for fixed number of parameters, deeper networks have less degrees of freedom exhibiting a regularization-by-depth.

The Schatten-p quasi-norm $(0

Note that V Y L Link set of G w ij W eight between two nodes in G G K -elite neighbor graph (K -ENG) V Node set of G . Note that V Y L Link set of G w ij W eight between two nodes in G p ij (1-step) transition probability fromy i to y j P (1-step) transition probability matrix,P { p ij } N N p T ij T -step transition probability fromy i to y j P T T -step transition probability matrix,P T { p T ij } N N p T i: The i -th row ofP T, p T i: { p T i 1,···,p T i N} PT T i Probability trajectory of a random walker starting fromnode y i with lengthT PTS ij Probability trajectory based similarity betweeny i and y j R (0) Set of the initial regions for PTA,R (0) { R (0) 1,···,R (0) R (0) } S (0) Initial similarity matrix for PTA,S (0) { s (0) ij } R (0) R (0) R ( t) Set of thet -step regions for PTA, R ( t) { R ( t) 1,···,R ( t) R ( t) } S ( t) The t -step similarity matrix for PTA,S ( t) { s ( t) ij } R ( t) R ( t) G Microcluster-cluster bipartite graph (MCBG) N Number of nodes in G V Node set of G L Link set of G w ij W eight between two nodes in G A sparse graph termedK -elite neighbor graph (K -ENG) is then constructed with only a small number of probably reliable links. The ENS strategy is a crucial step in our approach. W e argue that using a small number of probably reliable links may lead to significantly better consensus results than using all graph links regardless of their reliability . The random walk process driven by a new transition probability matrix is performed on theK -ENG to explore the global structure information.