Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches: constraint-based and score-based. The constraint-based approach is able to detect common causes of the observed variables but the use of independence tests makes it less reliable. The score-based approach produces a result that is easier to interpret as it also measures the reliability of the inferred causal relationships, but it is unable to detect common confounders of the observed variables. A drawback of both score-based and constrained-based approaches is the inherent instability in structure estimation. With finite samples small changes in the data can lead to completely different optimal structures. The present work introduces a new hypothesis-free score-based causal discovery algorithm, called stable specification search, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Structure search is performed over Structural Equation Models. Our approach uses exploratory search but allows incorporation of prior background knowledge. We validated our approach on one simulated data set, which we compare to the known ground truth, and two real-world data sets for Chronic Fatigue Syndrome and Attention Deficit Hyperactivity Disorder, which we compare to earlier medical studies. The results on the simulated data set show significant improvement over alternative approaches and the results on the real-word data sets show consistency with the hypothesis driven models constructed by medical experts.

Many problems in science and engineering can be formulated as a sequential decision-making problem under uncertainty. A common scenario in such problems that occurs in many different fields, such as online marketing, inventory control, health informatics, and computational finance, is to find a good or an optimal strategy/policy, given a batch of data generated by the current strategy of the company (hospital, investor). Although there are many techniques to find a good policy given a batch of data, only a few of them guarantee that the obtained policy will perform well, when it is deployed. Since deploying an untested policy can be risky for the business, the product (hospital, investment) manager does not usually allow it to happen, unless we provide her/him with some performance guarantees of the obtained strategy, in comparison to the baseline policy (e.g., the policy that is currently in use). In this paper, we focus on the model-based approach to this fundamental problem in the context of infinite-horizon discounted Markov decision processes (MDPs). In this approach, we use the batch of data and build a model or a simulator that approximates the true behavior of the dynamical system, together with an error function that captures the accuracy of the model at each state of the system. Our goal is to compute a safe policy, i.e., a policy that is guaranteed to perform at least as well as the baseline strategy, using the simulator and error function. Most of the work on this topic has been in the model-free setting, where safe policies are computed directly from the batch of data, without building an explicit model of the system [12, 13]. Another class of model-free algorithms are those that use a batch of data generated by the current policy and return a policy that is guaranteed to perform better.

Effective placement of charging stations plays a key role in Electric Vehicle (EV) adoption. In the placement problem, given a set of candidate sites, an optimal subset needs to be selected with respect to the concerns of both (a) the charging station service provider, such as the demand at the candidate sites and the budget for deployment, and (b) the EV user, such as charging station reachability and short waiting times at the station. This work addresses these concerns, making the following three novel contributions: (i) a supervised multi-view learning framework using Canonical Correlation Analysis (CCA) for demand prediction at candidate sites, using multiple datasets such as points of interest information, traffic density, and the historical usage at existing charging stations; (ii) a mixed-packing-and- covering optimization framework that models competing concerns of the service provider and EV users; (iii) an iterative heuristic to solve these problems by alternately invoking knapsack and set cover algorithms. The performance of the demand prediction model and the placement optimization heuristic are evaluated using real world data.

In this paper we present deterministic conditions for success of sparse subspace clustering (SSC) under missing data, when data is assumed to come from a Union of Subspaces (UoS) model. We consider two algorithms, which are variants of SSC with entry-wise zero-filling that differ in terms of the optimization problems used to find affinity matrix for spectral clustering. For both the algorithms, we provide deterministic conditions for any pattern of missing data such that perfect clustering can be achieved. We provide extensive sets of simulation results for clustering as well as completion of data at missing entries, under the UoS model. Our experimental results indicate that in contrast to the full data case, accurate clustering does not imply accurate subspace identification and completion, indicating the natural order of relative hardness of these problems.

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for these techniques. We propose a new approach to solve residual constrained formulations for interpolation. We represent the data volume using matrix factors, and build a block-coordinate algorithm with constrained convex subproblems that are solved with a primal-dual splitting scheme. The new approach is competitive with state of the art level-set algorithms that interchange the role of objectives with constraints. We use the new algorithm to successfully interpolate a large scale 5D seismic data volume, generated from the geologically complex synthetic 3D Compass velocity model, where 80% of the data has been removed.

The code in this repository provides a framework for solving arbitrary separable convex optimization problems with Alternating Direction Method of Multipliers (ADMM). Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. The framework is built over Spark and is generic: to apply it to an arbitrary separable convex problem, a developer needs to implement only three functions (one that reads data from a file, one that evaluates the objective function, and one that solves a local optimization problem with an additional proximal penalty term). An example implementation of logistic regression is included in the code. Updated spark installation instructions can be found here.

Ride sharing has important implications in terms of environmental, social and individual goals by reducing carbon footprints, fostering social interactions and economizing commuter costs. The ride sharing systems that are commonly available lack adaptive and scalable techniques that can simultaneously learn from the large scale data and predict in real-time dynamic fashion. In this paper, we study such a problem towards a smart city initiative, where a generic ride sharing system is conceived capable of making predictions about ride share opportunities based on the historically recorded data while satisfying real-time ride requests. Underpinning the system is an application of a powerful machine learning convex optimization framework called Network Lasso that uses the Alternate Direction Method of Multipliers (ADMM) optimization for learning and dynamic prediction. We propose an application of a robust and scalable unified optimization framework within the ride sharing case-study. The application of Network Lasso framework is capable of jointly optimizing and clustering different rides based on their spatial and model similarity. The prediction from the framework clusters new ride requests, making accurate price prediction based on the clusters, detecting hidden correlations in the data and allowing fast convergence due to the network topology. We provide an empirical evaluation of the application of ADMM network Lasso on real trip record and simulated data, proving their effectiveness since the mean squared error of the algorithm's prediction is minimized on the test rides.

Different versions of this problem have received is coping with uncertainties arising from limited a-considerable attention from several research communities, e.g., priori knowledge of the environment. Acquiring necessary as a "pursuit-evasion game" in game theory [13], [14], as information and achieving the overall goal are complementary a "cow-path problem" in computer science [15] or as a subtasks that require adapting the motion of a robot during "coverage problem" in control [16], [17], but its solution for mission execution, typically accompanied by minimizing a a general probability distribution or a general geometry of the performance criterion. In this work we address an Optimal region is, to a large extent, still an open question. Effective Control Problem (OCP) for a robot with fourth-order dynamics approaches for the related persistent monitoring problem based that has to find, collect and move a finite number of on estimation [18], linear programming [19] or parametric objects to a designated spot in minimum time. The objects optimization [20] have been also been proposed. OCPs with with a-priori known masses are located in a bounded twodimensional uncertainties have also been addressed by certainty equivalent space, where the robot is capable of localizing event-triggered [21], minimax [22] and sampling-based [23] itself using a state-of-the-art simultaneous localization and optimization schemes.

In this paper, we propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning when data size is large and thus it becomes impractical to use out-of-the-box algorithms. We rely on the principle of data aggregation and then subsequent disaggregations. While it is standard practice to aggregate the data and then calibrate the machine learning algorithm on aggregated data, we embed this into an iterative framework where initial aggregations are gradually disaggregated to the extent that even an optimal solution is obtainable. Early studies in data aggregation consider transportation problems [1, 10], where either demand or supply nodes are aggregated. Zipkin [31] studied data aggregation for linear programming (LP) and derived error bounds of the approximate solution.

We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal gradient scheme and a new homotopy strategy for smoothness parameter. By an appropriate choice of smoothing functions, we develop a new algorithm that has the $\mathcal{O}\left(\frac{1}{\varepsilon}\right)$-worst-case iteration-complexity while preserves the same complexity-per-iteration as in Nesterov's method and allows one to automatically update the smoothness parameter at each iteration. Then, we customize our algorithm to solve four special cases that cover various applications. We also specify our algorithm to solve constrained convex optimization problems and show its convergence guarantee on a primal sequence of iterates. We demonstrate our algorithm through three numerical examples and compare it with other related algorithms.