Most models of Stackelberg security games assume that the attacker only knows the defender's mixed strategy, but is not able to observe (even partially) the instantiated pure strategy. Such partial observation of the deployed pure strategy -- an issue we refer to as information leakage -- is a significant concern in practical applications. While previous research on patrolling games has considered the attacker's real-time surveillance, our settings, therefore models and techniques, are fundamentally different. More specifically, after describing the information leakage model, we start with an LP formulation to compute the defender's optimal strategy in the presence of leakage. Perhaps surprisingly, we show that a key subproblem to solve this LP (more precisely, the defender oracle) is NP-hard even for the simplest of security game models. We then approach the problem from three possible directions: efficient algorithms for restricted cases, approximation algorithms, and heuristic algorithms for sampling that improves upon the status quo. Our experiments confirm the necessity of handling information leakage and the advantage of our algorithms.

Artifact-centric models for business processes recently raised a lot of attention, as they manage to combine structural (i.e. data related) with dynamical (i.e. process related) aspects in a seamless way. Many frameworks developed under this approach, although, are not built explicitly for planning, one of the most prominent operations related to business processes. In this paper, we try to overcome this by proposing a framework named Dynamic Knowledge Bases, aimed at describing rich business domains through Description Logic-based ontologies, and where a set of actions allows the system to evolve by modifying such ontologies. This framework, by offering action rewriting and knowledge partialization, represents a viable and formal environment to develop decision making and planning techniques for DL-based artifact-centric business domains.

We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time.

This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of operations based on commutative semigroups. We then study the computational complexity of inference by organizing various problems into an "inference hierarchy". When the underlying structure of an inference problem is a commutative semiring -- i.e. a combination of two commutative semigroups with the distributive law -- a message passing procedure called belief propagation can leverage this distributive law to perform polynomial-time inference for certain problems. After establishing the NP-hardness of inference in any commutative semiring, we investigate the relation between algebraic properties in this setting and further show that polynomial-time inference using distributive law does not (trivially) extend to inference problems that are expressed using more than two commutative semigroups. We then extend the algebraic treatment of message passing procedures to survey propagation, providing a novel perspective using a combination of two commutative semirings. This formulation generalizes the application of survey propagation to new settings.

Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimensions. And under a low noise condition, the overall cluster risk is small even beyond the cores, in high dimensions.

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.

In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in the classifier case, the binary clustering model is expressed by a hyperplane in a high dimensional space induced by a kernel. In addition, the multi-way clustering can be obtained by combining a set of binary decision functions via an Error Correcting Output Codes (ECOC) encoding scheme. Because of its model-based nature, the KSC method encompasses three main steps: training, validation, testing. In the validation stage model selection is performed to obtain tuning parameters, like the number of clusters present in the data. This is a major advantage compared to classical spectral clustering where the determination of the clustering parameters is unclear and relies on heuristics. Once a KSC model is trained on a small subset of the entire data, it is able to generalize well to unseen test points. Beyond the basic formulation, sparse KSC algorithms based on the Incomplete Cholesky Decomposition (ICD) and $L_0$, $L_1, L_0 + L_1$, Group Lasso regularization are reviewed. In that respect, we show how it is possible to handle large scale data. Also, two possible ways to perform hierarchical clustering and a soft clustering method are presented. Finally, real-world applications such as image segmentation, power load time-series clustering, document clustering and big data learning are considered.

Evaluation often aims to reduce the correctness or error characteristics of a system down to a single number, but that always involves trade-offs. Another way of dealing with this is to quote two numbers, such as Recall and Precision, or Sensitivity and Specificity. But it can also be useful to see more than this, and a graphical approach can explore sensitivity to cost, prevalence, bias, noise, parameters and hyper-parameters. Moreover, most techniques are implicitly based on two balanced classes, and our ability to visualize graphically is intrinsically two dimensional, but we often want to visualize in a multiclass context. We review the dichotomous approaches relating to Precision, Recall, and ROC as well as the related LIFT chart, exploring how they handle unbalanced and multiclass data, and deriving new probabilistic and information theoretic variants of LIFT that help deal with the issues associated with the handling of multiple and unbalanced classes.

Kernel matrices are popular in machine learning and scientific computing, but they are limited by their quadratic complexity in both construction and storage. It is well-known that as one varies the kernel parameter, e.g., the width parameter in radial basis function kernels, the kernel matrix changes from a smooth low-rank kernel to a diagonally-dominant and then fully-diagonal kernel. Low-rank approximation methods have been widely-studied, mostly in the first case, to reduce the memory storage and the cost of computing matrix-vector products. Here, we use ideas from scientific computing to propose an extension of these methods to situations where the matrix is not well-approximated by a low-rank matrix. In particular, we construct an efficient block low-rank approximation method---which we call the Block Basis Factorization---and we show that it has $\mathcal{O}(n)$ complexity in both time and memory. Our method works for a wide range of kernel parameters, extending the domain of applicability of low-rank approximation methods, and our empirical results demonstrate the stability (small standard deviation in error) and superiority over current state-of-art kernel approximation algorithms.

Common statistical prediction models often require and assume stationarity in the data. However, in many practical applications, changes in the relationship of the response and predictor variables are regularly observed over time, resulting in the deterioration of the predictive performance of these models. This paper presents Linear Four Rates (LFR), a framework for detecting these concept drifts and subsequently identifying the data points that belong to the new concept (for relearning the model). Unlike conventional concept drift detection approaches, LFR can be applied to both batch and stream data; is not limited by the distribution properties of the response variable (e.g., datasets with imbalanced labels); is independent of the underlying statistical-model; and uses user-specified parameters that are intuitively comprehensible. The performance of LFR is compared to benchmark approaches using both simulated and commonly used public datasets that span the gamut of concept drift types. The results show LFR significantly outperforms benchmark approaches in terms of recall, accuracy and delay in detection of concept drifts across datasets.