In this paper, we propose a technique for time series clustering using community detection in complex networks. Firstly, we present a method to transform a set of time series into a network using different distance functions, where each time series is represented by a vertex and the most similar ones are connected. Then, we apply community detection algorithms to identify groups of strongly connected vertices (called a community) and, consequently, identify time series clusters. Still in this paper, we make a comprehensive analysis on the influence of various combinations of time series distance functions, network generation methods and community detection techniques on clustering results. Experimental study shows that the proposed network-based approach achieves better results than various classic or up-to-date clustering techniques under consideration. Statistical tests confirm that the proposed method outperforms some classic clustering algorithms, such as $k$-medoids, diana, median-linkage and centroid-linkage in various data sets. Interestingly, the proposed method can effectively detect shape patterns presented in time series due to the topological structure of the underlying network constructed in the clustering process. At the same time, other techniques fail to identify such patterns. Moreover, the proposed method is robust enough to group time series presenting similar pattern but with time shifts and/or amplitude variations. In summary, the main point of the proposed method is the transformation of time series from time-space domain to topological domain. Therefore, we hope that our approach contributes not only for time series clustering, but also for general time series analysis tasks.

We show new limits on the efficiency of using current techniques to make exact probabilistic inference for large classes of natural problems. In particular we show new lower bounds on knowledge compilation to SDD and DNNF forms. We give strong lower bounds on the complexity of SDD representations by relating SDD size to best-partition communication complexity. We use this relationship to prove exponential lower bounds on the SDD size for representing a large class of problems that occur naturally as queries over probabilistic databases. A consequence is that for representing unions of conjunctive queries, SDDs are not qualitatively more concise than OBDDs. We also derive simple examples for which SDDs must be exponentially less concise than FBDDs. Finally, we derive exponential lower bounds on the sizes of DNNF representations using a new quasipolynomial simulation of DNNFs by nondeterministic FBDDs.

Path queries on a knowledge graph can be used to answer compositional questions such as "What languages are spoken by people living in Lisbon?". However, knowledge graphs often have missing facts (edges) which disrupts path queries. Recent models for knowledge base completion impute missing facts by embedding knowledge graphs in vector spaces. We show that these models can be recursively applied to answer path queries, but that they suffer from cascading errors. This motivates a new "compositional" training objective, which dramatically improves all models' ability to answer path queries, in some cases more than doubling accuracy. On a standard knowledge base completion task, we also demonstrate that compositional training acts as a novel form of structural regularization, reliably improving performance across all base models (reducing errors by up to 43%) and achieving new state-of-the-art results.

We introduce the C++ application and R package ranger. The software is a fast implementation of random forests for high dimensional data. Ensembles of classification, regression and survival trees are supported. We describe the implementation, provide examples, validate the package with a reference implementation, and compare runtime and memory usage with other implementations. The new software proves to scale best with the number of features, samples, trees, and features tried for splitting. Finally, we show that ranger is the fastest and most memory efficient implementation of random forests to analyze data on the scale of a genome-wide association study.

We present a novel approach for fully non-stationary Gaussian process regression (GPR), where all three key parameters -- noise variance, signal variance and lengthscale -- can be simultaneously input-dependent. We develop gradient-based inference methods to learn the unknown function and the non-stationary model parameters, without requiring any model approximations. We propose to infer full parameter posterior with Hamiltonian Monte Carlo (HMC), which conveniently extends the analytical gradient-based GPR learning by guiding the sampling with model gradients. We also learn the MAP solution from the posterior by gradient ascent. In experiments on several synthetic datasets and in modelling of temporal gene expression, the nonstationary GPR is shown to be necessary for modeling realistic input-dependent dynamics, while it performs comparably to conventional stationary or previous non-stationary GPR models otherwise.

We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its optimal non-relaxed integral solution. Our algorithm is initialized with variables taking integral values in the solution of a convex relaxation of the MAP-inference problem and iteratively prunes those, which do not satisfy our criterion for partial optimality. We show that our pruning strategy is in a certain sense theoretically optimal. Also empirically our method outperforms previous approaches in terms of the number of persistently labelled variables. The method is very general, as it is applicable to models with arbitrary factors of an arbitrary order and can employ any solver for the considered relaxed problem. Our method's runtime is determined by the runtime of the convex relaxation solver for the MAP-inference problem.

The problem of finding the most probable explanation to a designated set of variables given partial evidence (the MAP problem) is a notoriously intractable problem in Bayesian networks, both to compute exactly and to approximate. It is known, both from theoretical considerations and from practical experience, that low tree-width is typically an essential prerequisite to efficient exact computations in Bayesian networks. In this paper we investigate whether the same holds for approximating MAP. We define four notions of approximating MAP (by value, structure, rank, and expectation) and argue that all of them are intractable in general. We prove that efficient value-approximations, structure-approximations, and rank-approximations of MAP instances with high tree-width will violate the Exponential Time Hypothesis. In contrast, we show that MAP can sometimes be efficiently expectation-approximated, even in instances with high tree-width, if the most probable explanation has a high probability. We introduce the complexity class FERT, analogous to the class FTP, to capture this notion of fixed-parameter expectation-approximability. We suggest a road-map to future research that yields fixed-parameter tractable results for expectation-approximate MAP, even in graphs with high tree-width.

The interaction of multiple autonomous agents gives rise to highly dynamic and nondeterministic environments, contributing to the complexity in applications such as automated financial markets, smart grids, or robotics. Due to the sheer number of situations that may arise, it is not possible to foresee and program the optimal behaviour for all agents beforehand. Consequently, it becomes essential for the success of the system that the agents can learn their optimal behaviour and adapt to new situations or circumstances. The past two decades have seen the emergence of reinforcement learning, both in single and multi-agent settings, as a strong, robust and adaptive learning paradigm. Progress has been substantial, and a wide range of algorithms are now available. An important challenge in the domain of multi-agent learning is to gain qualitative insights into the resulting system dynamics. In the past decade, tools and methods from evolutionary game theory have been successfully employed to study multi-agent learning dynamics formally in strategic interactions. This article surveys the dynamical models that have been derived for various multi-agent reinforcement learning algorithms, making it possible to study and compare them qualitatively. Furthermore, new learning algorithms that have been introduced using these evolutionary game theoretic tools are reviewed. The evolutionary models can be used to study complex strategic interactions. Examples of such analysis are given for the domains of automated trading in stock markets and collision avoidance in multi-robot systems. The paper provides a roadmap on the progress that has been achieved in analysing the evolutionary dynamics of multi-agent learning by highlighting the main results and accomplishments.

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis framework, which may potentially help in bridging sparse approximation based methods to the traditional total-variation minimization. Based on this, we introduce a sparsity based framework for solving overparameterized variational problems. The latter has been used to improve the estimation of optical flow and also for general denoising of signals and images. However, the recovery of the space varying parameters involved was not adequately addressed by traditional variational methods. We first demonstrate the efficiency of the new framework for one dimensional signals in recovering a piecewise linear and polynomial function. Then, we illustrate how the new technique can be used for denoising and segmentation of images.

A general tension-reduction (GTR) model was recently considered to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations, and explain their considerable success in describing experimental situations also outside of the domain of physics, for instance in the ambit of quantum models of cognition and decision. Yet, this result also highlighted the possibility of observing violations of the predictions of the Born rule, in those situations where the averaging would not be large enough, or would be altered because of the combination of multiple measurements. In this article we show that this is indeed the case in typical psychological measurements exhibiting question order effects, by showing that their statistics of outcomes are inherently non-Hilbertian, and require the larger framework of the GTR-model to receive an exact mathematical description. We also consider another unsolved problem of quantum cognition: response replicability. It is has been observed that when question order effects and response replicability occur together, the situation cannot be handled anymore by quantum theory. However, we show that it can be easily and naturally described in the GTR-model. Based on these findings, we motivate the adoption in cognitive science of a hidden-measurements interpretation of the quantum formalism, and of its GTR-model generalization, as the natural interpretational framework explaining the data of psychological measurements on conceptual entities.