Before he died, eccentric philosopher Jeremy Bentham asked that his body be stuffed and wheeled out at parties to help his friends with their grief. But the social reformer didn't stop there, bequeathing 26 memorial rings to those he knew and admired, featuring his bust in silhouette and strands of his hair. Now scientists are on the hunt for Bentham's rings, of which just six have been found since his death in 1832. The philosopher commissioned the rings a decade before he passed, leaving them in his will and testament to a list that included famous politicians, journalists, fellow philosophers and several of his servants. Researchers say the missing artefacts could be spread across the globe, after one was found in a jewellery shop in New Orleans.

There are two things I've always loved about Tomb Raider in all its incarnations over the years: beautiful, exciting and dangerous places to explore, and Lara Croft herself. Shadow of the Tomb Raider nails the former, with sumptuous South American locations to climb, dive and rappel around, ranging from ancient Inca cities and missionary crypts to modern-day Peruvian jungles and towns. But it does Lara a disservice, turning her into a deadly mud-camouflaged jungle warrior without much interesting to say, pushed along by a plot that's more concerned with prophecies and supernatural artefacts than with its main character. It is so silly that you can't explain it without sounding ridiculous: Lara is chasing a secret militia organisation across the south American continent to prevent them from stealing a silver box and bringing about the end of the world. Like the first two Tomb Raider games in this modern trilogy by Crystal Dynamics – though this concluding entry was developed by a different studio, Eidos Montréal - Shadow of the Tomb Raider relegates slower-paced exploring, treasure-hunting and puzzling around ancient tombs to make way for high-adrenaline action-movie-style play.

The increase in the number of Internet users and the strong interaction brought by Web 2.0 made the Opinion Mining an important task in the area of natural language processing. Although several methods are capable of performing this task, few use multi-label classification, where there is a group of true labels for each example. This type of classification is useful for situations where the opinions are analyzed from the perspective of the reader. Recently, Deep Learning has been registering the state of the art in several single-label problems. This paper discuss the efficiency of the Long Short-Term Memory compared to traditional multi-label classification approaches. To do that, extensive tests were carried out on two news corpora written in Brazilian Portuguese annotated with reactions. A new corpus called BFRC-PT is presented. In the tests performed, the highest number of correct predictions was obtained with the Classifier Chains method combined with the Random Forest algorithm. When considering the class distribution, the best results were obtained with the Binary Relevance method combined with the LSTM and Random Forest algorithms.

Feature selection can efficiently identify the most informative features with respect to the target feature used in training. However, state-of-the-art vector-based methods are unable to encapsulate the relationships between feature samples into the feature selection process, thus leading to significant information loss. To address this problem, we propose a new graph-based structurally interacting elastic net method for feature selection. Specifically, we commence by constructing feature graphs that can incorporate pairwise relationship between samples. With the feature graphs to hand, we propose a new information theoretic criterion to measure the joint relevance of different pairwise feature combinations with respect to the target feature graph representation. This measure is used to obtain a structural interaction matrix where the elements represent the proposed information theoretic measure between feature pairs. We then formulate a new optimization model through the combination of the structural interaction matrix and an elastic net regression model for the feature subset selection problem. This allows us to a) preserve the information of the original vectorial space, b) remedy the information loss of the original feature space caused by using graph representation, and c) promote a sparse solution and also encourage correlated features to be selected. Because the proposed optimization problem is non-convex, we develop an efficient alternating direction multiplier method (ADMM) to locate the optimal solutions. Extensive experiments on various datasets demonstrate the effectiveness of the proposed method. Keywords: Feature Selection; Graph; Interacting Elastic Net; Sparse; ADMM 1. Introduction There has recently been a rapid growth in both the size and dimension of the data encountered in many real world applications of pattern recognition including image processing, bioinformatics, and financial analysis. Finding useful information and building effective prediction models from such data presents new challenges for machine learning and pattern recognition [1]. One way to overcome this problem is to develop efficient spectral methods including stochastic neighbour embedding [2], elastic embedding methods [3] and feature selection [4] methods to reduce the dimensionality of the data.

In this work, we consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Examples of such data include brain connectivity networks from fMRI flow data, or word co-occurrence counts for populations of individuals. Current approaches to hypothesis testing for weighted networks typically requires thresholding the edge-weights, to transform the data to binary networks. This results in a loss of information, and outcomes are sensitivity to choice of threshold levels. Our work avoids this, and we consider weighted-graph observations in two situations, 1) where each graph belongs to one of two populations, and 2) where entities belong to one of two populations, with each entity possessing multiple graphs (indexed e.g. by time). Specifically, we propose a hierarchical Bayesian hypothesis testing framework that models each population with a mixture of latent space models for weighted networks, and then tests populations of networks for differences in distribution over components. Our framework is capable of population-level, entity-specific, as well as edge-specific hypothesis testing. We apply it to synthetic data and three real-world datasets: two social media datasets involving word co-occurrences from discussions on Twitter of the political unrest in Brazil, and on Instagram concerning Attention Deficit Hyperactivity Disorder (ADHD) and depression drugs, and one medical dataset involving fMRI brain-scans of human subjects. The results show that our proposed method has lower Type I error and higher statistical power compared to alternatives that need to threshold the edge weights. Moreover, they show our proposed method is better suited to deal with highly heterogeneous datasets.

In this thesis, we study the problem of feature learning on heterogeneous knowledge graphs. These features can be used to perform tasks such as link prediction, classification and clustering on graphs. Knowledge graphs provide rich semantics encoded in the edge and node types. Meta-paths consist of these types and abstract paths in the graph. Until now, meta-paths can only be used as categorical features with high redundancy and are therefore unsuitable for machine learning models. We propose meta-path embeddings to solve this problem by learning semantical and compact vector representations of them. Current graph embedding methods only embed nodes and edge types and therefore miss semantics encoded in the combination of them. Our method embeds meta-paths using the skipgram model with an extension to deal with the redundancy and high amount of meta-paths in big knowledge graphs. We critically evaluate our embedding approach by predicting links on Wikidata. The experiments indicate that we learn a sensible embedding of the meta-paths but can improve it further.

We present a data resource which can be useful for research purposes on language grounding tasks in the context of geographical referring expression generation. The resource is composed of two data sets that encompass 25 different geographical descriptors and a set of associated graphical representations, drawn as polygons on a map by two groups of human subjects: teenage students and expert meteorologists.

Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. GNNs employ trainable modules which can be assembled in different configurations that reflect the relational structure of each problem instance. In this paper, we show that GNNs can learn to solve, with very little supervision, the decision variant of the Traveling Salesperson Problem (TSP), a highly relevant $\mathcal{NP}$-Complete problem. Our model is trained to function as an effective message-passing algorithm in which edges (embedded with their weights) communicate with vertices for a number of iterations after which the model is asked to decide whether a route with cost $

Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations are available, where current methods fail to handle uncertainty appropriately. In this context, we propose a joint probabilistic model for signals, observations and spectra, where SE is addressed as an inference problem. Assuming a Gaussian process prior over the signal, we apply Bayes' rule to find the analytic posterior distribution of the spectrum given a set of observations. Besides its expressiveness and natural account of spectral uncertainty, the proposed model also provides a functional-form representation of the power spectral density, which can be optimised efficiently. Comparison with previous approaches is addressed theoretically, showing that the proposed method is an infinite-dimensional variant of the Lomb-Scargle approach, and also empirically through three experiments.

In this paper, we focus on escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a generic framework that yields convergence to a second-order stationary point of the problem, if the convex set $\mathcal{C}$ is simple for a quadratic objective function. To be more precise, our results hold if one can find a $\rho$-approximate solution of a quadratic program subject to $\mathcal{C}$ in polynomial time, where $\rho<1$ is a positive constant that depends on the structure of the set $\mathcal{C}$. Under this condition, we show that the sequence of iterates generated by the proposed framework reaches an $(\epsilon,\gamma)$-second order stationary point (SOSP) in at most $\mathcal{O}(\max\{\epsilon^{-2},\rho^{-3}\gamma^{-3}\})$ iterations. We further characterize the overall arithmetic operations to reach an SOSP when the convex set $\mathcal{C}$ can be written as a set of quadratic constraints. Finally, we extend our results to the stochastic setting and characterize the number of stochastic gradient and Hessian evaluations to reach an $(\epsilon,\gamma)$-SOSP.