Recently, considerable research attention has been paid to network embedding, a popular approach to construct feature vectors of vertices. Due to the curse of dimensionality and sparsity in graphical datasets, this approach has become indispensable for machine learning tasks over large networks. The majority of existing literature has considered this technique under the assumption that the network is static. However, networks in many applications, nodes and edges accrue to a growing network as a streaming. A small number of very recent results have addressed the problem of embedding for dynamic networks. However, they either rely on knowledge of vertex attributes, suffer high-time complexity or need to be re-trained without closed-form expression. Thus the approach of adapting the existing methods to the streaming environment faces non-trivial technical challenges. These challenges motivate developing new approaches to the problems of streaming network embedding. In this paper, We propose a new framework that is able to generate latent features for new vertices with high efficiency and low complexity under specified iteration rounds. We formulate a constrained optimization problem for the modification of the representation resulting from a stream arrival. We show this problem has no closed-form solution and instead develop an online approximation solution. Our solution follows three steps: (1) identify vertices affected by new vertices, (2) generate latent features for new vertices, and (3) update the latent features of the most affected vertices. The generated representations are provably feasible and not far from the optimal ones in terms of expectation. Multi-class classification and clustering on five real-world networks demonstrate that our model can efficiently update vertex representations and simultaneously achieve comparable or even better performance.

In this paper, we propose an effective TH resholding method based on ORder S tatistic, called THORS, to convert an arbitrary scoring-type classifier, which can induce a continuous cumulative distribution function of the score, into a cost-sensitive one. The procedure, uses order statistic to find an optimal threshold for classification, requiring almost no knowledge of classifiers itself. Unlike common data-driven methods, we analytically show that THORS has theoretical guaranteed performance, theoretical bounds for the costs and lower time complexity. Coupled with empirical results on several real-world data sets, we argue that THORS is the preferred cost-sensitive technique. Key words: Classification; Cost-sensitive learning; Imbalanced data set; Statistical learning; Threshold adjusting.

The ability to compose parts to form a more complex whole, and to analyze a whole as a combination of elements, is desirable across disciplines. This workshop bring together researchers applying compositional approaches to physics, NLP, cognitive science, and game theory. Within NLP, a long-standing aim is to represent how words can combine to form phrases and sentences. Within the framework of distributional semantics, words are represented as vectors in vector spaces. The categorical model of Coecke et al. [2010], inspired by quantum protocols, has provided a convincing account of compositionality in vector space models of NLP. There is furthermore a history of vector space models in cognitive science. Theories of categorization such as those developed by Nosofsky [1986] and Smith et al. [1988] utilise notions of distance between feature vectors. More recently G\"ardenfors [2004, 2014] has developed a model of concepts in which conceptual spaces provide geometric structures, and information is represented by points, vectors and regions in vector spaces. The same compositional approach has been applied to this formalism, giving conceptual spaces theory a richer model of compositionality than previously [Bolt et al., 2018]. Compositional approaches have also been applied in the study of strategic games and Nash equilibria. In contrast to classical game theory, where games are studied monolithically as one global object, compositional game theory works bottom-up by building large and complex games from smaller components. Such an approach is inherently difficult since the interaction between games has to be considered. Research into categorical compositional methods for this field have recently begun [Ghani et al., 2018]. Moreover, the interaction between the three disciplines of cognitive science, linguistics and game theory is a fertile ground for research. Game theory in cognitive science is a well-established area [Camerer, 2011]. Similarly game theoretic approaches have been applied in linguistics [J\"ager, 2008]. Lastly, the study of linguistics and cognitive science is intimately intertwined [Smolensky and Legendre, 2006, Jackendoff, 2007]. Physics supplies compositional approaches via vector spaces and categorical quantum theory, allowing the interplay between the three disciplines to be examined.

We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the purpose. We analyze the problem with an additional structure of relational graph $G([n],E)$ over the $n$ items added with an assumption of \emph{locality}: Neighboring items are similar in their rankings. Noting the preferential nature of the data, we choose to embed not the graph, but, its \emph{strong product} to capture the pairwise node relationships. Furthermore, unlike existing literature that uses Laplacian embedding for graph based learning problems, we use a richer class of graph embeddings---\emph{orthonormal representations}---that includes (normalized) Laplacian as its special case. Our proposed algorithm, {\it Pref-Rank}, predicts the underlying ranking using an SVM based approach over the chosen embedding of the product graph, and is the first to provide \emph{statistical consistency} on two ranking losses: \emph{Kendall's tau} and \emph{Spearman's footrule}, with a required sample complexity of $O(n^2 \chi(\bar{G}))^{\frac{2}{3}}$ pairs, $\chi(\bar{G})$ being the \emph{chromatic number} of the complement graph $\bar{G}$. Clearly, our sample complexity is smaller for dense graphs, with $\chi(\bar G)$ characterizing the degree of node connectivity, which is also intuitive due to the locality assumption e.g. $O(n^\frac{4}{3})$ for union of $k$-cliques, or $O(n^\frac{5}{3})$ for random and power law graphs etc.---a quantity much smaller than the fundamental limit of $\Omega(n^2)$ for large $n$. This, for the first time, relates ranking complexity to structural properties of the graph. We also report experimental evaluations on different synthetic and real datasets, where our algorithm is shown to outperform the state-of-the-art methods.

Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current deep structured models are restricted by oftentimes very local neighborhood structure, which cannot be increased for computational complexity reasons, and by the fact that the output configuration, or a representation thereof, cannot be transformed further. Very recent approaches which address those issues include graphical model inference inside deep nets so as to permit subsequent non-linear output space transformations. However, optimization of those formulations is challenging and not well understood. Here, we develop a novel model which generalizes existing approaches, such as structured prediction energy networks, and discuss a formulation which maintains applicability of existing inference techniques.

One of the fundamental requirements for models of semantic processing in dialogue is incrementality: a model must reflect how people interpret and generate language at least on a word-by-word basis, and handle phenomena such as fragments, incomplete and jointly-produced utterances. We show that the incremental word-by-word parsing process of Dynamic Syntax (DS) can be assigned a compositional distributional semantics, with the composition operator of DS corresponding to the general operation of tensor contraction from multilinear algebra. We provide abstract semantic decorations for the nodes of DS trees, in terms of vectors, tensors, and sums thereof; using the latter to model the underspecified elements crucial to assigning partial representations during incremental processing. As a working example, we give an instantiation of this theory using plausibility tensors of compositional distributional semantics, and show how our framework can incrementally assign a semantic plausibility measure as it parses phrases and sentences.

We consider the problem of classification in a comparison-based setting: given a set of objects, we only have access to triplet comparisons of the form "object $x_i$ is closer to object $x_j$ than to object $x_k$.'' In this paper we introduce TripletBoost, a new method that can learn a classifier just from such triplet comparisons. The main idea is to aggregate the triplets information into weak classifiers, which can subsequently be boosted to a strong classifier. Our method has two main advantages: (i) it is applicable to data from any metric space, and (ii) it can deal with large scale problems using only passively obtained and noisy triplets. We derive theoretical generalization guarantees and a lower bound on the number of necessary triplets, and we empirically show that our method is both competitive with state of the art approaches and resistant to noise.

Meta-data from photo-sharing websites such as Flickr can be used to obtain rich bag-of-words descriptions of geographic locations, which have proven valuable, among others, for modelling and predicting ecological features. One important insight from previous work is that the descriptions obtained from Flickr tend to be complementary to the structured information that is available from traditional scientific resources. To better integrate these two diverse sources of information, in this paper we consider a method for learning vector space embeddings of geographic locations. We show experimentally that this method improves on existing approaches, especially in cases where structured information is available.

This paper builds upon our prior formalisation of R^n in ACL2(r) by presenting a set of theorems for reasoning about convex functions. This is a demonstration of the higher-dimensional analytical reasoning possible in our metric space formalisation of R^n. Among the introduced theorems is a set of equivalent conditions for convex functions with Lipschitz continuous gradients from Yurii Nesterov's classic text on convex optimisation. To the best of our knowledge a full proof of the theorem has yet to be published in a single piece of literature. We also explore "proof engineering" issues, such as how to state Nesterov's theorem in a manner that is both clear and useful.

Of all the AI features that put the "smarts" in smart security cameras, facial detection is undoubtedly the most complex and frustrating. Thanks to the variable quality of the algorithms behind them, three different cameras with facial detection can give you maddeningly different results. My expectations, then, for Wisenet's SmartCam N2 with facial recognition were modest. But after using it for week or so, I'm ready to say the N2 is one of the better facial-recognition cameras out there. The N2's capsule-style body comes mounted to a metal base you can set on a table or shelf.