We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class of exponential families available (e.g., allowing multinomial and Dirichlet distributions). Specifically, VS-MRFs are the joint graphical model distributions where the node-conditional distributions belong to generic exponential families with general vector space domains. We also present a sparsistent $M$-estimator for learning our class of MRFs that recovers the correct set of edges with high probability. We validate our approach via a set of synthetic data experiments as well as a real-world case study of over four million foods from the popular diet tracking app MyFitnessPal. Our results demonstrate that our algorithm performs well empirically and that VS-MRFs are capable of capturing and highlighting interesting structure in complex, real-world data. All code for our algorithm is open source and publicly available.

There is rising interest in vector-space word embeddings and their use in NLP, especially given recent methods for their fast estimation at very large scale. Nearly all this work, however, assumes a single vector per word type ignoring polysemy and thus jeopardizing their usefulness for downstream tasks. We present an extension to the Skip-gram model that efficiently learns multiple embeddings per word type. It differs from recent related work by jointly performing word sense discrimination and embedding learning, by non-parametrically estimating the number of senses per word type, and by its efficiency and scalability. We present new state-of-the-art results in the word similarity in context task and demonstrate its scalability by training with one machine on a corpus of nearly 1 billion tokens in less than 6 hours.

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages the dual benefits of low dimensionality: (1) more efficient algorithms, e.g., for proximity search, and (2) more optimistic generalization bounds.

In relational databases, relations between objects, represented by binary matrices or tensors, may be arbitrarily complex. In practice however, there are recurring relational patterns such as transitive, permutation and sequential relationships, that seem to have a regular structure not captured by the classical notion of matrix rank or tensor rank. In this paper, we show that factorizing the relational tensor using a logistic or hinge loss instead of the more standard squared loss is more appropriate because it can accurately model many common relations with a fixed-size embedding that depends sub-linearly on the number of entities in the knowledge base. We illustrate this fact empirically by being able to efficiently predict missing links in several synthetic and real-world experiments. Further, we provide theoretical justification for logistic loss by studying its connection to a complexity measure from the field of information complexity called the sign rank. Sign rank is a more appropriate complexity measure as it has a low value for transitive, permutation, or sequential relationships, while being large for uniformly sampled binary matrices/tensors with a high probability.

We have recently shown how to combine random walk inference over knowledge bases with vector space representations of surface forms, improving performance on knowledge base inference. In this paper, we formalize the connection of our prior work to logical inference rules, giving some general observations about methods for incorporating vector space representations into symbolic logic systems. Additionally, we present some promising preliminary work that extends these techniques to learning open-domain relations for the purpose of answering multiple choice questions, achieving 67% accuracy on a small test set.

Traditional approaches to knowledge base completion have been based on symbolic representations. Low-dimensional vector embedding models proposed recently for this task are attractive since they generalize to possibly unlimited sets of relations. A significant draw- back of previous embedding models for KB completion is that they merely support reasoning on individual relations (e.g., bornIn ( X, Y ) ⇒ nationality ( X, Y ) ). In this work, we develop models for KB completion that support chains of reasoning on paths of any length using compositional vector space models. We construct compositional vector representations for the paths in the KB graph from the semantic vector representations of the binary relations in that path and perform inference directly in the vector space. Unlike previous methods, our approach can generalize to paths that are unseen in training and, in a zero-shot setting, predict target relations without supervised training data for that relation.

Predicting the affective valence of unknown multi-word expressions is key for concept-level sentiment analysis. AffectiveSpace 2 is a vector space model, built by means of random projection, that allows for reasoning by analogy on natural language con- cepts. By reducing the dimensionality of affec- tive common-sense knowledge, the model allows semantic features associated with concepts to be generalized and, hence, allows concepts to be intu- itively clustered according to their semantic and affective relatedness. Such an affective intuition (so called because it does not rely on explicit fea- tures, but rather on implicit analogies) enables the inference of emotions and polarity conveyed by multi-word expressions, thus achieving efficient concept-level sentiment analysis.

This paper introduces the concept and use of an Interaction History Architecture for use on a mobile domestic robot and analyses the limitations of this configuration. The interaction history architecture builds upon Shannon information theory and has been previously used in a humanoid robot to learn basic children’s games. Previous work has shown that experience spaces can be highly flexible when used for learning. In this paper we outline and experiment designed to test the abilities of the architecture and how it can be used with classic clicker style training to teach domestic robots simple tasks. It then presents results from an experiment exploring these capabilities as well as the limitation found therein.

Many classification problems can be difficult to formulate directly in terms of the traditional supervised setting, where both training and test samples are individual feature vectors. There are cases in which samples are better described by sets of feature vectors, that labels are only available for sets rather than individual samples, or, if individual labels are available, that these are not independent. To better deal with such problems, several extensions of supervised learning have been proposed, where either training and/or test objects are sets of feature vectors. However, having been proposed rather independently of each other, their mutual similarities and differences have hitherto not been mapped out. In this work, we provide an overview of such learning scenarios, propose a taxonomy to illustrate the relationships between them, and discuss directions for further research in these areas.

Finding a new mathematical representations for graph, which allows direct comparison between different graph structures, is an open-ended research direction. Having such a representation is the first prerequisite for a variety of machine learning algorithms like classification, clustering, etc., over graph datasets. In this paper, we propose a symmetric positive semidefinite matrix with the $(i,j)$-{th} entry equal to the covariance between normalized vectors $A^ie$ and $A^je$ ($e$ being vector of all ones) as a representation for graph with adjacency matrix $A$. We show that the proposed matrix representation encodes the spectrum of the underlying adjacency matrix and it also contains information about the counts of small sub-structures present in the graph such as triangles and small paths. In addition, we show that this matrix is a \emph{"graph invariant"}. All these properties make the proposed matrix a suitable object for representing graphs. The representation, being a covariance matrix in a fixed dimensional metric space, gives a mathematical embedding for graphs. This naturally leads to a measure of similarity on graph objects. We define similarity between two given graphs as a Bhattacharya similarity measure between their corresponding covariance matrix representations. As shown in our experimental study on the task of social network classification, such a similarity measure outperforms other widely used state-of-the-art methodologies. Our proposed method is also computationally efficient. The computation of both the matrix representation and the similarity value can be performed in operations linear in the number of edges. This makes our method scalable in practice. We believe our theoretical and empirical results provide evidence for studying truncated power iterations, of the adjacency matrix, to characterize social networks.