This paper studies the problem of linking string mentions from web tables in one language to the corresponding named entities in a knowledge base written in another language, which we call the cross-lingual table linking task. We present a joint statistical model to simultaneously link all mentions that appear in one table. The framework is based on neural networks, aiming to bridge the language gap by vector space transformation and a coherence feature that captures the correlations between entities in one table. Experimental results report that our approach improves the accuracy of cross-lingual table linking by a relative gain of 12.1%. Detailed analysis of our approach also shows a positive and important gain brought by the joint framework and coherence feature.

We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces $({\mathbb X}, d, \mu_1)$ and $({\mathbb X}, d, \mu_2)$, we are interested in the problem of determining from finite data whether or not $\mu_1$ is $\mu_2$. The key is to use pairwise distances between observations and, employing a reconstruction theorem of Gromov, we can perform such a test using a two sample Kolmogorov--Smirnov test. A real analysis using phylogenetic trees and flu data is presented.

Note, there are many variations in the way we calculate the term-frequency(tf) and inverse document frequency (idf), in this post we have seen one variation. Below images show as the other recommended variations of tf and idf, taken from wiki. Mathematically, closeness between two vectors is calculated by calculating the cosine angle between two vectors. In similar lines, we can calculate cosine angle between each document vector and the query vector to find its closeness. To find relevant document to the query term, we may calculate the similarity score between each document vector and the query term vector by applying cosine similarity .

Few prior works study deep learning on point sets. PointNet [20] is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

We consider the non-stochastic Multi-Armed Bandit problem in a setting where there is a fixed and known metric on the action space that determines a cost for switching between any pair of actions. The loss of the online learner has two components: the first is the usual loss of the selected actions, and the second is an additional loss due to switching between actions. Our main contribution gives a tight characterization of the expected minimax regret in this setting, in terms of a complexity measure $\mathcal{C}$ of the underlying metric which depends on its covering numbers. In finite metric spaces with $k$ actions, we give an efficient algorithm that achieves regret of the form $\widetilde(\max\set{\mathcal{C}^{1/3}T^{2/3},\sqrt{kT}})$, and show that this is the best possible. Our regret bound generalizes previous known regret bounds for some special cases: (i) the unit-switching cost regret $\widetilde{\Theta}(\max\set{k^{1/3}T^{2/3},\sqrt{kT}})$ where $\mathcal{C}=\Theta(k)$, and (ii) the interval metric with regret $\widetilde{\Theta}(\max\set{T^{2/3},\sqrt{kT}})$ where $\mathcal{C}=\Theta(1)$. For infinite metrics spaces with Lipschitz loss functions, we derive a tight regret bound of $\widetilde{\Theta}(T^{\frac{d+1}{d+2}})$ where $d \ge 1$ is the Minkowski dimension of the space, which is known to be tight even when there are no switching costs.

Classification in the dissimilarity space has become a very active research area since it provides a possibility to learn from data given in the form of pairwise non-metric dissimilarities, which otherwise would be difficult to cope with. The selection of prototypes is a key step for the further creation of the space. However, despite previous efforts to find good prototypes, how to select the best representation set remains an open issue. In this paper we proposed scalable methods to select the set of prototypes out of very large datasets. The methods are based on genetic algorithms, dissimilarity-based hashing, and two different unsupervised and supervised scalable criteria. The unsupervised criterion is based on the Minimum Spanning Tree of the graph created by the prototypes as nodes and the dissimilarities as edges. The supervised criterion is based on counting matching labels of objects and their closest prototypes. The suitability of these type of algorithms is analyzed for the specific case of dissimilarity representations. The experimental results showed that the methods select good prototypes taking advantage of the large datasets, and they do so at low runtimes. Preprint submitted to Elsevier December 27, 2017 1. Introduction The vector space representation is a common option to represent the data for learning tasks since many statistical techniques are applicable for this kind of representation. However, there is an increasing number of real-world problems which are not vectorial. Instead, the data are given in terms of pairwise dissimilarities which may be non-Euclidean and even non-metric.

A significantly faster algorithm is presented for the original kNN mode seeking procedure. It has the advantages over the well-known mean shift algorithm that it is feasible in high-dimensional vector spaces and results in uniquely, well defined modes. Moreover, without any additional computational effort it may yield a multi-scale hierarchy of clusterings. The time complexity is just O(n^1.5). resulting computing times range from seconds for 10^4 objects to minutes for 10^5 objects and to less than an hour for 10^6 objects. The space complexity is just O(n). The procedure is well suited for finding large sets of small clusters and is thereby a candidate to analyze thousands of clusters in millions of objects. The kNN mode seeking procedure can be used for active learning by assigning the clusters to the class of the modal objects of the clusters. Its feasibility is shown by some examples with up to 1.5 million handwritten digits. The obtained classification results based on the clusterings are compared with those obtained by the nearest neighbor rule and the support vector classifier based on the same labeled objects for training. It can be concluded that using the clustering structure for classification can be significantly better than using the trained classifiers. A drawback of using the clustering for classification, however, is that no classifier is obtained that may be used for out-of-sample objects.

Graphs (networks) are ubiquitous and allow us to model entities (nodes) and the dependencies (edges) between them. Learning a useful feature representation from graph data lies at the heart and success of many machine learning tasks such as classification, anomaly detection, link prediction, among many others. Many existing techniques use random walks as a basis for learning features or estimating the parameters of a graph model for a downstream prediction task. Examples include recent node embedding methods such as DeepWalk, node2vec, as well as graph-based deep learning algorithms. However, the simple random walk used by these methods is fundamentally tied to the identity of the node. This has three main disadvantages. First, these approaches are inherently transductive and do not generalize to unseen nodes and other graphs. Second, they are not space-efficient as a feature vector is learned for each node which is impractical for large graphs. Third, most of these approaches lack support for attributed graphs. To make these methods more generally applicable, we propose a framework for inductive network representation learning based on the notion of attributed random walk that is not tied to node identity and is instead based on learning a function $\Phi : \mathrm{\rm \bf x} \rightarrow w$ that maps a node attribute vector $\mathrm{\rm \bf x}$ to a type $w$. This framework serves as a basis for generalizing existing methods such as DeepWalk, node2vec, and many other previous methods that leverage traditional random walks.

Recent studies on knowledge base completion, the task of recovering missing facts based on observed facts, demonstrate the importance of learning embeddings from multi-step relations. Due to the size of knowledge bases, previous works manually design relation paths of observed triplets in symbolic space (e.g. random walk) to learn multi-step relations during training. However, these approaches suffer some limitations as most paths are not informative, and it is prohibitively expensive to consider all possible paths. To address the limitations, we propose learning to traverse in vector space directly without the need of symbolic space guidance. To remember the connections between related observed triplets and be able to adaptively change relation paths in vector space, we propose Implicit ReasoNets (IRNs), that is composed of a global memory and a controller module to learn multi-step relation paths in vector space and infer missing facts jointly without any human-designed procedure. Without using any axillary information, our proposed model achieves state-of-the-art results on popular knowledge base completion benchmarks.

Conceptual spaces are geometric representations of conceptual knowledge, in which entities correspond to points, natural properties correspond to convex regions, and the dimensions of the space correspond to salient features. While conceptual spaces enable elegant models of various cognitive phenomena, the lack of automated methods for constructing such representations have so far limited their application in artificial intelligence. To address this issue, we propose a method which learns a vector-space embedding of entities from Wikipedia and constrains this embedding such that entities of the same semantic type are located in some lower-dimensional subspace. We experimentally demonstrate the usefulness of these subspaces as (approximate) conceptual space representations by showing, among others, that important features can be modelled as directions and that natural properties tend to correspond to convex regions.