This paper introduces a new similarity measure, the covering similarity, which we formally define for evaluating the similarity between a symbolic sequence and a set of symbolic sequences. A pairwise similarity can also be directly derived from the covering similarity to compare two symbolic sequences. An efficient implementation to compute the covering similarity is proposed which uses a suffix-tree data structure, but other implementations, based on suffix array for instance, are possible and are possibly necessary for handling very large-scale problems. We have used this similarity to isolate attack sequences from normal sequences in the scope of host-based intrusion detection. We have assessed the covering similarity on two well-known benchmarks in the field. In view of the results reported on these two datasets for the state-of-the-art methods, according to the comparative study, we have carried out based on three challenging similarity measures commonly used for string processing, or in bioinformatics, we show that the covering similarity is particularly relevant to address the detection of anomalies in sequences of system calls.
have been proposed initially to extract very simple n-gram features to enhance a vector space model similar to the one used in text mining @cite_4 , @cite_1 . Recently, a much ambitious model has been proposed that proposes to enact phrases and sentences, hence a language, from sequences of system calls @cite_6 . Nevertheless, these approaches suffer from the combinatorics explosion. When simple @math -grams models are used (with @math lower than @math or @math ) the size of the vector space model is very high (several millions of dimension) and in general the lack of available data to train the model limits its accuracy. In the case of approach @cite_6 , the combinatorics is much higher with an estimated feature space dimension of @math which makes this model intractable for common hardware.
@cite_1 @cite_4 @cite_6
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We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Continuous word representations, trained on large unlabeled corpora are useful for many natural language processing tasks. Popular models that learn such representations ignore the morphology of words, by assigning a distinct vector to each word. This is a limitation, especially for languages with large vocabularies and many rare words. In this paper, we propose a new approach based on the skipgram model, where each word is represented as a bag of character @math -grams. A vector representation is associated to each character @math -gram; words being represented as the sum of these representations. Our method is fast, allowing to train models on large corpora quickly and allows us to compute word representations for words that did not appear in the training data. We evaluate our word representations on nine different languages, both on word similarity and analogy tasks. By comparing to recently proposed morphological word representations, we show that our vectors achieve state-of-the-art performance on these tasks. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Representing words into vectors in continuous space can form up a potentially powerful basis to generate high-quality textual features for many text mining and natural language processing tasks. Some recent efforts, such as the skip-gram model, have attempted to learn word representations that can capture both syntactic and semantic information among text corpus. However, they still lack the capability of encoding the properties of words and the complex relationships among words very well, since text itself often contains incomplete and ambiguous information. Fortunately, knowledge graphs provide a golden mine for enhancing the quality of learned word representations. In particular, a knowledge graph, usually composed by entities (words, phrases, etc.), relations between entities, and some corresponding meta information, can supply invaluable relational knowledge that encodes the relationship between entities as well as categorical knowledge that encodes the attributes or properties of entities. Hence, in this paper, we introduce a novel framework called RC-NET to leverage both the relational and categorical knowledge to produce word representations of higher quality. Specifically, we build the relational knowledge and the categorical knowledge into two separate regularization functions, and combine both of them with the original objective function of the skip-gram model. By solving this combined optimization problem using back propagation neural networks, we can obtain word representations enhanced by the knowledge graph. Experiments on popular text mining and natural language processing tasks, including analogical reasoning, word similarity, and topic prediction, have all demonstrated that our model can significantly improve the quality of word representations. The recent years have witnessed the emerging of vector quantization (VQ) techniques for efficient similarity search. VQ partitions the feature space into a set of codewords and encodes data points as integer indices using the codewords. Then the distance between data points can be efficiently approximated by simple memory lookup operations. By the compact quantization, the storage cost, and searching complexity are significantly reduced, thereby facilitating efficient large-scale similarity search. However, the performance of several celebrated VQ approaches degrades significantly when dealing with noisy data. In addition, it can barely facilitate a wide range of applications as the distortion measurement only limits to @math norm . To address the shortcomings of the squared Euclidean ( @math norm) loss function employed by the VQ approaches, in this paper, we propose a novel robust and general VQ framework, named RGVQ, to enhance both robustness and generalization of VQ approaches. Specifically, a @math -norm loss function is proposed to conduct the @math -norm similarity search, rather than the @math norm search, and the @math -th order loss is used to enhance the robustness. Despite the fact that changing the loss function to @math norm makes VQ approaches more robust and generic, it brings us a challenge that a non-smooth and non-convex orthogonality constrained @math - norm function has to be minimized. To solve this problem, we propose a novel and efficient optimization scheme and specify it to VQ approaches and theoretically prove its convergence. Extensive experiments on benchmark data sets demonstrate that the proposed RGVQ is better than the original VQ for several approaches, especially when searching similarity in noisy data. We investigate the diameter problem in the streaming and sliding-window models. We show that, for a stream of @math points or a sliding window of size @math , any exact algorithm for diameter requires @math bits of space. We present a simple @math -approximation algorithm for computing the diameter in the streaming model. Our main result is an @math -approximation algorithm that maintains the diameter in two dimensions in the sliding-window model using @math bits of space, where @math is the maximum, over all windows, of the ratio of the diameter to the minimum non-zero distance between any two points in the window. Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension @math and invariant with respect to the size of the state space. To further improve its sample efficiency, we exploit the monotonicity property and intrinsic noise structure of the Bellman operator, provided the existence of anchor state-actions that imply implicit non-negativity in the feature space. We augment the algorithm using techniques of variance reduction, monotonicity preservation, and confidence bounds. It is proved to find a policy which is @math -optimal from any initial state with high probability using @math sample transitions for arbitrarily large-scale MDP with a discount factor @math . A matching information-theoretical lower bound is proved, confirming the sample optimality of the proposed method with respect to all parameters (up to polylog factors). We study the recovery of sparse vectors from subsampled random convolutions via @math -minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a subgaussian generator with independent entries, we improve previously known estimates: if the sparsity @math is small enough, i.e., @math , we show that @math measurements are sufficient to recover @math -sparse vectors in dimension @math with high probability, matching the well-known condition for recovery from standard Gaussian measurements. If @math is larger, then essentially @math measurements are sufficient, again improving over previous estimates. Our results are shown via the so-called robust null space property which is weaker than the standard restricted isometry property. Our method of proof involves a novel combination of small ball estimates with chaining techniques which should be of independent interest. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Statistical physics models with hard constraints, such as the discrete hard-core gas model (random independent sets in a graph), are inherently combinatorial and present the discrete mathematician with a relatively comfortable setting for the study of phase transition. In this paper we survey recent work (concentrating on joint work of the authors) in which hard-constraint systems are modeled by the space @math of homomorphisms from an infinite graph @math to a fixed finite constraint graph @math . These spaces become sufficiently tractable when @math is a regular tree (often called a Cayley tree or Bethe lattice) to permit characterization of the constraint graphs @math which admit multiple invariant Gibbs measures. Applications to a physics problem (multiple critical points for symmetry-breaking) and a combinatorics problem (random coloring), as well as some new combinatorial notions, will be presented. In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension @math and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal components @math has at most @math non-zero entries. We are particularly interested in the high dimensional regime wherein @math is comparable to, or even much larger than @math . In an influential paper, johnstone2004sparse introduced a simple algorithm that estimates the support of the principal vectors @math by the largest entries in the diagonal of the empirical covariance. This method can be shown to identify the correct support with high probability if @math , and to fail with high probability if @math for two constants @math . Despite a considerable amount of work over the last ten years, no practical algorithm exists with provably better support recovery guarantees. Here we analyze a covariance thresholding algorithm that was recently proposed by KrauthgamerSPCA . On the basis of numerical simulations (for the rank-one case), these authors conjectured that covariance thresholding correctly recover the support with high probability for @math (assuming @math of the same order as @math ). We prove this conjecture, and in fact establish a more general guarantee including higher-rank as well as @math much smaller than @math . Recent lower bounds berthet2013computational, ma2015sum suggest that no polynomial time algorithm can do significantly better. The key technical component of our analysis develops new bounds on the norm of kernel random matrices, in regimes that were not considered before. This paper describes our system designed for the NLPCC 2015 shared task on Chinese word segmentation WS and POS tagging for Weibo Text. We treat WS and POS tagging as two separate tasks and use a cascaded approach. Our major focus is how to effectively exploit multiple heterogeneous data to boost performance of statistical models. This work considers three sets of heterogeneous data, i.e., Weibo @math , 10K sentences, Penn Chinese Treebank 7.0 @math , 50K, and People's Daily @math , 280K. For WS, we adopt the recently proposed coupled sequence labeling to combine @math , @math , and @math , boosting F1 score from @math baseline model trained on only @math to @math @math . For POS tagging, we adopt an ensemble approach combining coupled sequence labeling and the guide-feature based method, since the three datasets have three different annotation standards. First, we convert @math into the annotation style of @math based on coupled sequence labeling, denoted by @math . Then, we merge CTB7 and @math to train a POS tagger, denoted by @math , which is further used to produce guide features on @math . Finally, the tagging F1 score is improved from 87.93 to 88.99 +1.06 . Consider a uniform random rooted tree on vertices labelled by @math , with edges directed towards the root. We imagine that each node of the tree has space for a single car to park. A number @math of cars arrive one by one, each at a node chosen independently and uniformly at random. If a car arrives at a space which is already occupied, it follows the unique path oriented towards the root until it encounters an empty space, in which case it parks there; if there is no empty space, it leaves the tree. Consider @math and let @math denote the event that all @math cars find spaces in the tree. Lackner and Panholzer proved (via analytic combinatorics methods) that there is a phase transition in this model. Then if @math , we have @math , whereas if @math we have @math . We give a probabilistic explanation for this phenomenon, and an alternative proof via the objective method. Along the way, we are led to consider the following variant of the problem: take the tree to be the family tree of a Galton-Watson branching process with Poisson(1) offspring distribution, and let an independent Poisson( @math ) number of cars arrive at each vertex. Let @math be the number of cars which visit the root of the tree. Then for @math , we have @math , whereas for @math , we have @math . This discontinuous phase transition turns out to be a generic phenomenon in settings with an arbitrary offspring distribution of mean at least 1 for the tree and arbitrary arrival distribution. The growth of data, the need for scalability and the complexity of models used in modern machine learning calls for distributed implementations. Yet, as of today, distributed machine learning frameworks have largely ignored the possibility of arbitrary (i.e., Byzantine) failures. In this paper, we study the robustness to Byzantine failures at the fundamental level of stochastic gradient descent (SGD), the heart of most machine learning algorithms. Assuming a set of @math workers, up to @math of them being Byzantine, we ask how robust can SGD be, without limiting the dimension, nor the size of the parameter space. We first show that no gradient descent update rule based on a linear combination of the vectors proposed by the workers (i.e, current approaches) tolerates a single Byzantine failure. We then formulate a resilience property of the update rule capturing the basic requirements to guarantee convergence despite @math Byzantine workers. We finally propose Krum, an update rule that satisfies the resilience property aforementioned. For a @math -dimensional learning problem, the time complexity of Krum is @math . The study of compressed storage schemes for highly repetitive sequence collections has been recently boosted by the availability of cheaper sequencing technologies and the flood of data they promise to generate. Such a storage scheme may range from the simple goal of retrieving whole individual sequences to the more advanced one of providing fast searches in the collection. In this paper we study alternatives to implement a particularly popular index, namely, the one able of finding all the positions in the collection of substrings of fixed length ( @math -grams). We introduce two novel techniques and show they constitute practical alternatives to handle this scenario. They excel particularly in two cases: when @math is small (up to 6), and when the collection is extremely repetitive (less than 0.01 mutations). We consider the problem of learning an unknown function @math on the @math -dimensional sphere with respect to the square loss, given i.i.d. samples @math where @math is a feature vector uniformly distributed on the sphere and @math . We study two popular classes of models that can be regarded as linearizations of two-layers neural networks around a random initialization: (RF) The random feature model of Rahimi-Recht; (NT) The neural tangent kernel model of Jacot-Gabriel-Hongler. Both these approaches can also be regarded as randomized approximations of kernel ridge regression (with respect to different kernels), and hence enjoy universal approximation properties when the number of neurons @math diverges, for a fixed dimension @math . We prove that, if both @math and @math are large, the behavior of these models is instead remarkably simpler. If @math , then RF performs no better than linear regression with respect to the raw features @math , and NT performs no better than linear regression with respect to degree-one and two monomials in the @math . More generally, if @math then RF fits at most a degree- @math polynomial in the raw features, and NT fits at most a degree- @math polynomial. We study the asymptotic behavior of the persistent homology of i.i.d. samples from a @math -Ahlfors regular measure --- one that satisfies uniform bounds of the form for some @math all @math in the support of @math and all sufficiently small @math Our main result is that if @math are sampled from a @math -Ahlfors regular measure on @math and @math denotes the @math -weight of the minimal spanning tree on @math [E_ (x_1, ,x_n )= e T (x_1, ,x_n ) |e|^ ] then [E_ (x_1, ,x_n ) n^ d- d ] with high probability as @math We also prove theorems about the asymptotic behavior of weighted sums defined in terms of higher-dimensional persistent homology. As an application, we exhibit hypotheses under which the fractal dimension of a measure can be computed from the persistent homology of i.i.d. samples from that space, in a manner similar to that proposed in the experimental work of (2018). In models to generate program source code from natural language, representing this code in a tree structure has been a common approach. However, existing methods often fail to generate complex code correctly due to a lack of ability to memorize large and complex structures. We introduce ReCode, a method based on subtree retrieval that makes it possible to explicitly reference existing code examples within a neural code generation model. First, we retrieve sentences that are similar to input sentences using a dynamic-programming-based sentence similarity scoring method. Next, we extract n-grams of action sequences that build the associated abstract syntax tree. Finally, we increase the probability of actions that cause the retrieved n-gram action subtree to be in the predicted code. We show that our approach improves the performance on two code generation tasks by up to +2.6 BLEU. We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs at every temperature and for all @math . This immediately implies corresponding tight bounds on the anti-ferromagnetic Potts partition function. Taking the zero-temperature limit gives new results in extremal combinatorics: the number of @math -colorings of a @math -regular graph, for any @math , is maximized by a union of @math 's. This proves the @math case of a conjecture of Galvin and Tet ali. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text.