In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix $L_{2,1}$ norm minimization with rank constraint problem as a stochastic optimization approach constrained on Grassmann manifold. For each observed data vector, the low-rank subspace $\mathcal{S}$ is updated by taking a gradient step along the geodesic of Grassmannian. In order to accelerate the convergence rate of the stochastic gradient method, we choose to adaptively tune the constant step-size by leveraging the consecutive gradients. Furthermore, we demonstrate that with proper initialization, the K-subspaces extension, K-GASG21, can robustly cluster a large number of corrupted data vectors into a union of subspaces. Numerical experiments on synthetic and real data demonstrate the efficiency and accuracy of the proposed algorithms even with heavy column outliers corruption.

Modality is one of the important components of grammar in linguistics. It lets speaker to express attitude towards, or give assessment or potentiality of state of affairs. It implies different senses and thus has different perceptions as per the context. This paper presents an account showing the gap in the functionality of the current state of art Natural Language Processing (NLP) systems. The contextual nature of linguistic modality is studied. In this paper, the works and logical approaches employed by Natural Language Processing systems dealing with modality are reviewed. It sees human cognition and intelligence as multi-layered approach that can be implemented by intelligent systems for learning. Lastly, current flow of research going on within this field is talked providing futurology.

The performance of trust models highly depend on the characteristics of the environments where they are applied. Thus, it becomes challenging to choose a suitable trust model for a given e-marketplace environment, especially when ground truth about the agent (buyer and seller) behavior is unknown (called unknown environment). We propose a case-based reasoning framework to choose suitable trust models for unknown environments, based on the intuition that if a trust model performs well in one environment, it will do so in another similar environment. Firstly, we build a case base with a number of simulated environments (with known ground truth) along with the trust models most suitable for each of them. Given an unknown environment, case-based retrieval algorithms retrieve the most similar case(s), and the trust model of the most similar case(s) is chosen as the most suitable model for the unknown environment. Evaluation results confirm the effectiveness of our framework in choosing suitable trust models for different e-marketplace environments.

We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$ independent draws from an unknown distribution $p,$ and $m_2$ draws from an unknown distribution $q$, we describe a test for distinguishing the case that $p=q$ from the case that $||p-q||_1 \geq \varepsilon$. If $p$ and $q$ are supported on at most $n$ elements, then our test is successful with high probability provided $m_1\geq n^{2/3}/\varepsilon^{4/3}$ and $m_2 = \Omega(\max\{\frac{n}{\sqrt m_1\varepsilon^2}, \frac{\sqrt n}{\varepsilon^2}\});$ we show that this tradeoff is optimal throughout this range, to constant factors. These results extend the recent work of Chan et al. who established the sample complexity when the two samples have equal sizes, and tightens the results of Acharya et al. by polynomials factors in both $n$ and $\varepsilon$. As a consequence, we obtain an algorithm for estimating the mixing time of a Markov chain on $n$ states up to a $\log n$ factor that uses $\tilde{O}(n^{3/2} \tau_{mix})$ queries to a "next node" oracle, improving upon the $\tilde{O}(n^{5/3}\tau_{mix})$ query algorithm of Batu et al. Finally, we note that the core of our testing algorithm is a relatively simple statistic that seems to perform well in practice, both on synthetic data and on natural language data.

In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accuracy for observable variables, the theoretical analysis of estimating latent variables has not been thoroughly investigated. In a previous study, we determined the accuracy of a Bayes estimation for the joint probability of the latent variables in a dataset, and we proved that the Bayes method is asymptotically more accurate than the maximum-likelihood method. However, the accuracy of the Bayes estimation for a single latent variable remains unknown. In the present paper, we derive the asymptotic expansions of the error functions, which are defined by the Kullback-Leibler divergence, for two types of single-variable estimations when the statistical regularity is satisfied. Our results indicate that the accuracies of the Bayes and maximum-likelihood methods are asymptotically equivalent and clarify that the Bayes method is only advantageous for multivariable estimations.

We are proposing an extension of the recursive neural network that makes use of a variant of the long short-term memory architecture. The extension allows information low in parse trees to be stored in a memory register (the `memory cell') and used much later higher up in the parse tree. This provides a solution to the vanishing gradient problem and allows the network to capture long range dependencies. Experimental results show that our composition outperformed the traditional neural-network composition on the Stanford Sentiment Treebank.

In this work, we propose a new method to integrate two recent lines of work: unsupervised induction of shallow semantics (e.g., semantic roles) and factorization of relations in text and knowledge bases. Our model consists of two components: (1) an encoding component: a semantic role labeling model which predicts roles given a rich set of syntactic and lexical features; (2) a reconstruction component: a tensor factorization model which relies on roles to predict argument fillers. When the components are estimated jointly to minimize errors in argument reconstruction, the induced roles largely correspond to roles defined in annotated resources. Our method performs on par with most accurate role induction methods on English, even though, unlike these previous approaches, we do not incorporate any prior linguistic knowledge about the language.

Conditional random fields (CRFs) [Lafferty et al., 2001] are a ubiquitous tool in natural language processing. They are used for part-of-speech tagging [McCallum et al., 2003], semantic role labeling [Cohn and Blunsom, 2005], topic modeling [Zhu and Xing, 2010], information extraction [Peng and McCallum, 2006], shallow parsing [Sha and Pereira, 2003], named-entity recognition [Settles, 2004], as well as a host of other applications in natural language processing and in other fields such as computer vision [Nowozin and Lampert, 2011]. Similar to generative Markov random field (MRF) models, CRFs allow us to model probabilistic dependencies between output variables. The key advantage of discriminative CRF models is the ability to use a very highdimensional feature set, without explicitly building a model for these features (as required by MRF models). Despite the widespread use of CRFs, a major disadvantage of these models is that they can be very slow to train and the time needed for numerical optimization in CRF models remains a bottleneck in many applications. Due to the high cost of evaluating the CRF objective function on even a single training example, it is now common to train CRFs using stochastic gradient methods [Vishwanathan et al., 2006]. These methods are advantageous over deterministic methods because on each iteration they only require computing the gradient of a single example (and not all example as in deterministic methods). Thus, if we have a data set with n training examples, the iterations of stochastic gradient methods are n times faster than deterministic methods. However, the number of stochastic gradient iterations required might be very high.

In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. This requires careful characterization of robust complex-valued loss functions as well as Huber's criterion function for the multivariate sparse regression problem. We devise a greedy algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Unlike the conventional SNIHT method, our algorithm, referred to as HUB-SNIHT, is robust under heavy-tailed non-Gaussian noise conditions, yet has a negligible performance loss compared to SNIHT under Gaussian noise. Usefulness of the method is illustrated in source localization application with sensor arrays.

Twitter, a popular social network, presents great opportunities for on-line machine learning research. However, previous research has focused almost entirely on learning from passively collected data. We study the problem of learning to acquire followers through normative user behavior, as opposed to the mass following policies applied by many bots. We formalize the problem as a contextual bandit problem, in which we consider retweeting content to be the action chosen and each tweet (content) is accompanied by context. We design reward signals based on the change in followers. The result of our month long experiment with 60 agents suggests that (1) aggregating experience across agents can adversely impact prediction accuracy and (2) the Twitter community's response to different actions is non-stationary. Our findings suggest that actively learning on-line can provide deeper insights about how to attract followers than machine learning over passively collected data alone.