This paper tackles the problem of endogenous link prediction for knowledge base completion. Knowledge bases can be represented as directed graphs whose nodes correspond to entities and edges to relationships. Previous attempts either consist of powerful systems with high capacity to model complex connectivity patterns, which unfortunately usually end up overfitting on rare relationships, or in approaches that trade capacity for simplicity in order to fairly model all relationships, frequent or not. In this paper, we propose Tatec, a happy medium obtained by complementing a high-capacity model with a simpler one, both pre-trained separately and then combined. We present several variants of this model with different kinds of regularization and combination strategies and show that this approach outperforms existing methods on different types of relationships by achieving state-of-the-art results on four benchmarks of the literature.

We represent knowledge as integrity constraints in a formalization of probabilistic spatio-temporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown. We augment the previous definition by adding a type of non-atomic formula that expresses integrity constraints. The result is a highly expressive formalism for knowledge representation dealing with probabilistic spatio-temporal data. We obtain complexity results both for checking the consistency of PST knowledge bases and for answering queries in PST knowledge bases, and also specify tractable cases. All the domains in the PST framework are finite, but we extend our results also to arbitrarily large finite domains.

This work provides improved guarantees for streaming principle component analysis (PCA). Given $A_1, \ldots, A_n\in \mathbb{R}^{d\times d}$ sampled independently from distributions satisfying $\mathbb{E}[A_i] = \Sigma$ for $\Sigma \succeq \mathbf{0}$, this work provides an $O(d)$-space linear-time single-pass streaming algorithm for estimating the top eigenvector of $\Sigma$. The algorithm nearly matches (and in certain cases improves upon) the accuracy obtained by the standard batch method that computes top eigenvector of the empirical covariance $\frac{1}{n} \sum_{i \in [n]} A_i$ as analyzed by the matrix Bernstein inequality. Moreover, to achieve constant accuracy, our algorithm improves upon the best previous known sample complexities of streaming algorithms by either a multiplicative factor of $O(d)$ or $1/\mathrm{gap}$ where $\mathrm{gap}$ is the relative distance between the top two eigenvalues of $\Sigma$. These results are achieved through a novel analysis of the classic Oja's algorithm, one of the oldest and most popular algorithms for streaming PCA. In particular, this work shows that simply picking a random initial point $w_0$ and applying the update rule $w_{i + 1} = w_i + \eta_i A_i w_i$ suffices to accurately estimate the top eigenvector, with a suitable choice of $\eta_i$. We believe our result sheds light on how to efficiently perform streaming PCA both in theory and in practice and we hope that our analysis may serve as the basis for analyzing many variants and extensions of streaming PCA.

Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates are easy to derive for a wide class of mixture models. However, the likelihood of a mixture model is non-convex, so EM has no known global convergence guarantees. Recently, method of moments approaches offer global guarantees for some mixture models, but they do not extend easily to the range of mixture models that exist. In this work, we present Polymom, an unifying framework based on method of moments in which estimation procedures are easily derivable, just as in EM. Polymom is applicable when the moments of a single mixture component are polynomials of the parameters. Our key observation is that the moments of the mixture model are a mixture of these polynomials, which allows us to cast estimation as a Generalized Moment Problem. We solve its relaxations using semidefinite optimization, and then extract parameters using ideas from computer algebra. This framework allows us to draw insights and apply tools from convex optimization, computer algebra and the theory of moments to study problems in statistical estimation.

Estimating divergences in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential inequality convergence bound derived for any divergence estimators. The main contribution of our work is to provide such a bound for an estimator of R\'enyi-$\alpha$ divergence for a smooth H\"older class of densities on the $d$-dimensional unit cube $[0, 1]^d$. We also illustrate our theoretical results with a numerical experiment.

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the $d$-dimensional unit cube $[0,1]^d$ that lie in a $\beta$-H\"older smoothness class, we prove our estimator converges at the rate $O \left( n^{-\frac{\beta}{\beta + d}} \right)$. Furthermore, we prove the estimator is exponentially concentrated about its mean, whereas most previous related results have proven only expected error bounds on estimators.

-- The paper proposes a novel Kernelized image segmentation scheme for noisy images that utilizes the concept of Smallest Univalue Segment Assimilating Nucleus (SUSAN) and incorporates spatial constrai nts by computing circular colour map induced weights. Fuzzy damping coefficients are obtained for each nucleus or center pixel on the basis of the corresponding weighted SUSAN area values, the weights being equal to the inverse of the number of horizontal and vertical moves required to reach a neighborhood pixel from the center pixel. These weights are used to vary the contributions of the different nuclei in the Kernel based framework. The paper also presents an edge quality metric obtained by fuzzy decisi on based edge candidate selection and final computation of the blurriness of the edges after their selection. The inability of existing algorithms to preserve edge information and structural details in their segmented maps necessitates the computation of t he edge quality factor (EQF) for all the competing algorithms. Qualitative and quantitative analysis have been rendered with respect to state - of - the - art algorithms and for images ridden with varying types of noises. Speckle noise ridden SAR images and Rici an noise ridden Magnetic Resonance Images have also been considered for evaluating the effectiveness of the proposed algorithm in extracting important segmentation information. Image segmentation [1] constitutes an important part of image processing which has various applications in the fields of feature extraction and object recognition. The goal of image segmentation methods is to cluster t he pixels of an image into salient regions and hence these methods mainly involve various clustering techniques [2 - 6].

The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the robustness of classifiers to adversarial perturbations, and show fundamental upper bounds on the robustness of classifiers. Specifically, we establish a general upper bound on the robustness of classifiers to adversarial perturbations, and then illustrate the obtained upper bound on the families of linear and quadratic classifiers. In both cases, our upper bound depends on a distinguishability measure that captures the notion of difficulty of the classification task. Our results for both classes imply that in tasks involving small distinguishability, no classifier in the considered set will be robust to adversarial perturbations, even if a good accuracy is achieved. Our theoretical framework moreover suggests that the phenomenon of adversarial instability is due to the low flexibility of classifiers, compared to the difficulty of the classification task (captured by the distinguishability). Moreover, we show the existence of a clear distinction between the robustness of a classifier to random noise and its robustness to adversarial perturbations. Specifically, the former is shown to be larger than the latter by a factor that is proportional to \sqrt{d} (with d being the signal dimension) for linear classifiers. This result gives a theoretical explanation for the discrepancy between the two robustness properties in high dimensional problems, which was empirically observed in the context of neural networks. To the best of our knowledge, our results provide the first theoretical work that addresses the phenomenon of adversarial instability recently observed for deep networks. Our analysis is complemented by experimental results on controlled and real-world data.

No longer the exclusive domain of data-reliant businesses like Google, Microsoft, and Amazon, Machine learning has been making its way to the masses as an essential approach to data. Today, machine learning is understood and accepted by a more mainstream audience, and has become a measurable driver for big business both on and offline. There are three key reasons why machine learning has become one ofthe top 10 strategic technology trendsthat will shape digital business opportunities through 2020. First, the volume of data companies now collect is so massive that many struggle to make sense of it. Machine learning allows companies to take advantage of the information they already have.

Here are choice articles on hot leadership topics culled from the business schools, the business press and major consulting firms, to start off your work week. Highlights include leading in the digital age, changing the game in industrial goods through digital services, the rise of machine learning, how women and men internalise the glass ceiling, and the explosion of wearing work on our wrists. Note: Some links require you to register or are to publications that have some form of limited paywall. "Servant leadership is not a new concept. Robert Greenleaf introduced the idea back in 1977. In recent years, however, concrete evidence has emerged that the approach delivers more than warm, fuzzy feelings. Last month, the first quantitative study that begins to explain a connection between servant leadership and improved individual performance was published by researchers in Canada. This new evidence may help move servant leadership from a niche practice to one adopted by more executives."