Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of inferential reasoning in knowledge bases is implication discovery. Here, by learning when one relation implies another, we can extend our knowledge representation. There are several existing models for relational implication, however we argue they are motivated but not principled. To this end, we define a formal probabilistic model of relational implication. By using estimators based on the empirical distribution of our dataset, we demonstrate that our model outperforms existing approaches. While previous work achieves a best score of 0.7812 AUC on an evaluatory dataset, our ProbE model improves this to 0.7915. Furthermore, we demonstrate that our model can be improved substantially through the use of link prediction models and dense latent representations of the underlying argument and relations. This variant, denoted ProbL, improves the state of the art on our evaluation dataset to 0.8143. In addition to developing a new framework and providing novel scores of relational implication, we provide two pragmatic resources to assist future research. First, we motivate and develop an improved crowd framework for constructing labelled datasets of relational implication. Using this, we reannotate and make public a dataset comprised of 17,848 instances of labelled relational implication. We demonstrate that precision (as evaluated by expert consensus with the crowd labels) on the resulting dataset improves from 53% to 95%.

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orthogonality constraints. While effective, this approach is computationally burdensome so we also consider iterative deflation approaches which take advantage of efficient algorithms for rank-one SFPCA. We show that alternative deflation schemes can more efficiently extract signal from the data, in turn improving estimation of subsequent components. Finally, we compare the performance of our manifold optimization and deflation techniques in a scenario where orthogonality does not hold and find that they still lead to significantly improved performance.

The authors study and analyze methods using the sparsity property of some statistical models in order to recover the underlying signal in a dataset. They focus on the Lasso technique as an alternative to the standard least-squares method.

Welcome to the video series on Introduction to Machine Learning with Scikit-Learn. This video contains Chapter - 6.1. In this chapter, I've explained our first Machine Learning algorithm called Linear Regression using just five data points for easy understanding This video describes what is Linear Regression and how we can use the same using Scikit-learn. In context of this algorithm, I've also explained the unified machine learning algorithm and how generic interface can be used for almost all ML algorithms using scikit-Learn Feel free to connect with me @ YouTube: https://www.youtube.com/CodesBay

Summary: Python's open-source and high-level nature, as well as its comprehensive libraries, make it the perfect fit to solve the numerous real-life ML challenges. The increasing popularity and accessibility of Artificial Intelligence solutions is rapidly reshaping many industries, from healthcare through finance to aviation. Although the application of the latest technologies has always been an essential consideration for companies striving to get ahead of the curve, the ubiquity of AI means that it's becoming the core of many operations. But the increased use of ML, understood as a technical implementation of AI concepts, across the board has generated a wide range of problems that require both a creative approach and efficient tools to solve. Python, a highly versatile programming language, aids both; its significant flexibility and comprehensiveness, as well as availability of libraries and a supportive community, make it the perfect choice for developers who create ML solutions.

Many approaches have been proposed to discover clusters within networks. Community finding field encompasses approaches which try to discover clusters where nodes are tightly related within them but loosely related with nodes of other clusters. However, a community network configuration is not the only possible latent structure in a graph. Core-periphery and hierarchical network configurations are valid structures to discover in a relational dataset. On the other hand, a network is not completely explained by only knowing the membership of each node. A high level view of the inter-cluster relationships is needed. Blockmodelling techniques deal with these two issues. Firstly, blockmodelling allows finding any network configuration besides to the well-known community structure. Secondly, blockmodelling is a summary representation of a network which regards not only membership of nodes but also relations between clusters. Finally, a unique summary representation of a network is unlikely. Networks might hide more than one blockmodel. Therefore, our proposed problem aims to discover a secondary blockmodel representation of a network that is of good quality and dissimilar with respect to a given blockmodel. Our methodology is presented through two approaches, (a) inclusion of cannot-link constraints and (b) dissimilarity between image matrices. Both approaches are based on non-negative matrix factorisation NMF which fits the blockmodelling representation. The evaluation of these two approaches regards quality and dissimilarity of the discovered alternative blockmodel as these are the requirements of the problem.

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method are implemented to develop a matrix-free framework for likelihood maximization. Simulation results show that our method is substantially faster than the expectation-maximization solution without sacrificing accuracy. Our method is applied to fit factor models on data from suicide attempters, suicide ideators and a control group.

Inspired by the advances in biological science, the study of sparse binary projection models has attracted considerable recent research attention. The models project dense input samples into a higher-dimensional space and output sparse binary vectors after Winner-Take-All competition, subject to the constraint that the projection matrix is also sparse and binary. Following the work along this line, we developed a supervised-WTA model under the supervised setting where training samples with both input and output representations are available, from which the projection matrix can be obtained with a simple, efficient yet effective algorithm. We further extended the model and the algorithm to an unsupervised setting where only the input representation of the samples is available. In a series of empirical evaluation on similarity search tasks, both models reported significantly improved results over the state-of-the-art methods in both search accuracy and running time. The successful results give us strong confidence that the proposed work provides a highly practical tool to real world applications.

The biological processes involved in a drug's mechanisms of action are oftentimes dynamic, complex and difficult to discern. Time-course gene expression data is a rich source of information that can be used to unravel these complex processes, identify biomarkers of drug sensitivity and predict the response to a drug. However, the majority of previous work has not fully utilized this temporal dimension. In these studies, the gene expression data is either considered at one time-point (before the administration of the drug) or two timepoints (before and after the administration of the drug). This is clearly inadequate in modeling dynamic gene-drug interactions, especially for applications such as long-term drug therapy. In this work, we present a novel REcursive Prediction (REP) framework for drug response prediction by taking advantage of time-course gene expression data. Our goal is to predict drug response values at every stage of a long-term treatment, given the expression levels of genes collected in the previous time-points. To this end, REP employs a built-in recursive structure that exploits the intrinsic time-course nature of the data and integrates past values of drug responses for subsequent predictions. It also incorporates tensor completion that can not only alleviate the impact of noise and missing data, but also predict unseen gene expression levels (GELs). These advantages enable REP to estimate drug response at any stage of a given treatment from some GELs measured in the beginning of the treatment. Extensive experiments on a dataset corresponding to 53 multiple sclerosis patients treated with interferon are included to showcase the effectiveness of REP.

Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks, alternative non-likelihood training criteria have been proposed. Whilst not necessarily statistically efficient, these alternatives may better match user requirements such as sharp image generation. A general variational method for training probabilistic latent variable models using maximum likelihood is well established; however, how to train latent variable models using other f-divergences is comparatively unknown. We discuss a variational approach that, when combined with the recently introduced Spread Divergence, can be applied to train a large class of latent variable models using any f-divergence.