Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference orders), when consolidating conflicting views regarding the relationships between arguments in a debate (graphs as abstract argumentation frameworks), or when computing a consensus between several alternative clusterings of a given dataset (graphs as equivalence relations). In this paper, we introduce a formal framework for graph aggregation grounded in social choice theory. Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule. We consider both common properties of graphs, such as transitivity and reflexivity, and arbitrary properties expressible in certain fragments of modal logic. Our results establish several connections between the types of properties preserved under aggregation and the choice-theoretic axioms satisfied by the rules used. The most important of these results is a powerful impossibility theorem that generalises Arrow's seminal result for the aggregation of preference orders to a large collection of different types of graphs.

In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction errors as a function of the in-sample errors, in-sample data size, heaviness in the tails of the error distribution, and model complexity. We show that the error bounds may be used for tuning key estimation hyper-parameters, such as the number of folds K in cross-validation. We also show how K affects the bias-variance tradeoff for cross-validation. Simulations are used to demonstrate key results. We would also like to acknowledge participants at the 12th International Symposium on Econometric Theory and Applications and the 26th New Zealand Econometric Study Group as well as seminar participants at Utah, UNSW, and University of Melbourne for useful questions and comments. Fisher would like to acknowledge the financial support of the Australian Research Council, grant DP0663477. 1 1 Introduction Traditionally in econometrics, an estimation method is implemented on sample data in order to infer patterns in a population. Put another way, inference centers on generalizing to the population the pattern learned from the sample and evaluating how well the sample pattern fits the population. An alternative perspective is to consider how well a sample pattern fits another sample. In this paper, we study the ability of a model estimated from a given sample to fit new samples from the same population, referred to as the generalization ability (GA) of the model. As a way of evaluating the external validity of sample estimates, the concept of GA has been implemented in recent empirical research. For example, in the policy evaluation literature [Belloni et al., 2013, Gechter, 2015, Dolton, 2006, Blundell et al., 2004], the central question is whether any treatment effect estimated from a pilot program can be generalized to out-of-sample individuals.

Efficient usage of the knowledge provided by the Linked Data community is often hindered by the need for domain experts to formulate the right SPARQL queries to answer questions. For new questions they have to decide which datasets are suitable and in which terminology and modelling style to phrase the SPARQL query. In this work we present an evolutionary algorithm to help with this challenging task. Given a training list of source-target node-pair examples our algorithm can learn patterns (SPARQL queries) from a SPARQL endpoint. The learned patterns can be visualised to form the basis for further investigation, or they can be used to predict target nodes for new source nodes. Amongst others, we apply our algorithm to a dataset of several hundred human associations (such as "circle - square") to find patterns for them in DBpedia. We show the scalability of the algorithm by running it against a SPARQL endpoint loaded with > 7.9 billion triples. Further, we use the resulting SPARQL queries to mimic human associations with a Mean Average Precision (MAP) of 39.9 % and a Recall@10 of 63.9 %.

Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a general class of noisy matrix completion tasks where the underlying matrix is following an IMC model i.e., it is formed by a mixing matrix (a priori unknown) sandwiched between two known feature matrices. The mixing matrix here is assumed to be well approximated by the product of two sparse matrices---referred here to as "sparse factor models." We leverage the main theorem of Soni:2016:NMC and extend it to provide theoretical error bounds for the sparsity-regularized maximum likelihood estimators for the class of problems discussed in this paper. The main result is general in the sense that it can be used to derive error bounds for various noise models. In this paper, we instantiate our main result for the case of Gaussian noise and provide corresponding error bounds in terms of squared loss.

In binary classification and regression problems, it is well understood that Lipschitz continuity and smoothness of the loss function play key roles in governing generalization error bounds for empirical risk minimization algorithms. In this paper, we show how these two properties affect generalization error bounds in the learning to rank problem. The learning to rank problem involves vector valued predictions and therefore the choice of the norm with respect to which Lipschitz continuity and smoothness are defined becomes crucial. Choosing the $\ell_\infty$ norm in our definition of Lipschitz continuity allows us to improve existing bounds. Furthermore, under smoothness assumptions, our choice enables us to prove rates that interpolate between $1/\sqrt{n}$ and $1/n$ rates. Application of our results to ListNet, a popular learning to rank method, gives state-of-the-art performance guarantees.

We apply a novel spectral graph technique, that of locally-biased semi-supervised eigenvectors, to study the diversity of galaxies. This technique permits us to characterize empirically the natural variations in observed spectra data, and we illustrate how this approach can be used in an exploratory manner to highlight both large-scale global as well as small-scale local structure in Sloan Digital Sky Survey (SDSS) data. We use this method in a way that simultaneously takes into account the measurements of spectral lines as well as the continuum shape. Unlike Principal Component Analysis, this method does not assume that the Euclidean distance between galaxy spectra is a good global measure of similarity between all spectra, but instead it only assumes that local difference information between similar spectra is reliable. Moreover, unlike other nonlinear dimensionality methods, this method can be used to characterize very finely both small-scale local as well as large-scale global properties of realistic noisy data. The power of the method is demonstrated on the SDSS Main Galaxy Sample by illustrating that the derived embeddings of spectra carry an unprecedented amount of information. By using a straightforward global or unsupervised variant, we observe that the main features correlate strongly with star formation rate and that they clearly separate active galactic nuclei. Computed parameters of the method can be used to describe line strengths and their interdependencies. By using a locally-biased or semi-supervised variant, we are able to focus on typical variations around specific objects of astronomical interest. We present several examples illustrating that this approach can enable new discoveries in the data as well as a detailed understanding of very fine local structure that would otherwise be overwhelmed by large-scale noise and global trends in the data.

Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a Markov factor graph model, this exploration process is called structure discovery. For discrete-valued samples, estimates of the information divergence over the parametric class of multinomial models lead to structure discovery methods whose mean squared error achieves parametric convergence rates as the sample size grows. However, a naive application of this method to continuous nonparametric multivariate models converges much more slowly. In this paper we introduce a new method for nonparametric structure discovery that uses weighted ensemble divergence estimators that achieve parametric convergence rates and obey an asymptotic central limit theorem that facilitates hypothesis testing and other types of statistical validation.

Deep Learning: Keras Short Video Tutorial (youtu.be)

The variation between the thousands of languages spoken across the world would make you think that they have very little in common. An analysis of nearly two-thirds of the world's languages has shown humans tend to use the same sounds for common objects and ideas, no matter what language they are speaking. An analysis of nearly two-thirds of the world's languages has shown humans tend to use the same sounds for common objects and ideas, no matter what language they are speaking (stock image) The study, published today in the Proceedings of the National Academy of Sciences, looked at two thirds of the world's languages and found a pattern formed between the words used for certain basic concepts. The 100 words in the study include things like nose, tongue, leaf and sand. The researchers, from Cornell University in New York, say the study shatters a concept considered a cornerstone in linguistics - the century-old idea that the relationship between a sound of a word and its meaning is arbitrary.

I recently participated in a weekend-long data science hackathon, titled'The Smart Recruits'. Organized by the amazing folks at Analytics Vidhya, it saw some serious competition. Although my performance can be classified as decent at best (47 out of 379 participants), it was among the more satisfying ones I have participated in on both AV (profile) and Kaggle (profile) over the last few months. Thus, I decided it might be worthwhile to try and share some insights as a data science autodidact. The competition required us to use historical data to create a model to help an organization pick out better recruits. The evaluation metric to be used for judging the predictions was AUC (area under the ROC curve).