We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and, depending on the estimated mixture model, on the variation on group covariances. The proposed method aims at reducing the dimensionality by identifying a set of linear combinations, ordered by importance as quantified by the associated eigenvalues, of the original features which capture most of the cluster structure contained in the data. Observations may then be projected onto such a reduced subspace, thus providing summary plots which help to visualize the clustering structure. These plots can be particularly appealing in the case of high-dimensional data and noisy structure. The new constructed variables capture most of the clustering information available in the data, and they can be further reduced to improve clustering performance. We illustrate the approach on both simulated and real data sets.

Decadal climate predictions, which are initialized with observed conditions, are characterized by two main sources of uncertainties--internal and model variabilities. Using an ensemble of climate model simulations from the CMIP5 decadal experiments, we quantified the total uncertainty associated with these predictions and the relative importance of each source. Annual and monthly averages of the surface temperature and wind components were considered. We show that different definitions of the anomaly results in different conclusions regarding the variance of the ensemble members. However, some features of the uncertainty are common to all the measures we considered. We found that over decadal time scales, there is no considerable increase in the uncertainty with time. The model variability is more sensitive to the annual cycle than the internal variability. This, in turn, results in a maximal uncertainty during the winter in the northern hemisphere. The uncertainty of the surface temperature prediction is dominated by the model variability, whereas the uncertainty of the wind components is determined by both sources. Analysis of the spatial distribution of the uncertainty reveals that the surface temperature has higher variability over land and in high latitudes, whereas the surface zonal wind has higher variability over the ocean. The relative importance of the internal and model variabilities depends on the averaging period, the definition of the anomaly, and the location. These findings suggest that several methods should be combined in order to assess future climate prediction uncertainties and that weighting schemes of the ensemble members may reduce the uncertainties.

In this paper, we address the problem of identifying linear structural equation models. We first extend the edge set half-trek criterion to cover a broader class of models. We then show that any semi-Markovian linear model can be recursively decomposed into simpler sub-models, resulting in improved identification power. Finally, we show that, unlike the existing methods developed for linear models, the resulting method subsumes the identification algorithm of non-parametric models.

The output scores of a neural network classifier are converted to probabilities via normalizing over the scores of all competing categories. Computing this partition function, $Z$, is then linear in the number of categories, which is problematic as real-world problem sets continue to grow in categorical types, such as in visual object recognition or discriminative language modeling. We propose three approaches for sublinear estimation of the partition function, based on approximate nearest neighbor search and kernel feature maps and compare the performance of the proposed approaches empirically.

We present a sparse knowledge gradient (SpKG) algorithm for adaptively selecting the targeted regions within a large RNA molecule to identify which regions are most amenable to interactions with other molecules. Experimentally, such regions can be inferred from fluorescence measurements obtained by binding a complementary probe with fluorescence markers to the targeted regions. We use a biophysical model which shows that the fluorescence ratio under the log scale has a sparse linear relationship with the coefficients describing the accessibility of each nucleotide, since not all sites are accessible (due to the folding of the molecule). The SpKG algorithm uniquely combines the Bayesian ranking and selection problem with the frequentist $\ell_1$ regularized regression approach Lasso. We use this algorithm to identify the sparsity pattern of the linear model as well as sequentially decide the best regions to test before experimental budget is exhausted. Besides, we also develop two other new algorithms: batch SpKG algorithm, which generates more suggestions sequentially to run parallel experiments; and batch SpKG with a procedure which we call length mutagenesis. It dynamically adds in new alternatives, in the form of types of probes, are created by inserting, deleting or mutating nucleotides within existing probes. In simulation, we demonstrate these algorithms on the Group I intron (a mid-size RNA molecule), showing that they efficiently learn the correct sparsity pattern, identify the most accessible region, and outperform several other policies.

With the recent availability of much network data, such as world wide web, social networks, phone call networks, science collaboration graphs [1], [2], there is a renewed interest for the graph partitioning problem, especially for the automatic discovery of community structures in large networks [3], [4], [5]. Beyond clustering approaches, coclustering approaches aim at summarizing the relation between two entities in a many-to-many relationship. Such a relation can be represented as a graph, where the source and target vertices represent entities and the edges stand for relations between entities. A coclustering model provides a summary of a graph by grouping source vertices and target vertices. For example, in market analysis, the source vertices of the graph represent customers, the target vertices represent products and there is one edge each time a customer has purchased a product. A coclustering model summarizes the dataset by grouping customers that have purchased approximately the same products and grouping products that have been purchased by approximately the same customers. Coclustering models have been applied to many other domains, such as information retrieval (the entities are documents and their words in a text corpus), web log analysis (cookies and their visited web pages), web structure analysis (web pages with hyperlinks between them) or telecommunication network (the call detail records stand for the edges in a call graph between a caller and a called party). All these real-world graphs are directed multigraphs, meaning that two entities may be linked by multi-edges. We aim to summarize and discover insightful patterns in such graphs, using a method with the desired following properties: 1) Robustness, to avoid detecting spurious patterns in case of noisy data.

Approximate Newton methods are a standard optimization tool which aim to maintain the benefits of Newton's method, such as a fast rate of convergence, whilst alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov Decision Processes (MDPs). We first analyse the structure of the Hessian of the objective function for MDPs. We show that, like the gradient, the Hessian exhibits useful structure in the context of MDPs and we use this analysis to motivate two Gauss-Newton Methods for MDPs. Like the Gauss-Newton method for non-linear least squares, these methods involve approximating the Hessian by ignoring certain terms in the Hessian which are difficult to estimate. The approximate Hessians possess desirable properties, such as negative definiteness, and we demonstrate several important performance guarantees including guaranteed ascent directions, invariance to affine transformation of the parameter space, and convergence guarantees. We finally provide a unifying perspective of key policy search algorithms, demonstrating that our second Gauss-Newton algorithm is closely related to both the EM-algorithm and natural gradient ascent applied to MDPs, but performs significantly better in practice on a range of challenging domains.

In 2008, the CEO of the company that manages and maintains the public bicycle service in Barcelona recognized that one may not expect to always find a place to leave the rented bike nearby their destination, similarly to the case when, driving a car, people may not find a parking lot. In this work, we make predictions about the statuses of the stations of the public bicycle service in Barcelona. We show that it is feasible to correctly predict nearly half of the times when the stations are either completely full of bikes or completely empty, up to 2 days before they actually happen. That is, users might avoid stations at times when they could not return a bicycle that they have rented before, or when they would not find a bike to rent. To achieve that, we apply the Random Forest algorithm to classify the status of the stations and improve the lifetime of the models using publicly available data, such as information about the weather forecast. Finally, we expect that the results of the predictions can be used to improve the quality of the service and make it more reliable for the users.

Presently, a very large number of public and private data sets are available around the local governments. In most cases, they are not semantically interoperable and a huge human effort is needed to create integrated ontologies and knowledge base for smart city. Smart City ontology is not yet standardized, and a lot of research work is needed to identify models that can easily support the data reconciliation, the management of the complexity and reasoning. In this paper, a system for data ingestion and reconciliation smart cities related aspects as road graph, services available on the roads, traffic sensors etc., is proposed. The system allows managing a big volume of data coming from a variety of sources considering both static and dynamic data. These data are mapped to smart-city ontology and stored into an RDF-Store where they are available for applications via SPARQL queries to provide new services to the users. The paper presents the process adopted to produce the ontology and the knowledge base and the mechanisms adopted for the verification, reconciliation and validation. Some examples about the possible usage of the coherent knowledge base produced are also offered and are accessible from the RDF-Store.

In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropriate prior distribution, we show how the EM algorithm can be used to efficiently solve the corresponding optimization problem. To this end, we rely on variance-mean Gaussian mixtures (VMGM) to describe the prior distribution, while we incorporate many nice features of these mixtures to our estimation problem. The corresponding MAP estimation problem is completely expressed in terms of the EM algorithm, which allows for handling nonlinearities and hidden variables that cannot be easily handled with traditional methods. For comparison purposes, we also develop a Coordinate Descent algorithm for the $\ell_q$-norm penalized problem and present the performance results via simulations.