It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear aggregation approaches motivated by regression applications. We show that the proposed approach is minimax optimal when the true data-generating model is a convex or linear combination of models in the list. Moreover, the method can adapt to sparsity structure in which certain models should receive zero weights, and the method is tuning parameter free unlike competitors. More generally, under an M-open view when the truth falls outside the space of all convex/linear combinations, our theory suggests that the posterior measure tends to concentrate on the best approximation of the truth at the minimax rate. We illustrate the method through simulation studies and several applications.

The smart grid vision entails advanced information technology and data analytics to enhance the efficiency, sustainability, and economics of the power grid infrastructure. Aligned to this end, modern statistical learning tools are leveraged here for electricity market inference. Day-ahead price forecasting is cast as a low-rank kernel learning problem. Uniquely exploiting the market clearing process, congestion patterns are modeled as rank-one components in the matrix of spatio-temporally varying prices. Through a novel nuclear norm-based regularization, kernels across pricing nodes and hours can be systematically selected. Even though market-wide forecasting is beneficial from a learning perspective, it involves processing high-dimensional market data. The latter becomes possible after devising a block-coordinate descent algorithm for solving the non-convex optimization problem involved. The algorithm utilizes results from block-sparse vector recovery and is guaranteed to converge to a stationary point. Numerical tests on real data from the Midwest ISO (MISO) market corroborate the prediction accuracy, computational efficiency, and the interpretative merits of the developed approach over existing alternatives.

Support Vector Machine (SVM) is powerful classification technique based on the idea of structural risk minimization. Use of kernel function enables curse of dimensionality to be addressed. However, proper kernel function for certain problem is dependent on specific dataset and as such there is no good method on choice of kernel function. In this paper, SVM is used to build empirical models of currency crisis in Argentina. An estimation technique is developed by training model on real life data set which provides reasonably accurate model outputs and helps policy makers to identify situations in which currency crisis may happen. The third and fourth order polynomial kernel is generally best choice to achieve high generalization of classifier performance. SVM has high level of maturity with algorithms that are simple, easy to implement, tolerates curse of dimensionality and good empirical performance. The satisfactory results show that currency crisis situation is properly emulated using only small fraction of database and could be used as an evaluation tool as well as an early warning system. To the best of knowledge this is the first work on SVM approach for currency crisis evaluation of Argentina.

We present a new model for prediction markets, in which we use risk measures to model agents and introduce a market maker to describe the trading process. This specific choice on modelling tools brings us mathematical convenience. The analysis shows that the whole market effectively approaches a global objective, despite that the market is designed such that each agent only cares about its own goal. Additionally, the market dynamics provides a sensible algorithm for optimising the global objective. An intimate connection between machine learning and our markets is thus established, such that we could 1) analyse a market by applying machine learning methods to the global objective, and 2) solve machine learning problems by setting up and running certain markets.

With the rapid development of social media sharing, people often need to manage the growing volume of multimedia data such as large scale video classification and annotation, especially to organize those videos containing human activities. Recently, manifold regularized semi-supervised learning (SSL), which explores the intrinsic data probability distribution and then improves the generalization ability with only a small number of labeled data, has emerged as a promising paradigm for semiautomatic video classification. In addition, human action videos often have multi-modal content and different representations. To tackle the above problems, in this paper we propose multiview Hessian regularized logistic regression (mHLR) for human action recognition. Compared with existing work, the advantages of mHLR lie in three folds: (1) mHLR combines multiple Hessian regularization, each of which obtained from a particular representation of instance, to leverage the exploring of local geometry; (2) mHLR naturally handle multi-view instances with multiple representations; (3) mHLR employs a smooth loss function and then can be effectively optimized. We carefully conduct extensive experiments on the unstructured social activity attribute (USAA) dataset and the experimental results demonstrate the effectiveness of the proposed multiview Hessian regularized logistic regression for human action recognition.

The idea of "only knowing" a collection of sentences, as proposed by Levesque, has been previously shown to be very useful in characterizing knowledge-based agents: in terms of a specification, a precise and perspicuous account of the beliefs and non-beliefs is obtained in a monotonic setting. Levesque's logic is based on a first-order modal language with quantifying-in, thus allowing for de re versus de dicto distinctions, among other things. However, the logic and its recent dynamic extension only deal with the case of a single agent. In this work, we propose a first-order multiagent framework with knowledge, actions, sensing and only knowing, that is shown to inherit all the features of the single agent version. Most significantly, we prove reduction theorems by means of which reasoning about knowledge and actions in the framework simplifies to non-epistemic, non-dynamic reasoning about the initial situation.

Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary optimization can be costly and very hard to carry out in practice. Moreover, it creates serious theoretical concerns, as most of the convergence results assume that the exact optimum of the acquisition function can be found. In this paper, we introduce a new technique for efficient global optimization that combines Gaussian process confidence bounds and treed simultaneous optimistic optimization to eliminate the need for auxiliary optimization of acquisition functions. The experiments with global optimization benchmarks and a novel application to automatic information extraction demonstrate that the resulting technique is more efficient than the two approaches from which it draws inspiration. Unlike most theoretical analyses of Bayesian optimization with Gaussian processes, our finite-time convergence rate proofs do not require exact optimization of an acquisition function. That is, our approach eliminates the unsatisfactory assumption that a difficult, potentially NP-hard, problem has to be solved in order to obtain vanishing regret rates.

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response $y$, conditional on the model being selected (``condition on selection" framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix $X$. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit, non-negative least squares, and marginal screening+Lasso.

Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than columns, so-called "tall-and-skinny matrices". One key component to these improved methods is an orthogonal matrix transformation that preserves the separability of the NMF problem. Our final methods need a single pass over the data matrix and are suitable for streaming, multi-core, and MapReduce architectures. We demonstrate the efficacy of these algorithms on terabyte-sized synthetic matrices and real-world matrices from scientific computing and bioinformatics.

We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N-agent, C-resource allocation problems, where the resources are all homogeneous. Bhaskar proposed one way to achieve this in 2-agent, 1-resource games: Agents start by symmetrically randomizing their actions, and as soon as they each choose different actions, they start to follow a potentially asymmetric "convention" that prescribes their actions from then on. We extend the concept of convention to the general case of infinitely repeated resource allocation games with N agents and C resources. We show that for any convention, there exists a symmetric subgame-perfect equilibrium which implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal which allows them to alternate between different allocations. We define price of anonymity of a convention as a ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the subgame-perfect equilibrium which implements the convention. We show that while the price of anonymity of the bourgeois convention is infinite, the market convention decreases this price by reducing the conflict between the agents.