A fundamental limitation of the common machine learning methods is the cost incurred by the preparation of the large training samples required for good generalization. Multi-task learning (MTL) offers a potential remedy. Unlike common single task learning, MTL accomplishes tasks simultaneously with other related tasks, using a shared representation. One general assumption of multi-task learning is that all tasks should share some common structures, including a similarity metric matrix [3], a low ranksubspace [4, 5], parametersofBayesianmodels [6] oracommon set of features [7, 8, 9]. Improved generalization is achieved because what is learned from each task can help with the learning of other tasks [10]. MTL has been successfully applied to many applications such as stock selection [3], speech classification [11] and medical diagnoses [12]. While the majority of existing multi-task feature learning algorithms assume that the relevant features are shared by all tasks, some studies have begun to consider a more general case where features can be commonly shared only among most, but not necessarily all of them. In other word, they try to learn the features specific to each task as well as the common features shared among tasks [1]. In addition, MTL is commonly formulated as a convex regularization problem.

Due to rapid advancement in high-throughput techniques, such as microarrays and next generation sequencing technologies, biological data are increasing exponentially. The current challenge in computational biology and bioinformatics research is how to analyze these huge raw biological data to extract biologically meaningful knowledge. This review paper presents the applications of formal concept analysis for the analysis and knowledge discovery from biological data, including gene expression discretization, gene co-expression mining, gene expression clustering, finding genes in gene regulatory networks, enzyme/protein classifications, binding site classifications, and so on. It also presents a list of FCA-based software tools applied in biological domain and covers the challenges faced so far.

There has been significant recent work on the theory and application of randomized coordinate descent algorithms, beginning with the work of Nesterov [SIAM J. Optim., 22(2), 2012], who showed that a random-coordinate selection rule achieves the same convergence rate as the Gauss-Southwell selection rule. This result suggests that we should never use the Gauss-Southwell rule, as it is typically much more expensive than random selection. However, the empirical behaviours of these algorithms contradict this theoretical result: in applications where the computational costs of the selection rules are comparable, the Gauss-Southwell selection rule tends to perform substantially better than random coordinate selection. We give a simple analysis of the Gauss-Southwell rule showing that---except in extreme cases---it's convergence rate is faster than choosing random coordinates. Further, in this work we (i) show that exact coordinate optimization improves the convergence rate for certain sparse problems, (ii) propose a Gauss-Southwell-Lipschitz rule that gives an even faster convergence rate given knowledge of the Lipschitz constants of the partial derivatives, (iii) analyze the effect of approximate Gauss-Southwell rules, and (iv) analyze proximal-gradient variants of the Gauss-Southwell rule.

We introduce two Python frameworks to train neural networks on large datasets: Blocks and Fuel. Blocks is based on Theano, a linear algebra compiler with CUDA-support. It facilitates the training of complex neural network models by providing parametrized Theano operations, attaching metadata to Theano's symbolic computational graph, and providing an extensive set of utilities to assist training the networks, e.g. training algorithms, logging, monitoring, visualization, and serialization. Fuel provides a standard format for machine learning datasets. It allows the user to easily iterate over large datasets, performing many types of pre-processing on the fly.

It is well known in the literature that the problem of learning the structure of Bayesian networks is very hard to tackle: its computational complexity is super-exponential in the number of nodes in the worst case and polynomial in most real-world scenarios. Efficient implementations of score-based structure learning benefit from past and current research in optimisation theory, which can be adapted to the task by using the network score as the objective function to maximise. This is not true for approaches based on conditional independence tests, called constraint-based learning algorithms. The only optimisation in widespread use, backtracking, leverages the symmetries implied by the definitions of neighbourhood and Markov blanket. In this paper we illustrate how backtracking is implemented in recent versions of the bnlearn R package, and how it degrades the stability of Bayesian network structure learning for little gain in terms of speed. As an alternative, we describe a software architecture and framework that can be used to parallelise constraint-based structure learning algorithms (also implemented in bnlearn) and we demonstrate its performance using four reference networks and two real-world data sets from genetics and systems biology. We show that on modern multi-core or multiprocessor hardware parallel implementations are preferable over backtracking, which was developed when single-processor machines were the norm.

Can we develop a computer algorithm that assesses the creativity of a painting given its context within art history? This paper proposes a novel computational framework for assessing the creativity of creative products, such as paintings, sculptures, poetry, etc. We use the most common definition of creativity, which emphasizes the originality of the product and its influential value. The proposed computational framework is based on constructing a network between creative products and using this network to infer about the originality and influence of its nodes. Through a series of transformations, we construct a Creativity Implication Network. We show that inference about creativity in this network reduces to a variant of network centrality problems which can be solved efficiently. We apply the proposed framework to the task of quantifying creativity of paintings (and sculptures). We experimented on two datasets with over 62K paintings to illustrate the behavior of the proposed framework. We also propose a methodology for quantitatively validating the results of the proposed algorithm, which we call the "time machine experiment".

This paper examines the use of a residual bootstrap for bias correction in machine learning regression methods. Accounting for bias is an important obstacle in recent efforts to develop statistical inference for machine learning methods. We demonstrate empirically that the proposed bootstrap bias correction can lead to substantial improvements in both bias and predictive accuracy. In the context of ensembles of trees, we show that this correction can be approximated at only double the cost of training the original ensemble without introducing additional variance. Our method is shown to improve test-set accuracy over random forests by up to 70\% on example problems from the UCI repository.

In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal measure, proposed by Granger himself, calculates the Bhattacharyya distance between the joint probability density function (pdf) and the product of marginal pdfs. We call this measure the mutual dependence. However, to date this measure has not been directly computable from data. In this paper, we use our recently introduced maximum likelihood non-parametric estimator for band-limited pdfs, to compute the mutual dependence directly from the data. We construct the estimator of mutual dependence and compare its performance to standard measures (Pearson's and distance correlation) for different known pdfs by computing convergence rates, computational complexity, and the ability to capture nonlinear dependencies. Our mutual dependence estimator requires fewer samples to converge to theoretical values, is faster to compute, and captures more complex dependencies than standard measures.

We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles (bounded random variables) developed in the context of imprecise probability, which we extend here to make it deal with vector-valued gambles. The equivalence allows us to revisit incomplete preferences from the viewpoint, and with the tools, of desirability and through the derived notion of coherent lower previsions (i.e., lower expectation functionals). On this basis, we obtain new results and insights: in particular, we show that the theory of incomplete preferences can be developed assuming only the existence of a worst act--no best act is needed--, and that a weakened Archimedean axiom suffices too; this axiom allows us also to address some controversy about the regularity assumption (that probabilities should be positive--they need not), which enables us also to deal with uncountable possibility spaces; we show that it is always possible to extend in a minimal way a preference relation to one with a worst act, and yet the resulting relation is never Archimedean, except in a trivial case; we show that the traditional notion of state independence coincides with the notion called strong independence in imprecise probability (stochastic independence in the case of complete preferences)--this leads us to give much a weaker definition of state independence than the traditional one; we rework and uniform the notions of complete preferences, beliefs, values; we argue that Archimedeanity does not capture all the problems that can be modelled with sets of expected utilities and we provide a new notion that does precisely that. Perhaps most importantly, we argue throughout that desirability is a powerful and natural setting to model, and work with, incomplete preferences, even in the case of non-Archimedean problems. This leads us to suggest that desirability, rather than preference, should be the primitive notion at the basis of decision-theoretic axiomatisations. Keywords: Incomplete preferences, decision theory, expected utility, desirability, convex cones, imprecise probability.

Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable modelers to capture effects that are difficult to characterize analytically or summarize statistically. However, in many real-world applications, these simulations need to be inverted to match the observed data. This typically requires the custom design, derivation and implementation of sophisticated inversion algorithms. Here we give a framework for inverting a broad class of complex software simulators via probabilistic programming and automatic inference, using under 20 lines of probabilistic code. Our approach is based on a formulation of inversion as approximate inference in a simple sequential probabilistic model. We implement four inference strategies, including Metropolis-Hastings, a sequentialized Metropolis-Hastings scheme, and a particle Markov chain Monte Carlo scheme, requiring 4 or fewer lines of probabilistic code each. We demonstrate our framework by applying it to invert a real geological software simulator from the oil and gas industry.