Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allow for a classical description of such experiments. Here, we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality and bilocality assumptions, to a novel causal interpretation of CHSH inequality violations.

Random ferns is a machine learning algorithm proposed by [11] for matching same elements between two images of the same scene, allowing one to recognise certain objects or trace them on videos. The original motivation behind this method was to create a simple and efficient algorithm by extending the Naïve Bayes classifier; still the authors acknowledged its strong connection to the decision tree ensembles like the Random forest [2] algorithm. Since introduction, Random ferns have been applied in numerous computer vision application, like image recognition [1], action recognition [10] or augmented reality [14]. However, it has not gathered attention outside this field; thus, this work aims to bring this algorithm to a much wider spectrum of applications. In order to do that, I propose a generalised version of the algorithm, implemented as an R [13] package rFerns. The paper is organised as follows. Section 2 briefly recalls the Bayesian derivation of the original version of Random ferns, presents the decision tree ensemble interpretation of the algorithm and lists modifications leading to the rFerns variant.

Scene parsing is an important and challenging prob- lem in computer vision. It requires labeling each pixel in an image with the category it belongs to. Tradition- ally, it has been approached with hand-engineered features from color information in images. Recently convolutional neural networks (CNNs), which automatically learn hierar- chies of features, have achieved record performance on the task. These approaches typically include a post-processing technique, such as superpixels, to produce the final label- ing. In this paper, we propose a novel network architecture that combines deep deconvolutional neural networks with CNNs. Our experiments show that deconvolutional neu- ral networks are capable of learning higher order image structure beyond edge primitives in comparison to CNNs. The new network architecture is employed for multi-patch training, introduced as part of this work. Multi-patch train- ing makes it possible to effectively learn spatial priors from scenes. The proposed approach yields state-of-the-art per- formance on four scene parsing datasets, namely Stanford Background, SIFT Flow, CamVid, and KITTI. In addition, our system has the added advantage of having a training system that can be completely automated end-to-end with- out requiring any post-processing.

These efforts have produced a diverse ecology of models and methods. Despite this diversity, many of these models share a common underlying structure: pairwise interactions (edges) are generated with probability conditional on latent vertex attributes. Differences between models generally stem from different philosophical choices about how to learn from data or different empirically-motivated goals. The highly interdisciplinary nature of work on these generative models, however, has inhibited the development of a unified view of their similarities and differences. For instance, novel theoretical models and optimization techniques developed in machine learning are largely unknown within the social and biological sciences, which have instead emphasized model interpretability. Here, we describe a unified view of generative models for networks that draws together many of these disparate threads and highlights the fundamental similarities and differences that span these fields. We then describe a number of opportunities and challenges for future work that are revealed by this view.

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.

We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data.

Minwise hashing (Minhash) is a widely popular indexing scheme in practice. Minhash is designed for estimating set resemblance and is known to be suboptimal in many applications where the desired measure is set overlap (i.e., inner product between binary vectors) or set containment. Minhash has inherent bias towards smaller sets, which adversely affects its performance in applications where such a penalization is not desirable. In this paper, we propose asymmetric minwise hashing (MH-ALSH), to provide a solution to this problem. The new scheme utilizes asymmetric transformations to cancel the bias of traditional minhash towards smaller sets, making the final "collision probability" monotonic in the inner product. Our theoretical comparisons show that for the task of retrieving with binary inner products asymmetric minhash is provably better than traditional minhash and other recently proposed hashing algorithms for general inner products. Thus, we obtain an algorithmic improvement over existing approaches in the literature. Experimental evaluations on four publicly available high-dimensional datasets validate our claims and the proposed scheme outperforms, often significantly, other hashing algorithms on the task of near neighbor retrieval with set containment. Our proposal is simple and easy to implement in practice.

This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs, that does not require that the vertices in each DAG share a common ordering. Furthermore, we allow also for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.

One of the goals of any scientific study is to identify regularities in obs ervations and classify them into possibly separate and simpler structures or c ategories. These categories can in turn be used to make inferences on the obj ects of interest. The major advantage of this approach is that one breaks down a co mplicated reality into a collection of simpler structures. In a similar way, in patte rn recognition one is concern with discovery of regularities in data but t hrough use of computer algorithms which can be used to classify the data int o different categories [Bis06]. Independent of ones point of view, any such ana lysis must start with definition of the categories. If one has sufficient informa tion about the categories and their members, it is an easy task to establish a precis e definition. However, for most real life situations this is not the case and the no tion of category cannot be precisely defined. Under such conditions a fru itful approach is to consider a category as collection of objects which are likely to sh are the same properties.

Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the assumption of chordality which ensures that efficient scoring methods can be used. In general, non-chordal graphs have intractable normalizing constants which renders the calculation of Bayesian and other scores difficult beyond very small-scale systems. Recently, there has been a surge of interest towards the use of regularized pseudo-likelihood methods for structural learning of large-scale Markov network models, as such an approach avoids the assumption of chordality. The currently available methods typically necessitate the use of a tuning parameter to adapt the level of regularization for a particular dataset, which can be optimized for example by cross-validation. Here we introduce a Bayesian version of pseudo-likelihood scoring of Markov networks, which enables an automatic regularization through marginalization over the nuisance parameters in the model. We prove consistency of the resulting MPL estimator for the network structure via comparison with the pseudo information criterion. Identification of the MPL-optimal network on a prescanned graph space is considered with both greedy hill climbing and exact pseudo-Boolean optimization algorithms. We find that for reasonable sample sizes the hill climbing approach most often identifies networks that are at a negligible distance from the restricted global optimum. Using synthetic and existing benchmark networks, the marginal pseudo-likelihood method is shown to generally perform favorably against recent popular inference methods for Markov networks.