Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic terms. Our treatment starts from the complementary point of view of statistical modeling and prediction of dynamical systems. It is known that for finite amounts of training data, simpler models can have greater predictive power than more complex ones. We use the trade-off between model simplicity and predictive accuracy to generate optimal multiscale decompositions of dynamical networks into weakly-coupled, simple modules. State-dependent and causal versions of our method are also proposed.

--This article proposes the use of V ector Symbolic Architectures for implementing Hierarchical Graph Neuron, an architecture for memorizing patterns of generic sensor stimuli. The adoption of a V ector Symbolic representation ensures a one-layered design for the approach, while maintaining the previously reported properties and performance characteristics of Hierarchical Graph Neuron, and also improving the noise resistance of the architecture. The proposed architecture enables a linear (with respect to the number of stored entries) time search for an arbitrary sub-pattern. RAPH Neuron (GN) is an approach for memorizing patterns of generic sensor stimuli for later template matching. It is based on the hypothesis that a better associative memory resource can be created by changing the emphasis from high speed sequential CPU processing to parallel network-centric processing [2], [3]. In contrast to contemporary machine learning approaches, GN allows introduction of new patterns in the learning set without the need for retraining. Whilst doing so, it exhibits a high level of scalability i.e. its performance and accuracy do not degrade as the number of stored patterns increases over time. V ector Symbolic Architectures (VSA) [4] are a bio-inspired method of representing concepts and their meaning for modeling cognitive reasoning. It exhibits a set of unique properties which make it suitable for implementation of artificial general intelligence [5], [6], [7], and so, creation of complex systems for sensing and pattern recognition without reliance on complex computation. In the biological world, extremely successful applications of these approaches can be found.

In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.

We consider a situation in which we see samples in $\mathbb{R}^d$ drawn i.i.d. from some distribution with mean zero and unknown covariance A. We wish to compute the top eigenvector of A in an incremental fashion - with an algorithm that maintains an estimate of the top eigenvector in O(d) space, and incrementally adjusts the estimate with each new data point that arrives. Two classical such schemes are due to Krasulina (1969) and Oja (1983). We give finite-sample convergence rates for both.

Using nonparametric methods has been increasingly explored in Bayesian hierarchical modeling as a way to increase model flexibility. Although the field shows a lot of promise, inference in many models, including Hierachical Dirichlet Processes (HDP), remain prohibitively slow. One promising path forward is to exploit the submodularity inherent in Indian Buffet Process (IBP) to derive near-optimal solutions in polynomial time. In this work, I will present a brief tutorial on Bayesian nonparametric methods, especially as they are applied to topic modeling. I will show a comparison between different non-parametric models and the current state-of-the-art parametric model, Latent Dirichlet Allocation (LDA).

We consider using an ensemble of binary classifiers for transductive prediction, when unlabeled test data are known in advance. We derive minimax optimal rules for confidence-rated prediction in this setting. By using PAC-Bayes analysis on these rules, we obtain data-dependent performance guarantees without distributional assumptions on the data. Our analysis techniques are readily extended to a setting in which the predictor is allowed to abstain.

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering for the stochastic blockmodel and the degree-corrected stochastic blockmodel. We also show an analogous result for the more general random dot product graph model.

The computation of the global minimum energy conformation (GMEC) is an important and challenging topic in structure-based computational protein design. In this paper, we propose a new protein design algorithm based on the AND/OR branch-and-bound (AOBB) search, which is a variant of the traditional branch-and-bound search algorithm, to solve this combinatorial optimization problem. By integrating with a powerful heuristic function, AOBB is able to fully exploit the graph structure of the underlying residue interaction network of a backbone template to significantly accelerate the design process. Tests on real protein data show that our new protein design algorithm is able to solve many prob- lems that were previously unsolvable by the traditional exact search algorithms, and for the problems that can be solved with traditional provable algorithms, our new method can provide a large speedup by several orders of magnitude while still guaranteeing to find the global minimum energy conformation (GMEC) solution.

Progress in language and image understanding by machines has sparkled the interest of the research community in more open-ended, holistic tasks, and refueled an old AI dream of building intelligent machines. We discuss a few prominent challenges that characterize such holistic tasks and argue for "question answering about images" as a particular appealing instance of such a holistic task. In particular, we point out that it is a version of a Turing Test that is likely to be more robust to over-interpretations and contrast it with tasks like grounding and generation of descriptions. Finally, we discuss tools to measure progress in this field.

The production of renewable and sustainable energy is one of the most important challenges currently facing mankind. Wind has made an increasing contribution to the world's energy supply mix, but still remains a long way from reaching its full potential. In this paper, we investigate the use of artificial evolution to design vertical-axis wind turbine prototypes that are physically instantiated and evaluated under fan generated wind conditions. Initially a conventional evolutionary algorithm is used to explore the design space of a single wind turbine and later a cooperative coevolutionary algorithm is used to explore the design space of an array of wind turbines. Artificial neural networks are used throughout as surrogate models to assist learning and found to reduce the number of fabrications required to reach a higher aerodynamic efficiency. Unlike in other approaches, such as computational fluid dynamics simulations, no mathematical formulations are used and no model assumptions are made.