Noisy Hamiltonian Monte Carlo for doubly-intractable distributions

Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented state space with transitions based on a deterministic differential flow derived from Hamiltonian mechanics. In practice, the evolution of Hamiltonian systems cannot be solved analytically, requiring numerical integration schemes. Under numerical integration, the resulting approximate solution no longer preserves the measure of the target distribution, therefore an accept-reject step is used to correct the bias. For doubly-intractable distributions -- such as posterior distributions based on Gibbs random fields -- HMC suffers from some computational difficulties: computation of gradients in the differential flow and computation of the accept-reject proposals poses difficulty. In this paper, we study the behaviour of HMC when these quantities are replaced by Monte Carlo estimates

Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model

We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.Comment: 10 figure

Visual Representation Learning with Limited Supervision

The quality of a Computer Vision system is proportional to the rigor of data representation it is built upon. Learning expressive representations of images is therefore the centerpiece to almost every computer vision application, including image search, object detection and classification, human re-identification, object tracking, pose understanding, image-to-image translation, and embodied agent navigation to name a few. Deep Neural Networks are most often seen among the modern methods of representation learning. The limitation is, however, that deep representation learning methods require extremely large amounts of manually labeled data for training. Clearly, annotating vast amounts of images for various environments is infeasible due to cost and time constraints. This requirement of obtaining labeled data is a prime restriction regarding pace of the development of visual recognition systems. In order to cope with the exponentially growing amounts of visual data generated daily, machine learning algorithms have to at least strive to scale at a similar rate. The second challenge consists in the learned representations having to generalize to novel objects, classes, environments and tasks in order to accommodate to the diversity of the visual world. Despite the evergrowing number of recent publications tangentially addressing the topic of learning generalizable representations, efficient generalization is yet to be achieved. This dissertation attempts to tackle the problem of learning visual representations that can generalize to novel settings while requiring few labeled examples. In this research, we study the limitations of the existing supervised representation learning approaches and propose a framework that improves the generalization of learned features by exploiting visual similarities between images which are not captured by provided manual annotations. Furthermore, to mitigate the common requirement of large scale manually annotated datasets, we propose several approaches that can learn expressive representations without human-attributed labels, in a self-supervised fashion, by grouping highly-similar samples into surrogate classes based on progressively learned representations. The development of computer vision as science is preconditioned upon the seamless ability of a machine to record and disentangle pictures' attributes that were expected to only be conceived by humans. As such, particular interest was dedicated to the ability to analyze the means of artistic expression and style which depicts a more complex task than merely breaking an image down to colors and pixels. The ultimate test for this ability is the task of style transfer which involves altering the style of an image while keeping its content. An effective solution of style transfer requires learning such image representation which would allow disentangling image style and its content. Moreover, particular artistic styles come with idiosyncrasies that affect which content details should be preserved and which discarded. Another pitfall here is that it is impossible to get pixel-wise annotations of style and how the style should be altered. We address this problem by proposing an unsupervised approach that enables encoding the image content in such a way that is required by a particular style. The proposed approach exchanges the style of an input image by first extracting the content representation in a style-aware way and then rendering it in a new style using a style-specific decoder network, achieving compelling results in image and video stylization. Finally, we combine supervised and self-supervised representation learning techniques for the task of human and animals pose understanding. The proposed method enables transfer of the representation learned for recognition of human poses to proximal mammal species without using labeled animal images. This approach is not limited to dense pose estimation and could potentially enable autonomous agents from robots to self-driving cars to retrain themselves and adapt to novel environments based on learning from previous experiences

Cascades on clique-based graphs

peer-reviewedWe present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.PUBLISHEDpeer-reviewe

Coalitions, tipping points and the speed of evolution

This study considers pure coordination games on networks and the waiting time for an adaptive process of strategic change to achieve efficient coordination. Although it is in the interest of every player to coordinate on a single globally efficient norm, coalitional behavior at a local level can greatly slow, as well as hasten convergence to efficiency. For some networks, when one action becomes efficient enough relative to the other, the effect of coalitional behavior changes abruptly from a conservative effect to a reforming effect. These effects are confirmed for a variety of stylized and empirical social networks found in the literature. For coordination games in which the Pareto efficient and risk dominant equilibria differ, polymorphic states can be the only stochastically stable states