Normal Factor Graphs as Probabilistic Models

We present a new probabilistic modelling framework based on the recent notion of normal factor graph (NFG). We show that the proposed NFG models and their transformations unify some existing models such as factor graphs, convolutional factor graphs, and cumulative distribution networks. The two subclasses of the NFG models, namely the constrained and generative models, exhibit a duality in their dependence structure. Transformation of NFG models further extends the power of this modelling framework. We point out the well-known NFG representations of parity and generator realizations of a linear code as generative and constrained models, and comment on a more prevailing duality in this context. Finally, we address the algorithmic aspect of computing the exterior function of NFGs and the inference problem on NFGs

A Dynamic and Incentive Policy for Selecting D2D Mobile Relays

User-to-network relaying enabled via Device-to-Device (D2D) communications is a promising technique for improving the performance of cellular networks. Since in practice relays are in mobility, a dynamic relay selection scheme is unavoidable. In this paper, we propose a dynamic relay selection policy that maximizes the performance of cellular networks (e.g. throughput, reliability, coverage) under cost constraints (e.g. transmission power, power budget). We represent the relays' dynamics as a Markov Decision Process (MDP) and assume that only the locations of the selected relays are observable. Therefore, the dynamic relay selection process is modeled as a Constrained Partially Observable Markov Decision Process (CPOMDP). Since the exact solution of such framework is intractable to find, we develop a point-based value iteration solution and evaluate its performance. In addition, we prove the submodularity property of both the reward and cost value functions and deduce a greedy solution which is scalable with the number of discovered relays. For the muti-user scenario, a distributed approach is introduced in order to reduce the complexity and the overhead of the proposed solution. We illustrate the numerical results of the scenario where throughput is maximized under energy constraint and evaluate the gain that the proposed relay selection policy achieves compared to a traditional cellular network

Modeling Social Networks with Node Attributes using the Multiplicative Attribute Graph Model

Networks arising from social, technological and natural domains exhibit rich connectivity patterns and nodes in such networks are often labeled with attributes or features. We address the question of modeling the structure of networks where nodes have attribute information. We present a Multiplicative Attribute Graph (MAG) model that considers nodes with categorical attributes and models the probability of an edge as the product of individual attribute link formation affinities. We develop a scalable variational expectation maximization parameter estimation method. Experiments show that MAG model reliably captures network connectivity as well as provides insights into how different attributes shape the network structure.Comment: 15 pages, 7 figures, 7 table

Critical Network Cascades with Re-excitable nodes: Why tree-like approximations usually work, when they breakdown, and how to correct them

Network science is a rapidly expanding field, with a large and growing body of work on network-based dynamical processes. Most theoretical results in this area rely on the so-called \emph{locally tree-like approximation}. This is, however, usually an `uncontrolled' approximation, in the sense that the magnitudes of the error are typically unknown, although numerical results show that this error is often surprisingly small. In this paper, we place this approximation on more rigorous footing by calculating the magnitude of deviations away from tree-based theories in the context of discrete-time critical network cascades with re-excitable nodes. We discuss the conditions under which tree-like approximations give good results for calculating network criticality, and also explain the reasons for deviation from this approximation, in terms of the density of certain kinds of network motifs. Using this understanding, we derive results for network criticality that apply to general networks that explicitly do not satisfy the locally tree-like approximation. In particular, we focus on the bi-parallel motif, the smallest motif relevant to the failure of a tree-based theory in this context, and we derive the corrections due to such motifs on the conditions for criticality. We verify our claims on computer-generated networks, and we confirm that our theory accurately predicts the observed deviations from criticality. Using our theory, we explain why numerical simulations often show that deviations from a tree-based theory are surprisingly small. More specifically, we show that these deviations are negligible for networks whose average degree is even modestly large compared to one, justifying why tree-based theories appear to work well for most real-world networks.Comment: 22 pages, 8 figure

Neural Likelihoods via Cumulative Distribution Functions

We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response variables and then to parameters of this CDF representation, we are able to build black box CDF and density estimators. A suite of families is introduced as alternative constructions for the multivariate case. At one extreme, the simplest construction is a competitive density estimator against state-of-the-art deep learning methods, although it does not provide an easily computable representation of multivariate CDFs. At the other extreme, we have a flexible construction from which multivariate CDF evaluations and marginalizations can be obtained by a simple forward pass in a deep neural net, but where the computation of the likelihood scales exponentially with dimensionality. Alternatives in between the extremes are discussed. We evaluate the different representations empirically on a variety of tasks involving tail area probabilities, tail dependence and (partial) density estimation.Comment: 10 page

Enhancing approximation abilities of neural networks by training derivatives

A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several orders and uses this information in gradient based training. Forward pass calculates not only the values of the output layer of a network but also their derivatives. The deviations of those derivatives from the target ones are used in an extended cost function and then backward pass calculates the gradient of the extended cost with respect to weights, which can then be used by any weights update algorithm. Despite a substantial increase in arithmetic operations per pattern (if compared to the conventional training), the extended cost allows to obtain 140--1000 times more accurate approximation for simple cases if the total number of operations is equal. This precision also happens to be out of reach for the regular cost function. The method fits well into the procedure of solving differential equations with neural networks. Unlike training a network to match some target mapping, which requires an explicit use of the target derivatives in the extended cost function, the cost function for solving a differential equation is based on the deviation of the equation's residual from zero and thus can be extended by differentiating the equation itself, which does not require any prior knowledge. Solving an equation with such a cost resulted in 13 times more accurate result and could be done with 3 times larger grid step. GPU-efficient algorithm for calculating the gradient of the extended cost function is proposed

A Dynamical System for PageRank with Time-Dependent Teleportation

We propose a dynamical system that captures changes to the network centrality of nodes as external interest in those nodes vary. We derive this system by adding time-dependent teleportation to the PageRank score. The result is not a single set of importance scores, but rather a time-dependent set. These can be converted into ranked lists in a variety of ways, for instance, by taking the largest change in the importance score. For an interesting class of the dynamic teleportation functions, we derive closed form solutions for the dynamic PageRank vector. The magnitude of the deviation from a static PageRank vector is given by a PageRank problem with complex-valued teleportation parameters. Moreover, these dynamical systems are easy to evaluate. We demonstrate the utility of dynamic teleportation on both the article graph of Wikipedia, where the external interest information is given by the number of hourly visitors to each page, and the Twitter social network, where external interest is the number of tweets per month. For these problems, we show that using information from the dynamical system helps improve a prediction task and identify trends in the data.Comment: arXiv admin note: substantial text overlap with arXiv:1203.609

Learning and inference in knowledge-based probabilistic model for medical diagnosis

Based on a weighted knowledge graph to represent first-order knowledge and combining it with a probabilistic model, we propose a methodology for the creation of a medical knowledge network (MKN) in medical diagnosis. When a set of symptoms is activated for a specific patient, we can generate a ground medical knowledge network composed of symptom nodes and potential disease nodes. By Incorporating a Boltzmann machine into the potential function of a Markov network, we investigated the joint probability distribution of the MKN. In order to deal with numerical symptoms, a multivariate inference model is presented that uses conditional probability. In addition, the weights for the knowledge graph were efficiently learned from manually annotated Chinese Electronic Medical Records (CEMRs). In our experiments, we found numerically that the optimum choice of the quality of disease node and the expression of symptom variable can improve the effectiveness of medical diagnosis. Our experimental results comparing a Markov logic network and the logistic regression algorithm on an actual CEMR database indicate that our method holds promise and that MKN can facilitate studies of intelligent diagnosis.Comment: 32 pages, 8 figure

Network Reliability: The effect of local network structure on diffusive processes

This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is well-suited for estimation by distributed simulation. We describe a collection of graphs derived from Erd\H{o}s-R\'enyi and scale-free-like random graphs in which we have manipulated assortativity-by-degree and the number of triangles. We evaluate the network reliability for all these graphs under a reliability rule that is related to the expected size of a connected component. Through these extensive simulations, we show that for positively or neutrally assortative graphs, swapping edges to increase the number of triangles does not increase the network reliability. Also, positively assortative graphs are more reliable than neutral or disassortative graphs with the same number of edges. Moreover, we show the combined effect of both assortativity-by-degree and the presence of triangles on the critical point and the size of the smallest subgraph that is reliable.Comment: 12 pages, 8 figures, 1 tabl

Classification-based Financial Markets Prediction using Deep Neural Networks

Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et al., 2012) for their superior predictive properties including robustness to overfitting. However their application to algorithmic trading has not been previously researched, partly because of their computational complexity. This paper describes the application of DNNs to predicting financial market movement directions. In particular we describe the configuration and training approach and then demonstrate their application to backtesting a simple trading strategy over 43 different Commodity and FX future mid-prices at 5-minute intervals. All results in this paper are generated using a C++ implementation on the Intel Xeon Phi co-processor which is 11.4x faster than the serial version and a Python strategy backtesting environment both of which are available as open source code written by the authors