Foundational principles for large scale inference: Illustrations through correlation mining

When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset is often variable-rich but sample-starved: a regime where the number $n$ of acquired samples (statistical replicates) is far fewer than the number $p$ of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data." Sample complexity however has received relatively less attention, especially in the setting when the sample size $n$ is fixed, and the dimension $p$ grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. We demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks

Sparse Median Graphs Estimation in a High Dimensional Semiparametric Model

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected graphical structures. Utilizing the concept of median graphs in summarizing the commonality across these graphical structures, a novel semiparametric approach to modeling such complex aggregated data is provided along with robust estimation of the median graph, which is assumed to be sparse. The estimator is proved to be consistent in graph recovery and an upper bound on the rate of convergence is given. Experiments on both synthetic and real datasets are conducted to illustrate the empirical usefulness of the proposed models and methods

Blending Learning and Inference in Structured Prediction

In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional approaches, such as conditional random fields and structured support vector machines. For this purpose we utilize the structures of the predictors to describe a low dimensional structured prediction task which encourages local consistencies within the different structures while learning the parameters of the model. Convexity of the learning task provides the means to enforce the consistencies between the different parts. The inference-learning blending algorithm that we propose is guaranteed to converge to the optimum of the low dimensional primal and dual programs. Unlike many of the existing approaches, the inference-learning blending allows us to learn efficiently high-order graphical models, over regions of any size, and very large number of parameters. We demonstrate the effectiveness of our approach, while presenting state-of-the-art results in stereo estimation, semantic segmentation, shape reconstruction, and indoor scene understanding

Faithfulness and learning hypergraphs from discrete distributions

The concepts of faithfulness and strong-faithfulness are important for statistical learning of graphical models. Graphs are not sufficient for describing the association structure of a discrete distribution. Hypergraphs representing hierarchical log-linear models are considered instead, and the concept of parametric (strong-) faithfulness with respect to a hypergraph is introduced. Strong-faithfulness ensures the existence of uniformly consistent parameter estimators and enables building uniformly consistent procedures for a hypergraph search. The strength of association in a discrete distribution can be quantified with various measures, leading to different concepts of strong-faithfulness. Lower and upper bounds for the proportions of distributions that do not satisfy strong-faithfulness are computed for different parameterizations and measures of association.Comment: 23 pages, 6 figure

Analysis and design of multiagent systems using MAS-CommonKADS

This article proposes an agent-oriented methodology called MAS-CommonKADS and develops a case study. This methodology extends the knowledge engineering methodology CommonKADSwith techniquesfrom objectoriented and protocol engineering methodologies. The methodology consists of the development of seven models: Agent Model, that describes the characteristics of each agent; Task Model, that describes the tasks that the agents carry out; Expertise Model, that describes the knowledge needed by the agents to achieve their goals; Organisation Model, that describes the structural relationships between agents (software agents and/or human agents); Coordination Model, that describes the dynamic relationships between software agents; Communication Model, that describes the dynamic relationships between human agents and their respective personal assistant software agents; and Design Model, that refines the previous models and determines the most suitable agent architecture for each agent, and the requirements of the agent network

mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data

We present the R-package mgm for the estimation of k-order Mixed Graphical Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

A toolkit of mechanism and context independent widgets

Most human-computer interfaces are designed to run on a static platform (e.g. a workstation with a monitor) in a static environment (e.g. an office). However, with mobile devices becoming ubiquitous and capable of running applications similar to those found on static devices, it is no longer valid to design static interfaces. This paper describes a user-interface architecture which allows interactors to be flexible about the way they are presented. This flexibility is defined by the different input and output mechanisms used. An interactor may use different mechanisms depending upon their suitability in the current context, user preference and the resources available for presentation using that mechanism