High-Dimensional Dependency Structure Learning for Physical Processes

In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs (partial differential equations) and are observed in a variety of natural phenomena, including geoscience data capturing atmospheric and hydrological phenomena. Classical structure learning approaches such as the PC algorithm and variants are challenging to apply due to their high computational and sample requirements. Modern approaches, often based on sparse regression and variants, do come with finite sample guarantees, but are usually highly sensitive to the choice of hyper-parameters, e.g., parameter $\lambda$ for sparsity inducing constraint or regularization. In this paper, we present ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning, which estimates an edge specific parameter $\lambda_{ij}$ in the first step, and uses these parameters to learn the structure in the second step. Both steps of our algorithm use (inexact) ADMM to solve suitable linear programs, and all iterations can be done in closed form in an efficient block parallel manner. We compare ACLIME-ADMM with baselines on both synthetic data simulated by partial differential equations (PDEs) that model advection-diffusion processes, and real data (50 years) of daily global geopotential heights to study information flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and competitive, usually better than the baselines especially on difficult problems. On real data, ACLIME-ADMM recovers the underlying structure of global atmospheric circulation, including switches in wind directions at the equator and tropics entirely from the data.Comment: 21 pages, 8 figures, International Conference on Data Mining 201

Certainty Modeling of a Decision Support System for Mobile Monitoring of Exercise-induced Respiratory Conditions

Mobile health systems in recent times, have notably improved the healthcare sector by empowering patients to actively participate in their health, and by facilitating access to healthcare professionals. Effective operation of these mobile systems nonetheless, requires high level of intelligence and expertise implemented in the form of decision support systems (DSS). However, common challenges in the implementation include generalization and reliability, due to the dynamics and incompleteness of information presented to the inference models. In this paper, we advance the use of ad hoc mobile decision support system to monitor and detect triggers and early symptoms of respiratory distress provoked by strenuous physical exertion. The focus is on the application of certainty theory to model inexact reasoning by the mobile monitoring system. The aim is to develop a mobile tool to assist patients in managing their conditions, and to provide objective clinical data to aid physicians in the screening, diagnosis, and treatment of the respiratory ailments. We present the proposed model architecture and then describe an application scenario in a clinical setting. We also show implementation of an aspect of the system that enables patients in the self-management of their conditions

SAT Modulo the Theory of Linear Arithmetic: Exact, Inexact and Commercial Solvers

International audienceMany highly sophisticated tools exist for solving linear arith- metic optimization and feasibility problems. Here we analyze why it is difficult to use these tools inside systems for SAT Modulo Theories (SMT) for linear arithmetic: one needs support for disequalities, strict inequalities and, more importantly, for dealing with incorrect results due to the internal use of imprecise floating-point arithmetic. We explain how these problems can be overcome by means of result checking and error recovery policies. Second, by means of carefully designed experiments with, among other tools, the newest version of ILOG CPLEX and our own new Barcelogic T -solver for arithmetic, we show that, interestingly, the cost of result checking is only a small fraction of the total T -solver time. Third, we report on extensive experiments running exactly the same SMT search using CPLEX and Barcelogic as T -solvers, where CPLEX tends to be slower than Barcelogic. We analyze these at first sight surpris- ing results, explaining why tools such as CPLEX are not very adequate (nor designed) for this kind of relatively small incremental problems. Finally, we show how our result checking techniques can still be very use- ful in combination with inexact floating-point-based T -solvers designed for incremental SMT problems

A distributed primal-dual interior-point method for loosely coupled problems using ADMM

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of multipliers (ADMM) to compute the primal-dual directions at each iteration of the method. This enables us to join the exceptional convergence properties of primal-dual interior-point methods with the remarkable parallelizability of ADMM. The resulting algorithm has superior computational properties with respect to ADMM directly applied to our problem. The amount of computations that needs to be conducted by each computing agent is far less. In particular, the updates for all variables can be expressed in closed form, irrespective of the type of optimization problem. The most expensive computational burden of the algorithm occur in the updates of the primal variables and can be precomputed in each iteration of the interior-point method. We verify and compare our method to ADMM in numerical experiments.Comment: extended version, 50 pages, 9 figure

Quantum Computing for Dealing with Inaccurate Knowledge Related to the Certainty Factors Model

This article belongs to the Special Issue Advances in Quantum Artificial Intelligence and Machine Learning[Abstract] In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. In this context, a specific use case was built: an inferential network for testing the behaviour of the certainty factors approach in a quantum environment. After the design and execution of the experiments, the corresponding analysis of the obtained results was performed in three different scenarios: (1) inaccuracy in declarative knowledge, or imprecision, (2) inaccuracy in procedural knowledge, or uncertainty, and (3) inaccuracy in both declarative and procedural knowledge. This paper, as stated in the conclusions, is intended to pave the way for future quantum implementations of well-established methods for handling inaccurate knowledge.This work was supported by the European Union’s Horizon 2020 research and innovation programme under project NEASQC (grant agreement No. 951821) and by the Xunta de Galicia (grant ED431C 2018/34) with the European Union ERDF funds. We wish to acknowledge the support received from the Centro de Investigación de Galicia “CITIC”, funded by Xunta de Galicia and the European Union (European Regional Development Fund- Galicia 2014–2020 Program, grant ED431G 2019/01)Xunta de Galicia; ED431C 2018/34Xunta de Galicia; ED431G 2019/0

Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning