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A nested layered network model for parallel solutions of discrete SPPs

COMPUTERS & MATHEMATICS WITH APPLICATIONS 1997年第5期33卷 111-123页

作者： Joshi, RR Satyanarayana, DK INDIAN INST TECHNOL SCH BIOMED ENGNBOMBAY 400076MAHARASHTRAINDIA

A nested layered network mapping and algorithm is presented for parallel computational solutions of discrete stochastic programming problems with random coefficients. The algorithm is general purpose and efficiently implementable on multiprocessor systems with associative memory. Details of its implementation on a 64-CPU parallel computer and results are presented for a hard problem arising in antibody-inventory optimization in vitro. Performance is discussed along with scope vis-a-vis other general purpose efficient algorithms for discrete SPPs. Scope and Purpose: Many real world optimization problems require solutions of large scale discrete programming problems with random or uncertain coefficients and inputs. Computational difficulties arise owing to the involvement of multiple summations of large number of nonlinear mathematical terms which may not satisfy any common regularity condition within the range of summations. Parallel and associative memory based algorithms are currently in demand for solving such problems. A general purpose computing network design is presented here which contributes in the above direction. Parallel implementation and results are illustrated on a real-world problem of cost (energy) minimization.

关键词： neural network parallel computing probabilistic programming

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Modelling contextuality by probabilistic programs with hypergraph semantics

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THEORETICAL COMPUTER SCIENCE 2018年 752卷 56-70页

作者： Bruza, Peter D. Queensland Univ Technol Sch Informat Syst GPO Box 2434 Brisbane Qld 4001 Australia

Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of outcomes, can be defined independent of the measurement context. The phenomenon is deemed contextual when this assumption fails. Contextuality is an important issue in quantum physics. However, there has been growing speculation that it manifests outside the quantum realm with human cognition being a particularly prominent area of investigation. This article contributes the foundations of a probabilistic programming language that allows convenient exploration of contextuality in wide range of applications relevant to cognitive science and artificial intelligence. Using the style of syntax employed by the probabilistic programming language WebPPL, specific syntax is proposed to allow the specification of "measurement contexts". Each such context delivers a partial model of the phenomenon based on the associated experimental condition described by the measurement context. An important construct in the syntax determines if and how these partial models can be consistently combined into a single model of the phenomenon. The associated semantics are based on hypergraphs in two ways. Firstly, if the schema of random variables of the partial models is acyclic, a hypergraph approach from relational database theory is used to compute a join tree from which the partial models can be combined to form a single joint probability distribution. Secondly, if the schema is cyclic, measurement contexts are mapped to a hypergraph where edges correspond to sets of events denoting outcomes in measurement contexts. Recent theoretical results from the field of quantum physics show that contextuality can be equated with the possibility of constructing a probabilistic model on the resulting hypergraph. The use of hypergraphs opens the door for a theoreticall

关键词： probabilistic programming probabilistic modelling programming language semantics Contextuality

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A branch and bound method for stochastic integer problems under probabilistic constraints

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OPTIMIZATION METHODS & SOFTWARE 2002年第3期17卷 359-382页

作者： Beraldi, P Ruszczynski, A Rutgers State Univ Dept Management Sci & Informat Syst Piscataway NJ 08854 USA Rutgers State Univ RUTCOR Piscataway NJ 08854 USA Univ Calabria Dipartimento Elettron Informat & Sistemist I-87036 Arcavacata Di Rende Italy

Stochastic integer programming problems under probabilistic constraints are considered. Deterministic equivalent formulations of the original problem are obtained by using p -efficient points of the distribution function of the right hand side vector. A branch and bound solution method is proposed based on a partial enumeration of the set of these points. The numerical experience with the probabilistic lot-sizing problem shows the potential of the solution approach and the efficiency of the algorithms implemented.

关键词： stochastic integer programming probabilistic programming branch and bound

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Planning in hybrid relational MDPs

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MACHINE LEARNING 2017年第12期106卷 1905-1932页

作者： Nitti, Davide Belle, Vaishak De Laet, Tinne De Raedt, Luc Katholieke Univ Leuven Dept Comp Sci B-3001 Leuven Belgium Univ Edinburgh Sch Informat Edinburgh EH8 9AB Midlothian Scotland Katholieke Univ Leuven Fac Engn Sci B-3001 Leuven Belgium

We study planning in relational Markov decision processes involving discrete and continuous states and actions, and an unknown number of objects. This combination of hybrid relational domains has so far not received a lot of attention. While both relational and hybrid approaches have been studied separately, planning in such domains is still challenging and often requires restrictive assumptions and approximations. We propose HYPE: a sample-based planner for hybrid relational domains that combines model-based approaches with state abstraction. HYPE samples episodes and uses the previous episodes as well as the model to approximate the Q-function. In addition, abstraction is performed for each sampled episode, this removes the complexity of symbolic approaches for hybrid relational domains. In our empirical evaluations, we show that HYPE is a general and widely applicable planner in domains ranging from strictly discrete to strictly continuous to hybrid ones, handles intricacies such as unknown objects and relational models. Moreover, empirical results showed that abstraction provides significant improvements.

关键词： MDP probabilistic planning Logic programming Relational MDP Hybrid Hybrid relational MDP probabilistic programming Abstraction Logical regression Importance sampling

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CUQIpy: I. Computational uncertainty quantification for inverse problems in Python

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INVERSE PROBLEMS 2024年第4期40卷 045009-045009页

作者： Riis, Nicolai A. B. Alghamdi, Amal M. A. Uribe, Felipe Christensen, Silja L. Afkham, Babak M. Hansen, Per Christian Jorgensen, Jakob S. Tech Univ Denmark Dept Appl Math & Comp Sci Richard Petersens PladsBldg 324 DK-2800 Lyngby Denmark Lappeenranta Lahti Univ Technol LUT Sch Engn Sci Yliopistonkatu 34 Lappeenranta 53850 Finland Univ Manchester Dept Math Oxford Rd Alan Turing Bldg Manchester M13 9PL England Copenhagen Imaging ApS Herlev Denmark

This paper introduces CUQIpy, a versatile open-source Python package for computational uncertainty quantification (UQ) in inverse problems, presented as Part I of a two-part series. CUQIpy employs a Bayesian framework, integrating prior knowledge with observed data to produce posterior probability distributions that characterize the uncertainty in computed solutions to inverse problems. The package offers a high-level modeling framework with concise syntax, allowing users to easily specify their inverse problems, prior information, and statistical assumptions. CUQIpy supports a range of efficient sampling strategies and is designed to handle large-scale problems. Notably, the automatic sampler selection feature analyzes the problem structure and chooses a suitable sampler without user intervention, streamlining the process. With a selection of probability distributions, test problems, computational methods, and visualization tools, CUQIpy serves as a powerful, flexible, and adaptable tool for UQ in a wide selection of inverse problems. Part II of the series focuses on the use of CUQIpy for UQ in inverse problems with partial differential equations.

关键词： uncertainty quantification software computational imaging Bayesian statistics probabilistic programming

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Mastering uncertainty in performance estimations of configurable software systems

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EMPIRICAL SOFTWARE ENGINEERING 2023年第2期28卷 1-40页

作者： Dorn, Johannes Apel, Sven Siegmund, Norbert Univ Leipzig D-04109 Leipzig Germany Saarland Univ D-60041 Saarbrucken Germany Saarland Informat Campus D-60041 Saarbrucken Germany

Understanding the influence of configuration options on the performance of a software system is key for finding optimal system configurations, system understanding, and performance debugging. In the literature, a number of performance-influence modeling approaches have been proposed, which model a configuration option's influence and a configuration's performance as a scalar value. However, these point estimates falsely imply a certainty regarding an option's influence that neglects several sources of uncertainty within the assessment process, such as (1) measurement bias, choices of model representation and learning process, and incomplete data. This leads to the situation that different approaches and even different learning runs assign different scalar performance values to options and interactions among them. The true influence is uncertain, though. There is no way to quantify this uncertainty with state-of-the-art performance modeling *** propose a novel approach, P4, which is based on probabilistic programming, that explicitly models uncertainty for option influences and consequently provides a confidence interval for each prediction alongside a scalar. This way, we can explain, for the first time, why predictions may be erroneous and which option's influence may be unreliable. An evaluation on 13 real-world subject systems shows that P4's accuracy is in line with the state of the art while providing reliable confidence intervals, in addition to scalar predictions. We qualitatively explain how uncertain influences of individual options and interactions cause inaccurate predictions.

关键词： probabilistic programming Performance-influence modeling Configurable software systems Bayesian inference P4

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A GRADIENT ALGORITHM FOR CHANCE CONSTRAINED NONLINEAR GOAL programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1985年第3期22卷 359-369页

作者： LEE, SM OLSON, DL TEXAS A&M UNIV DEPT BUSINESS ANALCOLLEGE STNTX 77843

Decision environments involve high degrees of uncertainty as well as multiple, conflicting objectives. Often sampling information is available as a means of describing uncertainty. This description can be utilized in the form of chance constraints. Goal programming offers a means of considering multiple, conflicting objectives. A nonlinear goal programming algorithm is presented based upon the gradient method, utilizing an optimal step length for chance constrained goal programming models. The resulting algorithm requires assumptions of convex solution sets, differentiable and monotonic nonlinear constraints, and normally distributed variance of stochastic parameters. The algorithm is evaluated for generality, reliability, and precision; sensitivity to parameters and data; preparational and computational effort; and convergence. Model sensitivity to parameters is identified, as well as appropriate adjustment. The algorithm was found to require minimal preparational effort, favorable computation time, and rapid convergence to optimal solution with the exception of models containing high degrees of nonlinearity. [ABSTRACT FROM AUTHOR]

关键词： chance constrained programming goal programming gradient methods probabilistic programming

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Healthcare pathway discovery and probabilistic machine learning

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INTERNATIONAL JOURNAL OF MEDICAL INFORMATICS 2020年 137卷 104087-000页

作者： Kempa-Liehr, Andreas W. Lin, Christina Yin-Chieh Britten, Randall Armstrong, Delwyn Wallace, Jonathan Mordaunt, Dylan O'Sullivan, Michael Univ Auckland Dept Engn Sci 70 Symonds St Auckland New Zealand Auckland Dist Hlth Board 2 Pk Rd Auckland New Zealand Orion Hlth 181 Grafton Rd Auckland New Zealand Waitemata Dist Hlth Board 124 Shakespeare Rd Auckland New Zealand Univ Adelaide Adelaide SA Australia Flinders Univ S Australia Adelaide SA Australia

Background and purpose: Healthcare pathways define the execution sequence of clinical activities as patients move through a treatment process, and they are critical for maintaining quality of care. The aim of this study is to combine healthcare pathway discovery with predictive models of individualized recovery times. The pathway discovery has a particular emphasis on producing pathway models that are easy to interpret for clinicians without a sufficient background in process mining. The predictive model takes the stochastic volatility of pathway performance indicators into account. Method: This study utilizes the business process-mining software ProM to design a process mining pipeline for healthcare pathway discovery and enrichment using hospital records. The efficacy of combining learned healthcare pathways with probabilistic machine learning models is demonstrated via a case study that applies the proposed process mining pipeline to discover appendicitis pathways from hospital records. Machine learning methodologies based on probabilistic programming are utilized to explore pathway features that influence patient recovery time. Results: The produced appendicitis pathway models are easy for clinical interpretation and provide an unbiased overview of patient movements through the treatment process. Analysis of the discovered pathway model enables reasons for longer than usual treatment times to be explored and deviations from standard treatment pathways to be identified. A probabilistic regression model that estimates patient recovery time based on the information extracted by the process mining pipeline is developed and has the potential to be very useful for hospital scheduling purposes. Conclusion: This study establishes the application of the business process modelling tool ProM for the improvement of healthcare pathway mining methods. The proposed pipeline for healthcare pathway discovery has the potential to support the development of probabilistic machine l

关键词： Healthcare pathway Process mining Electronic health record probabilistic programming

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Bayesian Convolutional Neural Networks in Medical Imaging Classification: A Promising Solution for Deep Learning Limits in Data Scarcity Scenarios

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JOURNAL OF DIGITAL IMAGING 2023年第6期36卷 2567-2577页

作者： Bargagna, Filippo De Santi, Lisa Anita Martini, Nicola Genovesi, Dario Favilli, Brunella Vergaro, Giuseppe Emdin, Michele Giorgetti, Assuero Positano, Vincenzo Santarelli, Maria Filomena Univ Pisa Pisa Italy Fdn G Monasterio CNR Reg Toscana Pisa Italy Scuola Univ Super S Anna Pisa Italy CNR Inst Clin Physiol Pisa Italy

Deep neural networks (DNNs) have already impacted the field of medicine in data analysis, classification, and image processing. Unfortunately, their performance is drastically reduced when datasets are scarce in nature (e.g., rare diseases or early-research data). In such scenarios, DNNs display poor capacity for generalization and often lead to highly biased estimates and silent failures. Moreover, deterministic systems cannot provide epistemic uncertainty, a key component to asserting the model's reliability. In this work, we developed a probabilistic system for classification as a framework for addressing the aforementioned criticalities. Specifically, we implemented a Bayesian convolutional neural network (BCNN) for the classification of cardiac amyloidosis (CA) subtypes. We prepared four different CNNs: base-deterministic, dropout-deterministic, dropout-Bayesian, and Bayesian. We then trained them on a dataset of 1107 PET images from 47 CA and control patients (data scarcity scenario). The Bayesian model achieved performances (78.28 (1.99) % test accuracy) comparable to the base-deterministic, dropout-deterministic, and dropout-Bayesian ones, while showing strongly increased "Out of Distribution" input detection (validation-test accuracy mismatch reduction). Additionally, both the dropout-Bayesian and the Bayesian models enriched the classification through confidence estimates, while reducing the criticalities of the dropout-deterministic and base-deterministic approaches. This in turn increased the model's reliability, also providing much needed insights into the network's estimates. The obtained results suggest that a Bayesian CNN can be a promising solution for addressing the challenges posed by data scarcity in medical imaging classification tasks.

关键词： Bayesian convolutional neural networks Cardiac amyloidosis Data scarcity probabilistic programming Uncertainty Deep learning

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Computation of a multi-objective production planning model with probabilistic constraints

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2009年第1期86卷 185-198页

作者： Sahoo, N. P. Biswal, M. P. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In this paper, a multi-objective production planning model has been presented for a captive plant. The model includes multi-products, multi-plants, and multi-objective with some probabilistic constraints. The probabilistic constraints have been transformed into deterministic constraints assuming the parameters as independent normal random variables. The deterministic problem has been computed with two different methods, namely weighting method and fuzzy programming method. Finally, the integral solution obtained by these two methods have been compared.

关键词： captive plants production planning probabilistic programming multi-objective model non-linear programming weighting method fuzzy programming method and integral solution

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