5,854 research outputs found
Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena
Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is
further complicated by many theoretical issues, such as the I-equivalence among
different structures. In this work, we focus on a specific subclass of BNs,
named Suppes-Bayes Causal Networks (SBCNs), which include specific structural
constraints based on Suppes' probabilistic causation to efficiently model
cumulative phenomena. Here we compare the performance, via extensive
simulations, of various state-of-the-art search strategies, such as local
search techniques and Genetic Algorithms, as well as of distinct regularization
methods. The assessment is performed on a large number of simulated datasets
from topologies with distinct levels of complexity, various sample size and
different rates of errors in the data. Among the main results, we show that the
introduction of Suppes' constraints dramatically improve the inference
accuracy, by reducing the solution space and providing a temporal ordering on
the variables. We also report on trade-offs among different search techniques
that can be efficiently employed in distinct experimental settings. This
manuscript is an extended version of the paper "Structural Learning of
Probabilistic Graphical Models of Cumulative Phenomena" presented at the 2018
International Conference on Computational Science
Reliability-based economic model predictive control for generalized flow-based networks including actuators' health-aware capabilities
This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalized flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamically allocate safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the considered case study.Peer ReviewedPostprint (author's final draft
A Novel Deep Knowledge-based Learning Method for Wind Speed Forecast
The increasing installation rate of wind power poses great challenges to the
global power system. In order to ensure the reliable operation of the power
system, it is necessary to accurately forecast the wind speed and power of the
wind turbines. At present, deep learning is progressively applied to the wind
speed prediction. Nevertheless, the recent deep learning methods still reflect
the embarrassment for practical applications due to model interpretability and
hardware limitation. To this end, a novel deep knowledge-based learning method
is proposed in this paper. The proposed method hybridizes pre-training method
and auto-encoder structure to improve data representation and modeling of the
deep knowledge-based learning framework. In order to form knowledge and
corresponding absorbers, the original data is preprocessed by an optimization
model based on correlation to construct multi-layer networks (knowledge) which
are absorbed by sequence to sequence (Seq2Seq) models. Specifically, new
cognition and memory units (CMU) are designed to reinforce traditional deep
learning framework. Finally, the effectiveness of the proposed method is
verified by three wind prediction cases from a wind farm in Liaoning, China.
Experimental results show that the proposed method increases the stability and
training efficiency compared to the traditional LSTM method and LSTM/GRU-based
Seq2Seq method for applications of wind speed forecasting
Linear dimensionality reduction: Survey, insights, and generalizations
Linear dimensionality reduction methods are a cornerstone of analyzing high
dimensional data, due to their simple geometric interpretations and typically
attractive computational properties. These methods capture many data features
of interest, such as covariance, dynamical structure, correlation between data
sets, input-output relationships, and margin between data classes. Methods have
been developed with a variety of names and motivations in many fields, and
perhaps as a result the connections between all these methods have not been
highlighted. Here we survey methods from this disparate literature as
optimization programs over matrix manifolds. We discuss principal component
analysis, factor analysis, linear multidimensional scaling, Fisher's linear
discriminant analysis, canonical correlations analysis, maximum autocorrelation
factors, slow feature analysis, sufficient dimensionality reduction,
undercomplete independent component analysis, linear regression, distance
metric learning, and more. This optimization framework gives insight to some
rarely discussed shortcomings of well-known methods, such as the suboptimality
of certain eigenvector solutions. Modern techniques for optimization over
matrix manifolds enable a generic linear dimensionality reduction solver, which
accepts as input data and an objective to be optimized, and returns, as output,
an optimal low-dimensional projection of the data. This simple optimization
framework further allows straightforward generalizations and novel variants of
classical methods, which we demonstrate here by creating an
orthogonal-projection canonical correlations analysis. More broadly, this
survey and generic solver suggest that linear dimensionality reduction can move
toward becoming a blackbox, objective-agnostic numerical technology.JPC and ZG received funding from the UK Engineering and Physical Sciences Research Council (EPSRC EP/H019472/1). JPC received funding from a Sloan Research Fellowship, the Simons Foundation (SCGB#325171 and SCGB#325233), the Grossman Center at Columbia University, and the Gatsby Charitable Trust.This is the author accepted manuscript. The final version is available from MIT Press via http://jmlr.org/papers/v16/cunningham15a.htm
Workload-Aware Materialization of Junction Trees
Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in the data. However, exact inference in Bayesian networks is NP-hard, which has prompted the development of many practical inference methods. In this paper, we focus on improving the performance of the junction-tree algorithm, a well-known method for exact inference in Bayesian networks. In particular, we seek to leverage information in the workload of probabilistic queries to obtain an optimal workload-aware materialization of junction trees, with the aim to accelerate the processing of inference queries. We devise an optimal pseudo-polynomial algorithm to tackle this problem and discuss approximation schemes. Compared to state-of-the-art approaches for efficient processing of inference queries via junction trees, our methods are the first to exploit the information provided in query workloads. Our experimentation on several real-world Bayesian networks confirms the effectiveness of our techniques in speeding-up query processing.Peer reviewe
Networking - A Statistical Physics Perspective
Efficient networking has a substantial economic and societal impact in a
broad range of areas including transportation systems, wired and wireless
communications and a range of Internet applications. As transportation and
communication networks become increasingly more complex, the ever increasing
demand for congestion control, higher traffic capacity, quality of service,
robustness and reduced energy consumption require new tools and methods to meet
these conflicting requirements. The new methodology should serve for gaining
better understanding of the properties of networking systems at the macroscopic
level, as well as for the development of new principled optimization and
management algorithms at the microscopic level. Methods of statistical physics
seem best placed to provide new approaches as they have been developed
specifically to deal with non-linear large scale systems. This paper aims at
presenting an overview of tools and methods that have been developed within the
statistical physics community and that can be readily applied to address the
emerging problems in networking. These include diffusion processes, methods
from disordered systems and polymer physics, probabilistic inference, which
have direct relevance to network routing, file and frequency distribution, the
exploration of network structures and vulnerability, and various other
practical networking applications.Comment: (Review article) 71 pages, 14 figure
A data-driven and risk-based prudential approach to validate the DDMRP planning and control system
In this paper, we study the single-item dynamic lot-sizing problem in an environment characterized by stochastic demand and lead times. A recent heuristic called Demand Driven MRP, widely implemented using modern ERP systems, proposes an algorithm that is will effectively tackle this problem. Our primary goal is to propose a theoretical foundation for such a heuristic approach. To this aim, we develop an optimization model inspired by the main principles behind the heuristic algorithm. Specifically, controls are of the type (s(t), S(t)) with time varying thresholds that react to short-run real orders; in this respect, control is risk-based and data-driven. We also consider service levels derived as tail risk measures to ensure fulfillment of realized demand with a predetermined probability; in this respect, our approach is prudential. Finally, we use our model as a benchmark to theoretically validate and contextualize the aforementioned heuristic
Lp-Based Artificial Dependency for Probabilistic Etail Order Fulfillment
We consider an online multi-item retailer with multiple fulfillment facilities and finite inventory, with the objective of minimizing the expected shipping cost of fulfilling customer orders over a finite horizon. We approximate the stochastic dynamic programming formulation of the problem with an equivalent deterministic linear program, which we use to develop a probabilistic fulfillment heuristic that is provably optimal in the asymptotic sense. This first heuristic, however, relies on solving an LP that is exponential in the size of the input. Therefore, we subsequently provide another heuristic which solves an LP that is polynomial in the size of the input, and prove an upper bound on its asymptotic competitive ratio. This heuristic works by modifying the LP solution with artificial dependencies, with the resulting fractional variables used to probabilistically fulfill orders. A hardness result shows that asymptotically optimal policies that are computationally efficient cannot exist. Finally, we conduct numerical experiments that show that our heuristic's performance is very close to optimal for a range of parameters.http://deepblue.lib.umich.edu/bitstream/2027.42/108712/1/1250_ASinha.pd
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