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Power System Parameters Forecasting Using Hilbert-Huang Transform and Machine Learning
Kurbatsky, Victor, Tomin, Nikita, Spiryaev, Vadim, Leahy, Paul, Sidorov, Denis, Zhukov, Alexei
A novel hybrid data-driven approach is developed for forecasting power system parameters with the goal of increasing the efficiency of short-term forecasting studies for non-stationary time-series. The proposed approach is based on mode decomposition and a feature analysis of initial retrospective data using the Hilbert-Huang transform and machine learning algorithms. The random forests and gradient boosting trees learning techniques were examined. The decision tree techniques were used to rank the importance of variables employed in the forecasting models. The Mean Decrease Gini index is employed as an impurity function. The resulting hybrid forecasting models employ the radial basis function neural network and support vector regression. Apart from introduction and references the paper is organized as follows. The section 2 presents the background and the review of several approaches for short-term forecasting of power system parameters. In the third section a hybrid machine learning-based algorithm using Hilbert-Huang transform is developed for short-term forecasting of power system parameters. Fourth section describes the decision tree learning algorithms used for the issue of variables importance. Finally in section six the experimental results in the following electric power problems are presented: active power flow forecasting, electricity price forecasting and for the wind speed and direction forecasting.
Data mining for censored time-to-event data: A Bayesian network model for predicting cardiovascular risk from electronic health record data
Bandyopadhyay, Sunayan, Wolfson, Julian, Vock, David M., Vazquez-Benitez, Gabriela, Adomavicius, Gediminas, Elidrisi, Mohamed, Johnson, Paul E., O'Connor, Patrick J.
Models for predicting the risk of cardiovascular events based on individual patient characteristics are important tools for managing patient care. Most current and commonly used risk prediction models have been built from carefully selected epidemiological cohorts. However, the homogeneity and limited size of such cohorts restricts the predictive power and generalizability of these risk models to other populations. Electronic health data (EHD) from large health care systems provide access to data on large, heterogeneous, and contemporaneous patient populations. The unique features and challenges of EHD, including missing risk factor information, non-linear relationships between risk factors and cardiovascular event outcomes, and differing effects from different patient subgroups, demand novel machine learning approaches to risk model development. In this paper, we present a machine learning approach based on Bayesian networks trained on EHD to predict the probability of having a cardiovascular event within five years. In such data, event status may be unknown for some individuals as the event time is right-censored due to disenrollment and incomplete follow-up. Since many traditional data mining methods are not well-suited for such data, we describe how to modify both modelling and assessment techniques to account for censored observation times. We show that our approach can lead to better predictive performance than the Cox proportional hazards model (i.e., a regression-based approach commonly used for censored, time-to-event data) or a Bayesian network with {\em{ad hoc}} approaches to right-censoring. Our techniques are motivated by and illustrated on data from a large U.S. Midwestern health care system.
A Naive Bayes machine learning approach to risk prediction using censored, time-to-event data
Wolfson, Julian, Bandyopadhyay, Sunayan, Elidrisi, Mohamed, Vazquez-Benitez, Gabriela, Musgrove, Donald, Adomavicius, Gediminas, Johnson, Paul, O'Connor, Patrick
Predicting an individual's risk of experiencing a future clinical outcome is a statistical task with important consequences for both practicing clinicians and public health experts. Modern observational databases such as electronic health records (EHRs) provide an alternative to the longitudinal cohort studies traditionally used to construct risk models, bringing with them both opportunities and challenges. Large sample sizes and detailed covariate histories enable the use of sophisticated machine learning techniques to uncover complex associations and interactions, but observational databases are often ``messy,'' with high levels of missing data and incomplete patient follow-up. In this paper, we propose an adaptation of the well-known Naive Bayes (NB) machine learning approach for classification to time-to-event outcomes subject to censoring. We compare the predictive performance of our method to the Cox proportional hazards model which is commonly used for risk prediction in healthcare populations, and illustrate its application to prediction of cardiovascular risk using an EHR dataset from a large Midwest integrated healthcare system.
Efficiency of conformalized ridge regression
Burnaev, Evgeny, Vovk, Vladimir
Conformal prediction is a method of producing prediction sets that can be applied on top of a wide range of prediction algorithms. The method has a guaranteed coverage probability under the standard IID assumption regardless of whether the assumptions (often considerably more restrictive) of the underlying algorithm are satisfied. However, for the method to be really useful it is desirable that in the case where the assumptions of the underlying algorithm are satisfied, the conformal predictor loses little in efficiency as compared with the underlying algorithm (whereas being a conformal predictor, it has the stronger guarantee of validity). In this paper we explore the degree to which this additional requirement of efficiency is satisfied in the case of Bayesian ridge regression; we find that asymptotically conformal prediction sets differ little from ridge regression prediction intervals when the standard Bayesian assumptions are satisfied.
A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection
Sabourin, Jeremy, Valdar, William, Nobel, Andrew
The analysis of high dimensional data, in which the number of measured predictors is large and can exceed the number of samples, is an important and common problem in statistical applications. When samples are accompanied by a real or categorical response, data analysis typically includes model fitting with the aim of doing prediction or variable selection, or both. The goal of prediction is to derive a rule capable of accurately predicting the response of a new, unlabeled sample. The goal of variable selection is to select a (small) subset of the measured predictors whose individual or coordinated activity is significantly related to the response. In both cases, it is common to assume that the observed data arise from an underlying model that is sparse, in the sense that only a small subset of the predictors are related to the response. Whether sparsity is assumed, or viewed as a desirable feature of a model, analysis of high dimensional data is often carried out by penalized methods that produce models in which a relatively small subset of the available predictors are included. Popular penalized methods include the LASSO (Tibshirani, 1996), its numerous variations, and SCAD (Fan and Li, 2001). In what follows, we focus our attention on the LASSO. The LASSO and its variants require specification of a penalty/tuning parameter that controls the tradeoff between model fit and model size.
Probabilistic Archetypal Analysis
Seth, Sohan, Eugster, Manuel J. A.
Archetypal analysis (AA) represents observations as composition of pure patterns, i.e., archetypes, or equivalently convex combinations of extreme values (Cutler and Breiman, 1994). Although AA bears resemblance with many well established prototypical analysis tools, such as principal component analysis (PCA, Mohamed et al, 2009), nonnegative matrix factorization (NMF, F evotte and Idier, 2011), probabilistic latent semantic analysis (Hofmann, 2013), andk -means (Steinley, 2006); AA is arguably unique, both conceptually and computationally . Conceptually, AA imitates the human tendency of representing a group of objects by its extreme elements (Davis and Love, 2010): this makes AA an interesting exploratory tool for applied scientists (e.g., Eugster, 2012; Seiler and Wohlrabe, 2013). Computationally, AA is data-driven, and requires the factors to be probability vectors: these make AA a computationally demanding tool, yet brings better interpretability . The concept of AA was originally formulated by Cutler and Breiman (1994).
Pseudo-Marginal Bayesian Inference for Gaussian Processes
Filippone, Maurizio, Girolami, Mark
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior. This is particularly important as it offers a powerful tool to carry out full Bayesian inference of Gaussian Process based hierarchic statistical models in general. The results also demonstrate that Monte Carlo based integration of all model parameters is actually feasible in this class of models providing a superior quantification of uncertainty in predictions. Extensive comparisons with respect to state-of-the-art probabilistic classifiers confirm this assertion.
Structural Intervention Distance (SID) for Evaluating Causal Graphs
Peters, Jonas, Bühlmann, Peter
Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) distance between DAGs, the structural intervention distance (SID). The SID is based on a graphical criterion only and quantifies the closeness between two DAGs in terms of their corresponding causal inference statements. It is therefore well-suited for evaluating graphs that are used for computing interventions. Instead of DAGs it is also possible to compare CPDAGs, completed partially directed acyclic graphs that represent Markov equivalence classes. Since it differs significantly from the popular Structural Hamming Distance (SHD), the SID constitutes a valuable additional measure. We discuss properties of this distance and provide an efficient implementation with software code available on the first author's homepage (an R package is under construction).
Inapproximability of Treewidth and Related Problems
Wu, Y., Austrin, P., Pitassi, T., Liu, D.
Graphical models, such as Bayesian Networks and Markov networks play an important role in artificial intelligence and machine learning. Inference is a central problem to be solved on these networks. This, and other problems on these graph models are often known to be hard to solve in general, but tractable on graphs with bounded Treewidth. Therefore, finding or approximating the Treewidth of a graph is a fundamental problem related to inference in graphical models. In this paper, we study the approximability of a number of graph problems: Treewidth and Pathwidth of graphs, Minimum Fill-In, One-Shot Black (and Black-White) pebbling costs of directed acyclic graphs, and a variety of different graph layout problems such as Minimum Cut Linear Arrangement and Interval Graph Completion. We show that, assuming the recently introduced Small Set Expansion Conjecture, all of these problems are NP-hard to approximate to within any constant factor in polynomial time.
AAAI Conferences Calendar
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