Nearly-Isotonic Regression

Tibshirani, Ryan J.; Hoefling, Hölger; Tibshirani, Robert

doi:10.1198/tech.2010.10111

Cited by 101 publications

(110 citation statements)

References 18 publications

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“…where λ is the tuning parameter on the sum of absolute values for the coe cients |β j | (Tibshirani, 1996). Larger values for λ provide more regularization, whereas λ = 0 results in a nonpenalized model.…”

Section: Gaussian Graphical Modelmentioning

confidence: 99%

Back to the Basics: Rethinking Partial Correlation Network Methodology

Williams¹,

Rast²

2018

Preprint

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Gaussian graphical models are an increasingly popular technique in psychology to characterize relationships among observed variables. These relationships are represented as covariances in the precision matrix. Standardizing this covariance matrix and reversing the sign yields corresponding partial correlations that imply pairwise dependencies in which the e ects of all other variables have been controlled for. In order to estimate the precision matrix, the graphical lasso (glasso) has emerged as the default estimation method, which uses 1 -based regularization. Glasso was developed and optimized for high dimensional settings where the number of variables (p) exceeds the number of observations (n) which are uncommon in psychological applications. Here we propose to go "back to the basics", wherein the precision matrix is rst estimated with non-regularized maximum likelihood and then Fisher Z-transformed con dence intervals are used to determine non-zero relationships. We rst show the exact correspondence between the con dence level and speci city, which is due to 1 -speci city denoting the false positive rate (i.e., α). With simulations in low-dimensional settings (p n), we then demonstrate superior performance compared to glasso for determining conditional relationships, in addition to frequentist risk measured with various loss functions. Further, our results indicate that glasso is inconsistent for the purpose of model selection, whereas the proposed method converged on the true model with a probability that approached 100%. We end by discussing implications for estimating Gaussian graphical models in psychology.

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Section: Gaussian Graphical Modelmentioning

confidence: 99%

Back to the Basics: Rethinking Partial Correlation Network Methodology

Williams¹,

Rast²

2018

Preprint

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“…By recognizing the constraints as block-simplex constraints, we apply a standard equality constraint elimination technique (Boyd and Vandenberghe, 2004, Section 4.2.4) with a particular change of variables to convert the non-negativity constraints on the variables into ordering constraints. In the new space induced by the change of variables, we show that the projection on the feasible set (characterized by the ordering constraints) can be performed in linear time via bounded isotonic regression (see (Tibshirani et al, 2011) for a short survey on isotonic regression), where n is the number of routes per OD pair. This is an improvement over the O n log n ð Þtime required by the projection onto the simplex Wang and Carreira-Perpin, 2013).…”

Section: Contributions Of This Articlementioning

confidence: 99%

Cellpath: Fusion of cellular and traffic sensor data for route flow estimation via convex optimization

Thai

Yadlowsky

et al. 2015

Transportation Research Part C: Emerging Technologies

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a b s t r a c tA new convex optimization framework is developed for the route flow estimation problem from the fusion of vehicle count and cellular network data. The issue of highly underdetermined link flow based methods in transportation networks is investigated, then solved using the proposed concept of cellpaths for cellular network data. With this data-driven approach, our proposed approach is versatile: it is compatible with other data sources, and it is model agnostic and thus compatible with user equilibrium, system-optimum, Stackelberg concepts, and other models. Using a dimensionality reduction scheme, we design a projected gradient algorithm suitable for the proposed route flow estimation problem. The algorithm solves a block isotonic regression problem in the projection step in linear time. The accuracy, computational efficiency, and versatility of the proposed approach are validated on the I-210 corridor near Los Angeles, where we achieve 90% route flow accuracy with 1033 traffic sensors and 1000 cellular towers covering a large network of highways and arterials with more than 20,000 links. In contrast to long-term land use planning applications, we demonstrate the first system to our knowledge that can produce route-level flow estimates suitable for short time horizon prediction and control applications in traffic management. Our system is open source and available for validation and extension.

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“…Consider the special case of the problem (8) such that the expert estimations of the objects y 0 are linearly scaled and the expert estimations of the criteria weights are ordinalscaled. In this case, the problem can be formulated in the terms of the wellknown isotonic regression problem [15,16]. Let w = X + y 0 .…”

Section: The Algorithm Of Minimizing Distance Between Vectors In Conesmentioning

confidence: 99%