Statistical inference under order restrictions : the theory and application of isotonic regression

By H. D. Brunk, R. Barlow, David J. Bartholomew, J. M. Bremner. 1973

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In Statistics and Probability

Citations in the corpus

UNICORN on RAINBOW: A Universal Commonsense Reasoning Model on a New Multitask Benchmark (2021, methodology): “Since the cost and beneﬁt share a monotonic relationship, we estimate the cost-beneﬁt trade-offs using isotonic regression (Barlow et al. 1972).”
Convex-constrained Sparse Additive Modeling and Its Extensions (2017, methodology): “ descent) algorithm for solving (3) while ignoring the centering constraint zj 2 H : in each step, all components except for one zj are xed, and the well-known pool-adjacent-violators (PAV) algorithm [BBBB72] is applied to optimize zj under the isotonic constraint I . Oracle property of the backttin”
Obtaining Well Calibrated Probabilities Using Bayesian Binning (2015, methodology): “A commonly used method for computing the isotonic regression is pool adjacent violators (PAV) algorithm (Barlow et al. 1972).”
Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals (2018, background): “1000). These qualities are different than the popular constrained machine learning problem of shape constraints, which may entail adding constraints to training to make the model monotonic (see e.g. (Barlow et al., 1972; Groeneboom and Jongbloed, 2014; Gupta et al., 2016; Canini et al., 2016; Luss a”
Monotonic Calibrated Interpolated Look-Up Tables (2015, background): “d close to the original labels. These monotonically re-labeled samples can then be used, for example, to dene a monotonic piecewise constant or piecewise linear surface. This is an old approach; see Barlow et al. (1972) for an early survey. Isotonic regression can be solved in O(n) time if monotonic”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “sotonic regression has several applications in machine learning and statistics, where these monotonic constraints arerelevant, for example in genetics [138], biology [176], medicine [186], statistics [17] and multidimensional scaling for psychology applications [128]. See an example for the linear o”
Score estimation in the monotone single‐index model (2017, background): “This result, which goes back to Brillinger (1983), can be extended to any elliptically symmetric distribution, a fact that has been exploited by Duan and Li (1991) in inverse regression.”
1 Trend Filtering (2009, background): “Minimizing (5) subject to this monotonicity constraint is an extension of isotonic regression, which has been extensively studied in statistics [3, 82].”
Using the Gene Ontology Hierarchy when Predicting Gene Function (2009, background): “, xd], xc ∈ <, IR (Barlow et al., 1972) solves the following problem:”
Fine-Grained Car Detection for Visual Census Estimation (2017, methodology): “s a learned weight on the location prior. This improves detection AP by 1.92 at a negligible time cost. During analysis, DPM scores are converted into estimated probabilities via isotonic regression (Barlow et al. 1972), learned on the validation set. The ﬁnal output of the detection step provides u”
Estimating a Convex Function in Nonparametric Regression (2007, methodology): “Much effort has been spent on the problem of estimating a monotone regression function using the least squares approach (see, e.g. Brunk, 1955; Mukerjee, 1988, among others and Barlow et al. (1972) or Robertsen et al. (1988) for a summary of this work).”
Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints (2021, background): “Related works Estimating discrete distributions is a fundamental task in statistical inference and has a rich literature (Barlow, 1972; Devroye and Gábor, 1985; Devroye and Lugosi, 2012; Silverman, 1986).”