An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l_inf norm, and we present an optimal linear time algorithm based on novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labeling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142

A Unified Framework of Constrained Regression

Generalized additive models (GAMs) play an important role in modeling and understanding complex relationships in modern applied statistics. They allow for flexible, data-driven estimation of covariate effects. Yet researchers often have a priori knowledge of certain effects, which might be monotonic or periodic (cyclic) or should fulfill boundary conditions. We propose a unified framework to incorporate these constraints for both univariate and bivariate effect estimates and for varying coefficients. As the framework is based on component-wise boosting methods, variables can be selected intrinsically, and effects can be estimated for a wide range of different distributional assumptions. Bootstrap confidence intervals for the effect estimates are derived to assess the models. We present three case studies from environmental sciences to illustrate the proposed seamless modeling framework. All discussed constrained effect estimates are implemented in the comprehensive R package mboost for model-based boosting.Comment: This is a preliminary version of the manuscript. The final publication is available at http://link.springer.com/article/10.1007/s11222-014-9520-

Conditional Transformation Models

The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only estimate the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and noise. We propose to relax this common assumption in the framework of transformation models. The novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables. These transformation functions are estimated by regularised optimisation of scoring rules for probabilistic forecasts, e.g. the continuous ranked probability score. The corresponding estimated conditional distribution functions are consistent. Conditional transformation models are potentially useful for describing possible heteroscedasticity, comparing spatially varying distributions, identifying extreme events, deriving prediction intervals and selecting variables beyond mean regression effects. An empirical investigation based on a heteroscedastic varying coefficient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more beneficial than kernel-based non-parametric approaches or parametric generalised additive models for location, scale and shape

Non-parametric production analysis under alternative price conditions.

The literature on non-parametric production analysis has formulated tests for profit maximizing behavior that do not require a parametric specification of technology. Negative test results have conventionally been interpreted as inefficiency, or have been attributed to data perturbations. In this paper, we exploit the possibility that negative test results reveal violations of the underlying neoclassical assumption that prices are exogenously fixed and perfectly certain. We propose non-parametric tests that do allow for endogenous price formation and price uncertainty. In addition, we investigate how to recover the technology and how to forecast behavior in new economic situations.Non-parametric production analysis; Endogenous price formation; Price uncertainty;

Nonparametric Production Analysis under Alternative Price Conditions

The literature on non-parametric production analysis has formulated tests for profit maximizing behavior that do not require a parametric specification of technology. Negative test results have conventionally been interpreted as inefficiency, or have been attributed to data perturbations. In this paper, we exploit the possibility that negative test results reveal violations of the underlying neoclassical assumption that prices are exogenously fixed and perfectly certain. We propose non-parametric tests that do allow for endogenous price formation and price uncertainty. In addition, we investigate how to recover the technology and how to forecast behavior in new economic situations.non-parametric production analysis; endogenous price formation; price uncertainty

Comparison and contrast in perceptual categorization

People categorized pairs of perceptual stimuli that varied in both category membership and pairwise similarity. Experiments 1 and 2 showed categorization of 1 color of a pair to be reliably contrasted from that of the other. This similarity-based contrast effect occurred only when the context stimulus was relevant for the categorization of the target (Experiment 3). The effect was not simply owing to perceptual color contrast (Experiment 4), and it extended to pictures from common semantic categories (Experiment 5). Results were consistent with a sign-and-magnitude version of N. Stewart and G. D. A. Brown's (2005) similarity-dissimilarity generalized context model, in which categorization is affected by both similarity to and difference from target categories. The data are also modeled with criterion setting theory (M. Treisman & T. C. Williams, 1984), in which the decision criterion is systematically shifted toward the mean of the current stimuli