We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function f , we want to recover f up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on dynamic programming (DP) and, while sample efficient, have running time quadratic in the sample size. As our main contribution, we provide new sample near-linear...

Simple linear regression tries to determine a linear relationship between a given variable X (predictor) and a dependent variable Y. Since most of the environmental problems involve complex relationships, X-Y relationship is often better modeled through a regression where, instead of fitting a single straight line to the data, the algorithm allows the fitting to bend. Piecewise regressions just...

a segmented regression model for the description of microbial growth has been suggested. the model is able to predict the exponential growth, logistic growth, logistic growth with a phase of decline, diauxic growth, microbial growth in synchronous cultures and the oscillatory growth

BACKGROUND An interrupted time series design is a powerful quasi-experimental approach for evaluating effects of interventions introduced at a specific point in time. To utilize the strength of this design, a modification to standard regression analysis, such as segmented regression, is required. In segmented regression analysis, the change in intercept and/or slope from pre- to post-interventi...

This study aims to accurately predict glaucomatous visual-field loss from patient disease data. In general, medical data show two kinds of heterogeneity: 1) internal heterogeneity, in which the phase of disease progression changes in an individual patient’s time series dataset; and 2) external heterogeneity, in which the trends of disease progression differ among patients. Although some previou...

The growth rate of fingers of a Newtonian fluid can be modeled by a power law dependence on time. In this experiment, we examine whether the model can be adapted to describe a fluid with changing viscosity. We provide two possible interpretations. For PVA and a PVA/glycerol solution, we show that by assuming a constant exponent, the changing behavior of the fluid can be captured by a coefficien...