On Asymptotic Distribution Theory in Segmented Regression Problems-- Identified Case

On Segmented Multivariate Regression

This paper concerns segmented multivariate regression models, models which have different linear forms in different subdomains of the domain of an independent variable. Without knowing that number and their boundaries, we first estimate the number of these subdomains using a modified Schwarz criterion. The estimated number of regions proves to be weakly consistent under fairly general condition...

Learning Theory for Distribution Regression

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning or point estimation problems without analytical solution such as hyperparameter or entropy estimation. Despite the large number of available heuristics in the literature, t...

Asymptotic distribution theory for Hoare's selection algorithm

Fast Algorithms for Segmented Regression

We study the fixed design segmented regression problem – a classical statistical inference task that encompasses several natural problems as a special case. 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 r...

A SEGMENTED REGRESSION MODEL FOR DESCRIPTION OF MICROBIAL GROWTH

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