A Hypergradient Approach to Robust Regression without Correspondence

by   Yujia Xie, et al.

We consider a regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring instruments are unable to preserve the correspondence between the samples and the measurements. Due to the combinatorial nature, most of existing methods are only applicable when the sample size is small, and limited to linear regression models. To overcome such bottlenecks, we propose a new computational framework - ROBOT- for the shuffled regression problem, which is applicable to large data and complex models. Specifically, we propose to formulate the regression without correspondence as a continuous optimization problem. Then by exploiting the interaction between the regression model and the data correspondence, we propose to develop a hypergradient approach based on differentiable programming techniques. Such a hypergradient approach essentially views the data correspondence as an operator of the regression, and therefore allows us to find a better descent direction for the model parameter by differentiating through the data correspondence. ROBOT is quite general, and can be further extended to the inexact correspondence setting, where the input and output data are not necessarily exactly aligned. Thorough numerical experiments show that ROBOT achieves better performance than existing methods in both linear and nonlinear regression tasks, including real-world applications such as flow cytometry and multi-object tracking.



There are no comments yet.


page 12

page 15

page 31


A Deep Learning Model for Structured Outputs with High-order Interaction

Many real-world applications are associated with structured data, where ...

Bayesian Analysis on Limiting the Student-t Linear Regression Model

For the outlier problem in linear regression models, the Student-t linea...

Robust approximate linear regression without correspondence

Estimating regression coefficients using unordered multisets of covariat...

A Robust Regression Approach for Robot Model Learning

Machine learning and data analysis have been used in many robotics field...

Multivariate Regression with Grossly Corrupted Observations: A Robust Approach and its Applications

This paper studies the problem of multivariate linear regression where a...

Convolutional Regression for Visual Tracking

Recently, discriminatively learned correlation filters (DCF) has drawn m...

Semi-supervised Classification using Attention-based Regularization on Coarse-resolution Data

Many real-world phenomena are observed at multiple resolutions. Predicti...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.