# Differential Network Analysis via the Lasso Penalized D-Trace Loss

arXiv: https://arxiv.org/abs/1511.09188 · HTML: https://mlsanity.com/paper/1511.09188/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2015.

## Built on by (most cited first, 10 of 10)

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Scalable Intervention Target Estimation in Linear Models](https://mlsanity.com/paper/2111.07512/) (2021)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Learning High-Dimensional Differential Graphs From Multi-Attribute Data](https://mlsanity.com/paper/2312.03761/) (2023)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Spectral Differential Network Analysis for High-Dimensional Time Series](https://mlsanity.com/paper/2412.07905/) (2024)
- [Learning Multi-Attribute Differential Graphs with Non-Convex Penalties](https://mlsanity.com/paper/2505.09748/) (2025)
- [Classification of High-dimensional Time Series in Spectral Domain using Explainable Features](https://mlsanity.com/paper/2408.08388/) (2024)
- [Efficient learning of differential network in multi-source non-paranormal graphical models](https://mlsanity.com/paper/2410.02496/) (2024)
- [Learning Conditional Independence Differential Graphs From Time-Dependent Data](https://mlsanity.com/paper/2512.06960/) (2025)

## Abstract (arXiv)

Biological networks often change under different environmental and genetic conditions. Understanding how these networks change becomes an important problem in biological studies. In this paper, we model the network change as the difference of two precision matrices and propose a novel loss function for estimating the precision matrix difference. Under a new irrepresentability condition, we show that the new loss function with the lasso penalty can give consistent estimates in high-dimensional setting for sub-Gaussian and polynomial-tailed distributions. An efficient algorithm is developed based on the alternating direction method to solve the optimization problem. Simulation studies and a real data analysis about colorectal cancer show that the proposed method outperforms other available methods.