---
# System prepended metadata

title: 'Perturbation analysis of black-box predictions: Unifying and generalising leverage and influence scores'
tags: [RIKEN]

---

# Perturbation analysis of black-box predictions: Unifying and generalising leverage and influence scores

###### tags: `RIKEN`

One of the main questions practioners of machine learning face is understanding which pieces of data highly affect their model. This could for the removal of outliers or poisiones data. It could also be for the use of selecting points for a replay buffer in continual learning or even understanding our model. better. 

In this paper, we use perturbation analysis of the posterior distribution to re-derive and generalise influence and leverage functions — a classical techniques from robust statistics — to trace a model’s prediction through the learning algorithm and back to its training data, thereby identifying training points most responsible for a given prediction. We also provide computation methods for both. 

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The main challenge in Continual Learning (CL) is the stability-plasticity dilemma. The main difficulty in addressing the stability-plasticity dilemma lies in carefully deciding which information to store from previous tasks. Most existing works develop heuristics for this purpose, and lack a rigorous justification for why they should work. In particular, they do not attempt to approach the best possible model that is obtained by doing batch-training on all task data jointly. 

The goal of this project is to approach this optimal model by finding points that are most responsible for generalisation. The idea is to find points using leverage scores. However, leverage scores are computationally expensive. We thus provide scalable ways of computing leverage scores using the nystrom approximation. Furthermore, we show how the points we select minimise the error of not storing everything and using neural networks instead of glms. We also discuss how leverage scores are connected to recovering second order information as well. 

