Benchmarking Deletion Metrics With The Principles Explanations

Contributions

Formalization of deletion metrics

New attribution function

Study OOD problem

Formalization of deletion metrics

     Formalization

f: \mathbb{R}^d \longrightarrow \mathbb{R}
\begin{array}{lccc} \varphi_f: & \mathbb{R}^d & \longrightarrow & \mathbb{R}^d \\ & x & \longmapsto & \psi \\ & \text{\tiny (image)} & & \text{\tiny(heatmap)} \end{array}

The black-box model to study

Attribution function

(i)  Delete the most relevant first: MoRF

Two evaluation scenarios of     (and therefore of       ):

\psi
\varphi_f

MoRF:

small AUC is better

nb area masked

Prediction

(ii) Delete the least relevant first: LeRF

small AUC is better

large AUC is better

     Formalization

f: \mathbb{R}^d \longrightarrow \mathbb{R}
\begin{array}{lccc} \varphi_f: & \mathbb{R}^d & \longrightarrow & \mathbb{R}^d \\ & x & \longmapsto & \psi \\ & \text{\tiny (image)} & & \text{\tiny(heatmap)} \end{array}

The black-box model to study

Attribution function

Attribution rank

\sigma(\psi) = \text{\texttt{argsort}}(\psi)

(increasing order)

\text{MoRF}(\psi) = \sum_{k=0}^d f( x_{\setminus \sigma[k:]}) %= \sum_{k=0}^d f( x_{\sigma[:k]})

Evaluation function

     Formalization

Remarks

(i)   Deletion or Insertion is the same problem.

\text{MoRF}(\psi) = \sum_{k=0}^d f( x_{\setminus \sigma[k:]}) %= \sum_{k=0}^d f( x_{\sigma[:k]})
\text{MoRF}(\psi) = \sum_{k=0}^d f( x_{\setminus \sigma[k:]}) = \sum_{k=0}^d f( x_{\sigma[:k]})

(ii)  logit vs proba

(iii) MoRF and LeRF are different problems

\text{LeRF}-\text{MoRF}(\psi) = \sum_{k=0}^d f( x_{\sigma[k:]}) - f( x_{\sigma[:k]})

max

min

Average

Treatment Effect?

Contributions

Formalization of deletion metrics

New attribution function

Study OOD problem

New attribution function

     TRACE

Current Problem:

Too complicated and too vast.

NP-hard

Let's convert the problem in       into one in       (permutations).

\mathbb{R}^d
\mathcal{S}_d
\mathcal{S}_d

      is big (    ) but finite!

d!

     TRACE

for each k finds the set minimizing

f(x_{\setminus s_k})

Optimality

Greedy / SA

Global Optimum

(GO)

Complete Search

(CS)

\geq
\geq

Algorithms

* patches instead of pixels

 

- Greedy

- Simulated Annealing (SA)

     TRACE

How order

is evaluated

How order

is computed

TRACE-Mo performs poorly in the LeRF test.

 

 

Recommendation for computing order

LeRF−MoRF > LeRF >> MoRG

TRACE-Mo performs poorly in the LeRF test.

TRACE-Le performs well in the MoRF test.

 

TRACE-Mo performs poorly in the LeRF test.

TRACE-Le performs well in the MoRF test.

TRACE-Le−Mo is most consistent in both tests.

Contributions

Formalization of deletion metrics

New attribution function

Study OOD problem

Study OOD problem

     OOD Problem

Reference Value and OOD

Benchmarking Deletion Metrics With The Principles Explanations