Background

Machine learning is usually considered as a ​black box

I'd really like to know which treatment my patient should undergo to reduce the threat of a heart attack

According to our records, we expect to lower your risk if you will do more fitness

How do we provide such insights?

How do we provide such insights?

We focus on tree(s) models

• Widely used
• Easy to open the black box

Problem Formulation

• First we let \(\mathcal{X} \subseteq \mathbb{R}^n \) be the n-dimentional feature vector space.
• So feature vector is represented as \(\mathbf{x} = (x_1, x_2, ..., x_n)^T \in \mathcal{X}\).
• WLOG, the problem simplified as a binary classification problem, i.e. \(\mathbf{y} = \{-1,+1\}\).
• Also, there's a function \(f: \mathcal{X} \mapsto \mathbf{y}\), i.e. classifier, and \(\hat{f} \approx f\) as the classifier learned from data.
• Here we assume \(f\) to be an ensemble of K tree-based classifiers, i.e. \(\hat{f} = \phi(\hat{h}_1,...,\hat{h}_k)\).
• WLOG, we assume \(\phi\) to be the majority vote.

Goal

\[x' = \arg \min_{X^*} \{1|\hat{f}(x) = -1 \wedge \hat{f}(x^*) = +1 \}\]

Goal

\[x' = \arg \min_{X^*} \{1|\hat{f}(x) = -1 \wedge \hat{f}(x^*) = +1 \}\]

unbound?

• Given a distance measurement \(\delta: \mathcal{X} \times \mathcal{X} \mapsto \mathbb{R}\)
• We want to find a \(x'\) so that 

Goal

\[x' = \arg \min_{X^*} \{\delta(x,x^*)|\hat{f}(x) = -1 \wedge \hat{f}(x^*) = +1 \}\]

Goal

\[x' = \arg \min_{X^*} \{\delta(x,x^*)|\hat{f}(x) = -1 \wedge \hat{f}(x^*) = +1 \}\]

The solution

Observation

Each instance follows a root-to-leaf path for each tree

True negative instance 

Key Idea

Perturbation

Key Idea

Perturbation

Perturbation: Diff, i.e. a potential suggestion 

Step 1

Select one tree giving out the negative label

Step 2

Find all the paths in that tree that outputs positive label

\(\in\)

Step 3

Generate instances satisfying each paths

+

=

Formally

• \(p^+_{k,j}\) as the j-th path in tree \(T_k\).
• For all \(T_k \in T^-\), we calculate the perturbed feature vector \(x^+_{j(\epsilon)}\), by
• \(x^+_{j(\epsilon)}[i] = \theta_i - \epsilon \text{ if the i-th condition is } (x_i \leq \theta_i) \) or,
• \(x^+_{j(\epsilon)}[i] = \theta_i + \epsilon \text{ if the i-th condition is } (x_i \gt \theta_i) \)

= \(140/90 + \epsilon\)

Problem

Do we need a \(\epsilon\) for every case?

Problem

Do we need a \(\epsilon\) for every case?

Global \(\epsilon\)!

No

Problem

Do we need a \(\epsilon\) for every case?

Global \(\epsilon\)!

No

If all the features is standardized to z-score, then a single \(\epsilon\) is enough.

i.e. \(\theta_i = \frac{t_i - u_i}{\sigma_i}\)

Solution

Problem

Perturb on one tree may invalid other trees

Problem

Perturb on one tree may invalid other trees

Solution

Have a round of check on the whole forest

Recap

1. For all trees, get positive paths \(p^+_k\).
2. Get perturbed instance \(x^+_{j(\epsilon)}\) by \(buildPositiveInst(x, p^+_{k,j}, \epsilon)\)
3. Check if \(\hat{f}(x^+_{j(\epsilon)}) = +1\), and put the instance to a set \(S\)if satisfied.
4. For each instances in \(S\), select the one with smallest \(\delta(x, x^+_{j(\epsilon)})\) as \(x'\)

Use case at Yahoo

Ad quality

Ad quality varies, for low quality Ads, 

Motivation

Ad quality varies, for low quality Ads, 

Not serving them is not an option

Motivation

Ad quality varies, for low quality Ads, 

Not serving them is not an option

Serving them hurts the user experience 

Motivation

Ad quality varies, for low quality Ads, 

Not serving them is not an option

Serving them hurts the user experience 

As the platform, gives out suggestions is a win-win

Motivation

Model settings

The impact of hyperparameters

Assessing the recommendation quality

1. Feature ranking

ϵ = 0.05 and δ = cosine distance

Assessing the recommendation quality

2. Top K recommendations based on cost, rank them based on feature importance

ϵ = 0.05 and δ = cosine distance

Assessing the recommendation quality

3. Use user study to test the performance, result shows:

• helpful: 57.3%,
• not helpful: 42.3% (25% neutral)
• not actionable: 0.4%

ϵ = 0.05 and δ = cosine distance

Assessing the recommendation quality

ϵ = 0.05 and δ = cosine distance

\( helpfulness(i) = \frac{helpful(i)}{helpful(i) + \neg helptul(i)} \)

Showcase of helpfulness for top features