Bachelor and Master Theses

Background of PAF

Modern ML models can make highly accurate predictions, but understanding why a model makes a particular prediction remains challenging. Explainable AI (XAI) methods address this by assigning importance to input features. The Probabilistic Attribution Framework (PAF) takes a different perspective: it represents attribution as a probability distribution over the input units, where each unit receives non-negative probability mass and the total mass is one. For an image, the units may correspond to pixels or spatial regions. This gives the explanation a natural interpretation --- a distribution of the model's attribution mass.

PAF supports the Mass-in-Box (MiB) metric when a relevant region G is known. MiB is the total attribution probability assigned to G. For example, MiB = 0.8 means that 80% of the attribution mass lies inside the region of interest.

However, MiB summarizes the distribution into a single number. Two explanations can have the same MiB while distributing their attribution mass very differently: one may concentrate the mass on a few units, while another may spread it across many units.

This motivates the central question of the thesis: Does the full PAF distribution contain useful information about explanation quality beyond MiB?

Research Problem

The thesis investigates whether properties of the PAF distribution provide additional information about explanation quality that is not captured by MiB. Possible descriptors include entropy (distributional dispersion), top-k concentration (mass assigned to the most highly attributed k units), effective number of units, and within-region entropy (how attribution mass is distributed inside the relevant region).

These measures capture different aspects of an explanation. MiB describes how much attribution reaches the relevant region, while within-region measures describe how that mass is distributed. The thesis should not assume that a concentrated or low-entropy explanation is necessarily better: a concentrated explanation can be wrong, and a diffuse explanation can be correct.

Main Research Question

Does the distributional structure of PAF provide information about explanation quality beyond MiB?

Research Questions (sample only)

·      RQ1. What does the PAF distribution reveal beyond MiB? How can explanations with similar MiB differ in their distributional structure?

·      RQ2. Which distributional properties are informative? Do entropy, concentration, effective number of units, or within-region entropy provide useful information about explanation quality?

·      RQ3. Does distributional structure add information beyond MiB? After accounting for MiB, do distributional descriptors explain additional variation in ground-truth alignment or behavioral faithfulness?

·       RQ4. Under what conditions is distributional structure informative? Does the relationship vary across models, datasets, tasks, or types of explanation?

Experimental Approach

The study will use datasets with annotated relevant regions and, where useful, controlled or synthetic data with known relevant features. For each selected image and neural network, PAF will generate an attribution distribution. The student will compute MiB together with several complementary distributional descriptors.

The main analysis will compare explanations with similar MiB but different distributional structures and test whether those differences are associated with explanation quality. Statistical analyses will explicitly control for MiB, so that the thesis tests whether the additional structure of the probability distribution contributes information beyond the existing metric.

Where feasible, the study will also evaluate behavioral faithfulness by perturbing highly attributed regions and measuring the resulting change in the model's prediction. This helps distinguish ground-truth alignment from behavioral faithfulness.

Methodology

1.     Study PAF and its probabilistic attribution mechanism (Available upon request)

2.     Select suitable ground-truth benchmarks, preferably including controlled/synthetic and real-world annotated data.

3.     Generate PAF explanations for selected neural-network models.

4.     Compute MiB and complementary explanation metrics.

5.     Extract distributional descriptors such as entropy, concentration, effective number of units, and within-region entropy.

6.     Compare explanations with similar MiB but different distributional structures.

7.     Test whether distributional descriptors provide explanatory power beyond MiB.

8.     Where feasible, perform behavioral faithfulness experiments.

9.     Analyze results across datasets, models, and experimental conditions.

The project will use Python and modern machine-learning/XAI tooling. Familiarity with Python and machine learning is expected; previous XAI experience is useful but not required.

Expected Contribution

The thesis aims to provide an empirical characterization of what information is contained in a PAF attribution distribution beyond its total mass in a relevant region. The outcome may show that distributional properties provide useful additional information, are informative only under certain conditions, or add little beyond MiB. The goal is to improve the understanding and evaluation of probabilistic explanations rather than simply introduce another saliency metric.

The project combines Explainable AI, machine learning, probabilistic methods, and empirical research. The student will work with an existing research framework while investigating a clearly defined and genuinely open question. The project has a manageable progression from understanding PAF, through implementation and statistical analysis, to a potentially publishable research result.