|
|
@@ -1,27 +1,58 @@ |
|
|
Abductive Learning |
|
|
Abductive Learning |
|
|
================== |
|
|
================== |
|
|
|
|
|
|
|
|
Traditional supervised machine learning, e.g. classification, is predominantly data-driven. Here, a set of training examples \left\{\left(x_1, y_1\right), \ldots,\left(x_m, y_m\right)\right\} is given, where x_i \in \mathcal{X} is the i-th training instance, y_i \in \mathcal{Y} is the corresponding ground-truth label. These data are then used to train a classifier model f: \mathcal{X} \mapsto \mathcal{Y} to accurately predict the unseen data. |
|
|
|
|
|
|
|
|
|
|
|
（可能加一张图，比如左边是ML，右边是ML+KB） |
|
|
|
|
|
|
|
|
|
|
|
In Abductive Learning (ABL), we assume that, in addition to data as examples, there is also a knowledge base \mathcal{KB} containing domain knowledge at our disposal. We aim for the classifier f: \mathcal{X} \mapsto \mathcal{Y} to make correct predictions on unseen data, and meanwhile, the logical facts grounded by \left\{f(\boldsymbol{x}_1), \ldots, f(\boldsymbol{x}_m)\right\} should be compatible with \mathcal{KB}. |
|
|
|
|
|
|
|
|
|
|
|
The process of ABL is as follows: |
|
|
|
|
|
|
|
|
|
|
|
1. Upon receiving data inputs \left\{x_1,\dots,x_m\right\}, pseudo-labels \left\{f(\boldsymbol{x}_1), \ldots, f(\boldsymbol{x}_m)\right\} are obtained, predicted by a data-driven classifier model. |
|
|
|
|
|
2. These pseudo-labels are then converted into logical facts \mathcal{O} that are acceptable for logical reasoning. |
|
|
|
|
|
3. Conduct joint reasoning with \mathcal{KB} to find any inconsistencies. |
|
|
|
|
|
4. If found, the logical facts contributing to minimal inconsistency can be identified and then modified through abductive reasoning, returning modified logical facts \Delta(\mathcal{O}) compatible with \mathcal{KB}. |
|
|
|
|
|
5. These modified logical facts are converted back to the form of pseudo-labels, and used for further learning of the classifier. |
|
|
|
|
|
6. As a result, the classifier is updated and replaces the previous one in the next iteration. |
|
|
|
|
|
|
|
|
|
|
|
This process is repeated until the classifier is no longer updated, or the logical facts \mathcal{O} are compatible with the knowledge base. |
|
|
|
|
|
|
|
|
Traditional supervised machine learning, e.g. classification, is |
|
|
|
|
|
predominantly data-driven. Here, a set of training examples |
|
|
|
|
|
:math:`\left\{\left(x_1, y_1\right), \ldots,\left(x_m, y_m\right)\right\}` |
|
|
|
|
|
is given, where :math:`x_i \in \mathcal{X}` is the :math:`i`-th training |
|
|
|
|
|
instance, :math:`y_i \in \mathcal{Y}` is the corresponding ground-truth |
|
|
|
|
|
label. These data are then used to train a classifier model :math:`f: |
|
|
|
|
|
\mathcal{X} \mapsto \mathcal{Y}` to accurately predict the unseen data. |
|
|
|
|
|
|
|
|
|
|
|
In **Abductive Learning (ABL)**, we assume that, in addition to data as |
|
|
|
|
|
examples, there is also a knowledge base :math:`\mathcal{KB}` containing |
|
|
|
|
|
domain knowledge at our disposal. We aim for the classifier :math:`f: |
|
|
|
|
|
\mathcal{X} \mapsto \mathcal{Y}` to make correct predictions on unseen |
|
|
|
|
|
data, and meanwhile, the logical facts grounded by |
|
|
|
|
|
:math:`\left\{f(\boldsymbol{x}_1), \ldots, f(\boldsymbol{x}_m)\right\}` |
|
|
|
|
|
should be compatible with :math:`\mathcal{KB}`. |
|
|
|
|
|
|
|
|
|
|
|
The process of ABL is as follows: |
|
|
|
|
|
|
|
|
|
|
|
1. Upon receiving data inputs :math:`\left\{x_1,\dots,x_m\right\}`, |
|
|
|
|
|
pseudo-labels |
|
|
|
|
|
:math:`\left\{f(\boldsymbol{x}_1), \ldots, f(\boldsymbol{x}_m)\right\}` |
|
|
|
|
|
are predicted by a data-driven classifier model. |
|
|
|
|
|
2. These pseudo-labels are then converted into logical facts |
|
|
|
|
|
:math:`\mathcal{O}` that are acceptable for logical reasoning. |
|
|
|
|
|
3. Conduct joint reasoning with :math:`\mathcal{KB}` to find any |
|
|
|
|
|
inconsistencies. If found, the logical facts that lead to minimal |
|
|
|
|
|
inconsistency can be identified. |
|
|
|
|
|
4. Modify the identified facts through abductive reasoning, returning |
|
|
|
|
|
revised logical facts :math:`\Delta(\mathcal{O})` which are |
|
|
|
|
|
compatible with :math:`\mathcal{KB}`. |
|
|
|
|
|
5. These revised logical facts are converted back to the form of |
|
|
|
|
|
pseudo-labels, and used for further learning of the classifier. |
|
|
|
|
|
6. As a result, the classifier is updated and replaces the previous one |
|
|
|
|
|
in the next iteration. |
|
|
|
|
|
|
|
|
|
|
|
This process is repeated until the classifier is no longer updated, or |
|
|
|
|
|
the logical facts :math:`\mathcal{O}` are compatible with the knowledge |
|
|
|
|
|
base. |
|
|
|
|
|
|
|
|
The following figure illustrates this process: |
|
|
The following figure illustrates this process: |
|
|
|
|
|
|
|
|
一张图 |
|
|
一张图 |
|
|
|
|
|
|
|
|
We can observe that in the above figure, the left half involves machine learning, while the right half involves logical reasoning. Thus, the entire abductive learning process is a continuous cycle of machine learning and logical reasoning. This effectively form a dual-driven (data & knowledge driven) learning system, integrating and balancing the use of machine learning and logical reasoning in a unified model. |
|
|
|
|
|
|
|
|
We can observe that in the above figure, the left half involves machine |
|
|
|
|
|
learning, while the right half involves logical reasoning. Thus, the |
|
|
|
|
|
entire abductive learning process is a continuous cycle of machine |
|
|
|
|
|
learning and logical reasoning. This effectively forms a paradigm that |
|
|
|
|
|
is dual-driven by both data and domain knowledge, integrating and |
|
|
|
|
|
balancing the use of machine learning and logical reasoning in a unified |
|
|
|
|
|
model. |
|
|
|
|
|
|
|
|
|
|
|
What is Abductive Reasoning? |
|
|
|
|
|
^^^^^^^^^^^^^^^^^^^^^^^^^^^^ |
|
|
|
|
|
|
|
|
|
|
|
|
troyyyyy
1 year ago