29 research outputs found
Systematic Analysis of Cluster Similarity Indices: How to Validate Validation Measures
Many cluster similarity indices are used to evaluate clustering algorithms,
and choosing the best one for a particular task remains an open problem. We
demonstrate that this problem is crucial: there are many disagreements among
the indices, these disagreements do affect which algorithms are preferred in
applications, and this can lead to degraded performance in real-world systems.
We propose a theoretical framework to tackle this problem: we develop a list of
desirable properties and conduct an extensive theoretical analysis to verify
which indices satisfy them. This allows for making an informed choice: given a
particular application, one can first select properties that are desirable for
the task and then identify indices satisfying these. Our work unifies and
considerably extends existing attempts at analyzing cluster similarity indices:
we introduce new properties, formalize existing ones, and mathematically prove
or disprove each property for an extensive list of validation indices. This
broader and more rigorous approach leads to recommendations that considerably
differ from how validation indices are currently being chosen by practitioners.
Some of the most popular indices are even shown to be dominated by previously
overlooked ones
Neural Algorithmic Reasoning Without Intermediate Supervision
Neural Algorithmic Reasoning is an emerging area of machine learning focusing
on building models which can imitate the execution of classic algorithms, such
as sorting, shortest paths, etc. One of the main challenges is to learn
algorithms that are able to generalize to out-of-distribution data, in
particular with significantly larger input sizes. Recent work on this problem
has demonstrated the advantages of learning algorithms step-by-step, giving
models access to all intermediate steps of the original algorithm. In this
work, we instead focus on learning neural algorithmic reasoning only from the
input-output pairs without appealing to the intermediate supervision. We
propose simple but effective architectural improvements and also build a
self-supervised objective that can regularise intermediate computations of the
model without access to the algorithm trajectory. We demonstrate that our
approach is competitive to its trajectory-supervised counterpart on tasks from
the CLRS Algorithmic Reasoning Benchmark and achieves new state-of-the-art
results for several problems, including sorting, where we obtain significant
improvements. Thus, learning without intermediate supervision is a promising
direction for further research on neural reasoners