Summary of On Probabilistic Embeddings in Optimal Dimension Reduction, by Ryan Murray and Adam Pickarski
On Probabilistic Embeddings in Optimal Dimension Reduction
by Ryan Murray, Adam Pickarski
First submitted to arxiv on: 5 Aug 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Analysis of PDEs (math.AP)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper presents a theoretical investigation into a generalized version of multidimensional scaling, a crucial dimension reduction algorithm used in various data science pipelines. The authors pose this algorithm as an optimization problem that seeks to preserve inner products or norms of the feature space distribution in a lower-dimensional embedding space. They analytically explore the variational properties of this problem, leading to insights on non-deterministic embeddings, probabilistic formulations, and globally optimal solutions. These findings mirror classical developments in optimal transportation and provide explicit insight into the structure of optimal embeddings. The authors also demonstrate that standard computational implementations can learn sub-optimal mappings with misleading clustering structures. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper looks at a way to shrink really big data sets down to smaller ones while keeping important information. They take an old idea called multidimensional scaling and make it more general so it can be used in many different situations. By studying this problem mathematically, they find some interesting things: sometimes the answers aren’t perfect, sometimes you can get good enough answers by making a few changes to the way you do things, and sometimes there’s only one perfect answer. They also show that when people try to use computers to solve this problem, they don’t always get the best results. |
Keywords
» Artificial intelligence » Clustering » Embedding space » Optimization
