Allison Gilmore, Data Scientist, Ayasdi at MLconf SF - 11/13/15
Dr. Gilmore is currently a data scientist on the team at Ayasdi where she specializes in highly complex and dimensional data across a variety of industries. Prior to joining Ayasdi, Allison served as a National Science Foundation Post-Doctoral Fellow and an Assistant Adjunct Professor in mathematics at the University of California Los Angeles. Dr. Gilmore also did post-doctoral research at Princeton University. She received her Ph.D. in mathematics from Columbia University in New York in May 2011. Allison completed her undergraduate and masters degrees from Washington University where she was selected as a Rhodes Scholar. She studied at Green College, Oxford University, and graduated in 2006 with an M.Phil. (with distinction) in sociology. Her research interests include topology, geometry, network analysis and social movements. Dr. Gilmore serves on the board of The Friends of the Mandela Rhodes Foundation whose mission is to fund the development of exceptional leadership capacity in southern Africa.
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Allison Gilmore, Data Scientist, Ayasdi at MLconf SF - 11/13/15
- 1. The Shape of Data Allison Gilmore Principal Data Scientist November 13, 2015
- 2. Company Confidential & Proprietary 2 Data has shape. Shape has meaning. You already know this.
- 3. Company Confidential & Proprietary Shape as Organizing Principle
- 4. Company Confidential & Proprietary Geometry or Topology? Geometry : Metric Topology : Locality ≅
- 5. Company Confidential & Proprietary Topological Summaries Capture Shape Lens
- 6. Company Confidential & Proprietary Topological Summaries Capture Shape
- 7. Company Confidential & Proprietary Topological Summaries Capture Shape
- 8. Company Confidential & Proprietary Enhancing Traditional Methods
- 9. Company Confidential & Proprietary 9 Topological Summaries Capture Shape Nodes are groups of similar data points. Edges connect similar nodes. Node position on the screen does not matter.
- 10. Company Confidential & Proprietary Enhancing Traditional Methods PCA sees 3 clusters. Using PCA coordinates as lenses, we can see more.
- 11. Company Confidential & Proprietary Topological Summary Shows 4 Clusters
- 12. Company Confidential & Proprietary Disease State & Model Choice David Schneider, Stanford Microbiology and Immunology
- 13. Company Confidential & Proprietary 14 Topological Model for Total Knee Replacement Low length of stay Low to moderate length of stay Long length of stay
- 14. Company Confidential & Proprietary Carepaths for Total Knee Replacement 16
- 15. Company Confidential & Proprietary Beating* the Curse of Dimensionality 18 * I mean, there are always conditions. Niyogi, Smale, and Weinberger, A Topological View of Unsupervised Learning from Noisy Data, SIAM J. of Computing 20(2011) 646-663. http://math.uchicago.edu/~shmuel/noise.pdf If a dataset is supported near a manifold, its key topological features can be detected from a sample whose size is independent of the dimension of ambient space. Doesn’t matter! Dimension d < N
- 16. Company Confidential & Proprietary 19 Questions? Allison.Gilmore@Ayasdi.com www.ayasdi.com
- 17. Company Confidential & Proprietary 20 Understanding Shape Improves Models 20 HighLow Ground Truth Fraud Model Predicted Fraud HighLow
- 18. Company Confidential & Proprietary Topology Guides Model Creation 21
Notas do Editor
- Real data has all these shapes and more.
- Next time show a second toy example as well, to demonstrate how different shapes would give different graphs. One audience member later asked about a horizontal ellipse and vertical ellipse intersecting. This also gives an opening to talk about invariance.
- The output is a graph. Just the nodes and edges, not the embedding. It’s a simple, combinatorial summary of something much more complex. It stays a simple combinatorial object even if your original data is in a very high dimensional space. Also, this is topology (mostly) – would have gotten the same graph if the points had been sampled from an ellipse or a square.
- So, objects close together in the network (in the same or nearby nodes) are similar (on whatever features you used to build the network).
- PCA captures 98.4% of variance. TDA with PCA lenses shows 4 clusters.
- With the best practices that are surfaced, you can start to create a care path that will be the baseline or template going forward. You can add and subtract events into this care path.