Allison Gilmore, Data Scientist, Ayasdi at MLconf ATL - 9/18/15

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Topological Learning with Ayasdi: Ayasdi has a unique approach to machine learning and data analysis using topology. This framework represents a revolutionary way to look at and understand data that is orthogonal but complementary to traditional machine learning and statistical tools. In this presentation I will show you what is meant by this statement: How does topology help with data analysis? Why would you use topology? I will illustrate with both synthetic examples and problems we’ve solved for our clients.

Technologie

Topological Learning
September 18, 2015
Allison Gilmore, Ph.D.

Company Confidential & Proprietary 2
Why Topology?
Data has shape.
Shape has meaning.
You already know this.

Company Confidential & Proprietary
Shape Encodes Structure and Meaning
3
Line Clusters Flares
v v
v
v
vv
v
v
v v
v
v
v v
v
v
v
v
v
Loop

Company Confidential & Proprietary
Complex Data Has ALL These Shapes
4

Company Confidential & Proprietary
Data Comes With the Wrong Coordinates
5

Company Confidential & Proprietary
Topological Networks Capture Shape
6
• Color by a real-valued
function
• Bin in the image of that
function
• Cluster within bins, in
the original space
• Connect clusters that
share data points

Company Confidential & Proprietary
Capturing Complex Shapes

Company Confidential & Proprietary 8
Shape shows underlying properties of
data that yield insights and meaning.
• Nodes are groups of similar
objects
• Edges connect similar nodes
• Colors let you see values of
interest
• Node position on the screen
does not matter
Network Orientation

Company Confidential & Proprietary
Disease State & Model Choice

Company Confidential & Proprietary 10
1982 2015
30 years of market
and economic data
and 150+ variables
The Shape of a Market
Regimes
Progressions
Cycles

Company Confidential & Proprietary 11
All Recessions – 1980-Present
Recessions Are Similar…

Company Confidential & Proprietary 12
1982 Recovery 2002 Recovery
…But Recoveries Are Different

Company Confidential & Proprietary
Build Better Models
13
Identify market regimes
that are analogous to
the current state.
Profit from precise asset
allocation and liquidity
forecasting strategies.

Company Confidential & Proprietary
Topology Yields Principled Local Models
16

Company Confidential & Proprietary 17
Questions?
Allison.Gilmore@Ayasdi.com
www.ayasdi.com

Corporate Headquarters
4400 Bohannon Drive
Suite #200
Menlo Park, CA 94025
ayasdi.com

Company Confidential & Proprietary
PCA Finds 3 Clusters

Company Confidential & Proprietary
TDA Finds 4 Clusters

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Allison Gilmore, Data Scientist, Ayasdi at MLconf ATL - 9/18/15

1. Topological Learning September 18, 2015 Allison Gilmore, Ph.D.

2. Company Confidential & Proprietary 2 Why Topology? Data has shape. Shape has meaning. You already know this.

3. Company Confidential & Proprietary Shape Encodes Structure and Meaning 3 Line Clusters Flares v v v v vv v v v v v v v v v v v v v Loop

4. Company Confidential & Proprietary Complex Data Has ALL These Shapes 4

5. Company Confidential & Proprietary Data Comes With the Wrong Coordinates 5

6. Company Confidential & Proprietary Topological Networks Capture Shape 6 • Color by a real-valued function • Bin in the image of that function • Cluster within bins, in the original space • Connect clusters that share data points

7. Company Confidential & Proprietary Capturing Complex Shapes

8. Company Confidential & Proprietary 8 Shape shows underlying properties of data that yield insights and meaning. • Nodes are groups of similar objects • Edges connect similar nodes • Colors let you see values of interest • Node position on the screen does not matter Network Orientation

9. Company Confidential & Proprietary Disease State & Model Choice

10. Company Confidential & Proprietary 10 1982 2015 30 years of market and economic data and 150+ variables The Shape of a Market Regimes Progressions Cycles

11. Company Confidential & Proprietary 11 All Recessions – 1980-Present Recessions Are Similar…

12. Company Confidential & Proprietary 12 1982 Recovery 2002 Recovery …But Recoveries Are Different

13. Company Confidential & Proprietary Build Better Models 13 Identify market regimes that are analogous to the current state. Profit from precise asset allocation and liquidity forecasting strategies.

14. Company Confidential & Proprietary Topology Yields Principled Local Models 16

15. Company Confidential & Proprietary 17 Questions? Allison.Gilmore@Ayasdi.com www.ayasdi.com

16. Corporate Headquarters 4400 Bohannon Drive Suite #200 Menlo Park, CA 94025 ayasdi.com

17. Company Confidential & Proprietary PCA Finds 3 Clusters

18. Company Confidential & Proprietary TDA Finds 4 Clusters

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If you know the shape, you don’t need to query – everything significant is represented in the shape. General ML algorithms only provide access to handful of shapes. Often, data exhibits multiple shapes simultaneously Complex data requires methods that can represent all shapes and combinations of shape = TDA
So, objects close together in the network (in the same or nearby nodes) are similar (on whatever features you used to build the network).
In reality, all these shapes exist in any complex data set. Here’s a data set that is being used by a major hedge fund to guide their investment strategy. Applying Ayasdi Machine Intelligence to 30 years of market and macroeconomic data, results in this topological summary. Each node in this diagram represents a collection of time periods where equity prices and other market indicators behaved similarly. From this data, you can discern specific market regimes, progressions and cycles. Imagine if you can reliably understand the current regime in which we exist today and what are the most likely next progressions in market behavior based on analyzing historical trends. This technique reduces and simplifies thousands of man-hours of systematic and quantitative market research.
If we interrogate for all the recessions included in the set, the result shows that the months that were in a recession cluster quite nicely (lower, right corner of the network) So what other information can we extract from this shape?
The paths to recovery can be different Let’s look at the path out of the 1982 recession (left panel) and out of the 2002 recession (right panel) They took very different paths and that should affirm our understanding that in 30 years of market cycles, the path taken out of each recession has been quite different The next step is to see if we can gain a better understanding of the current state and the implications for the future
The type of advanced discovery enables the traders to build precise trading models that fit current market regimes. They can interrogate time periods of interest, and see exactly what are the driving indicators of similarity, and determine what indicators typically followed next. From this they can build models to drive trading strategies. These same types of analyses can also be used to assess risk by the CRO within the bank, to anticipate periods of increased uncertainty, or the likelihood of volatility.
PCA captures 98.4% of variance. TDA with PCA lenses shows 4 clusters.

Allison Gilmore, Data Scientist, Ayasdi at MLconf ATL - 9/18/15

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Allison Gilmore, Data Scientist, Ayasdi at MLconf ATL - 9/18/15

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