2019 GDRR: Blockchain Data Analytics - Dissecting Blockchain Price Analytics: What We Learn from the Geometry of Ethereum - Umar Islambekov, October 6, 2019
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The document discusses the application of topological data analysis (TDA) for detecting price anomalies in the Ethereum network, addressing challenges posed by sparse and dynamic transaction graphs. It outlines a methodology that utilizes Betti sequences and data depth functions to model token price dynamics, aiming to predict anomalous price days based on the network's evolving topology. The study presents experimental results, demonstrating gains in accuracy, recall, and precision for the predictive models used.
![Notion of data depth
Let X be a space of multivariate or functional data points
(e.g., Rm or C([a, b]))
Definition 3 (Data depth)
With respect to a probability distribution P, a data depth function
D : X → [0, 1] provides a center-outward ordering of points of X.
There are several data depth functions that yield different
such orderings.
Highest depth values =⇒ most central points.
Lowest depth values =⇒ most outlying points.
0 20 40 60 80 100
2.02.53.03.54.04.55.05.5
Modified Band Depth (MBD)
deepest sample
12/19](https://image.slidesharecdn.com/8-islambekov-tdaforethereumrev-191007182427/85/2019-GDRR-Blockchain-Data-Analytics-Dissecting-Blockchain-Price-Analytics-What-We-Learn-from-the-Geometry-of-Ethereum-Umar-Islambekov-October-6-2019-12-320.jpg)
2019 GDRR: Blockchain Data Analytics - Dissecting Blockchain Price Analytics: What We Learn from the Geometry of Ethereum - Umar Islambekov, October 6, 2019
- 1. Dissecting Blockchain Price Analytics: What We Learn from Geometry of Ethereum Umar Islambekov (Bowling Green State University) joint work with Y. Li, C. Ak¸cora, E. Smirnova, Y. Gel and M. Kantarcıo˘glu October 6, 2019 SAMSI Blockchain Analytics Workshop Partially supported by NSF DMS 1736417, ECCS 1824710, and IIS 1633331 1/19
- 2. Overview Motivation Intro to Topological Data Analysis (TDA) Standard TDA pipeline Method of Persistence Homology Topological summaries TDA for price anomaly detection in Ethereum network Problem description and main idea Methodology Experimental results 2/19
- 3. Motivation. Challenges posed by Ethereum networks Ethereum transaction graphs are very sparse and dynamic. Conventional graph analytic tools may not be good indicators of token activity. Need to explore the link between token price dynamics and topological structure underlying the transaction graph. This structure can be described using TDA methods and incorporated into statistical models for price dynamics. 3/19
- 4. Standard TDA pipeline in applications 4/19
- 5. Simplicial complexes Definition 1 (Abstract simplicial complex) Let X be a discrete set. An abstract simplicial complex is a collection C of finite subsets of X such that if σ ∈ C then τ ∈ C for all τ ⊆ σ. If |σ| = p + 1 then σ is called a p-simplex. Simplicial complexes: are higher-dimensional generalizations of graphs, are both topological spaces and combinatorial objects. identify topological features such as connected components, loops and voids. have simplices as their building blocks. 5/19
- 6. Vietoris-Rips complex Vietoris-Rips (VR) is one of the most widely used simplicial complexes in applications. Definition 2 (Vietoris-Rips complex) Let X be a discrete set in a metric space (M, ρ). A Vietoris-Rips complex on X at scale ≥ 0 is defined as VR = {σ | ρ(xi , xj ) ≤ for all xi , xj ∈ σ} 6/19
- 8. Why nested family of simplicial complexes? The method of Persistence Homology Simplicial complexes are constructed from a certain procedure involving a scale parameter. A key to obtain useful topological information is to avoid a fixed value of the scale. Instead, choose a range of increasing scale parameters. Construct a simplicial complex for each scale and compute topological summaries. Keep track of topological features as they appear and disappear. Features persisting across many scales are likely to be true features. Features with short lifespans correspond to noise. 8/19
- 9. Persistence diagrams vs Betti sequences A persistence diagram (PD) is a multiset of paired scale values corresponding to the appearance and disappearance of topological features. Drawback: often cannot be directly incorporated into statistical or machine learning methods for further analysis of data. Betti sequences consist of the counts of topological features at increasing scale values. Advantage: can easily be used in a variety of settings such as statistical modeling, machine learning and functional data analysis. 9/19
- 11. TDA for price anomaly detection in Ethereum network Given: Time evolving transaction network of an Ethereum token and time series of the token price. Nodes are user addresses. Edge weights represent dissimilarity between nodes based on transaction amount. Goal: Predict days of future anomalous prices. Main idea: Identify anomalous price events through discerning changes in topology/geometry of the evolving network. 11/19
- 12. Notion of data depth Let X be a space of multivariate or functional data points (e.g., Rm or C([a, b])) Definition 3 (Data depth) With respect to a probability distribution P, a data depth function D : X → [0, 1] provides a center-outward ordering of points of X. There are several data depth functions that yield different such orderings. Highest depth values =⇒ most central points. Lowest depth values =⇒ most outlying points. 0 20 40 60 80 100 2.02.53.03.54.04.55.05.5 Modified Band Depth (MBD) deepest sample 12/19
- 13. Methodology Consider an evolving token transaction network over days t = 1, 2, . . . , T. Trim the network keeping only the top K nodes and compute the associated Betti sequences {βp,t}T t=1. Employ a concept of functional data depth to track changes in Betti sequences. Calculate the modified band depth (MBD) (Pintado and Romo, 2005) of each day’s Betti sequence with respect to those of past w days: RDw (βp,t) := MBD(βp,t|βp,t, βp,t−1, . . . βp,t−w+1). 13/19
- 14. Predictive machine learning models Model Explanation F : Input M1 Baseline Model PN, nE, nV , GC M2 Betti 0 PN, nE, nV , GC, RD7(β0) M3 Betti 0, 1 PN, nE, nV , GC, RD7(β0), RD7(β1) M4 Full model PN, nE, nV , GC, RD7(β0), . . . , RD7(β2) Token price return on day t: Rt = (Pt − Pt−1)/(Pt−1) . Normalized token open price: PNt = Pt/ max{P1, . . . , PTk }. # of edges: nEt; # of nodes: nVt. Average clustering coefficient: GCt. If |Rt| ≥ δ, δ > 0, then day t is considered as anomalous. Fit Random Forest models to data using 2/3 of a token’s lifetime for training, and the remaining 1/3 for testing. Examine performance for different prediction horizons h > 0. 14/19
- 15. Prediction results - Gain in accuracy 15/19
- 16. Gain in recall (sensitivity) 16/19
- 18. References Akcora C, Dey A, Gel Y, Kantarcioglu M, 2018. Forecasting bitcoin price with graph chainlets. In PaKDD, 765–776. Carlsson G, 2009. Topology and data. Bull. Amer. Math. Soc. (N.S.) 46(2): 255–308. Chazal F, Michel B, 2017. An introduction to topological data analysis: fundamental and practical aspects for data scientists. arXiv preprint arXiv:1710.04019 . Dey A, Akcora C, Gel Y, Kantarcioglu M, 2018. On the role of local blockchain network features in cryptocurrency price formation. Under Submission : 1–35. Maria C, Boissonnat J, Glisse M, Yvinec M, 2014. The gudhi library: Simplicial complexes and persistent homology. In Int. Congress on Mathematical Software, 167–174. Pintado S, Romo J, 2005. Depth-based classification for functional data 72. 18/19
- 19. Thank you very much for attending! 19/19