Adversarial Machine Learning

• the study of the attacks on AI algorithms, and of the defenses against such attacks.

Source: I. J. Goodfellow, J. Shlens, and C. Szegedy, “Explaining and harnessing adversarial examples

• Attacks: evasion attacks (attack on the learned model), data poisoning attacks(attack on the learning process), Byzantine attacks and model extraction…

Adversarial Example: FGSM, BIM, PGD, CW, MIM, EAD, ZOO …

• Defenses: Detecting and mitigating potential adversarial threats → Make model robust!

Defensive distillation, Adversarial training, and …

• Verification: Provable  robustness assessment and  quantification

Source: Adversarial Machine Learning for *Good by Pin-Yu Chen*

• [S Lee, J Lee, S Park*, 2020], [H Kim, W Lee, J Lee, 2021], [S Lee, W Lee, J Park, J Lee, 2021], [J Byun, W Lee, J Lee, 2021], [S Lee, H Kim, J Lee, 2022], [H Kim, J Park, J Lee, 2023], [S Lee, J Park, J Lee, 2023], [H Kim, W Lee, S Lee, J Lee, 2023]

Privacy-preserving AI techniques

• Homomorphic Encryption (HE)

  • A form of encryption with an additional evaluation capability for computing over encrypted data without access to the secret key ****

  • We aim to develop HE-friendly AI algorithms that are both efficient and free from specific parameter requirements, suitable for implementation with any commonly used HE scheme.

[S Park, J Lee, JH Cheon, J Lee, J Kim, J Byun, 2019], [S Park, J Byun, J Lee, JH Cheon, J Lee, 2020], [J Byun, J Lee, S Park, 2021], [J Byun, S Park, Y Choi, J Lee, 2023], [J Byun, H Ko, J Lee, 2023] 

• Differential Privacy

  • Designed in such a way that the outputs of a data analysis do not reveal whether a specific individual's information has been utilized in the analysis and formation of those results.

  • Stability analysis and statistical error bound analysis can help safeguarding the identity of individuals with private data and privacy concerns, particularly in large databases.

[J Park, Y Choi, J Byun, J Lee, S Park*, 2023], [J Park, H Kim, Y Choi, J Lee, 2023], [J Byun, J Lee, 2023] 

Blockchain and DeFi Markets

• Blockchain is an open, distributed ledger that can record transactions between two parties efficiently and in a verifiable and permanent way.

• Decentralized finance (DeFi) aims to create an open, permissionless, and highly interoperable financial ecosystem using smart contracts on blockchains, primarily Ethereum, to provide financial instruments without central intermediaries.

[H Ko, B Son, Y Lee, H Jang, J Lee, 2022], [S Lee, J Lee, Y Lee, 2023], [S Park, S Lee, Y Lee, H Ko, B Son, J Lee, H Jang, 2023]

By Fabian Schär - https://research.stlouisfed.org/publications/review/2021/02/05/decentralized-finance-on-blockchain-and-smart-contract-based-financial-markets, CC BY-SA 4.0,

• Cryptocurrencey
  [H Jang, J Lee, 2018], [S Pyo, J Lee, 2020]

• CBDC: Atomic cross-chain settlement model for central banks digital currency
  [Y Lee, B Son, H Jang, J Byun, T Yoon, J Lee, 2021]

Risk and portfolio management: the P world

• Modeling the statistically derived 'real' probability measure P of market prices for assets at a future investment horizon enables the buy-side community to make informed decisions on security purchases to enhance their portfolio's profit-and-loss profile. With the advent of AI, more and more of this process is being automated.

Derivatives Pricing: the Q world

• Derivatives pricing, a complex extrapolation exercise used by the sell-side community, aims to establish a fair, arbitrage-free price for a claim based on the prices of more liquid underlying securities determined by supply and demand, using a risk-neutral measure Q equivalent to the real probability measure, P.

• Econometric models (with jumps) widely used in derivative pricing include Black-Sholes Models, Affine Jump Diffusion Models, Infinite Activity Levy Process Models, Local Volatility Models, GARCH models, and etc.

• Stability analysis for nonlinear optimization can be applied to developing efficient and stable calibration of the financial models with jumps to market data under risk-neutral measure Q.
  [S Yang, Y Lee, G Oh, J Lee, 2011], [S Yang, J Lee, 2012], [J Lee, Y Lee, 2013], [N Kim, J Lee, 2013], [S Yang, J Lee, 2014], [J Lee, Y Lee, 2015]

• Machine learning (ML) is the study of designing and implementing statistical algorithms that can learn from data and generalize to unseen data, extract knowledge or hypothesis from data, make predictions on data, and perform tasks without explicit instructions.

• Stability analysis of multi-basin systems (MBS) with toolkits from differential/algebraic topology and dynamical systems can be applied to developing efficient and stable machine learning models.

Stable Clustering

• The clustering algorithm consists of three steps: (i) construct a support function f that estimates the support of a given data distribution; (ii) construct an MBS associated with f to decompose the data space into several disjoint groups, each represented by a stable equilibrium vector (SEV); and (iii) label each data into a cluster based on the similarity or connectivity of the topological graph of the constructed SEV.

• Equilibrium-based support vector clustering, Multi-basin support-based clustering, Gaussian processes clustering, Fast support-based clustering, Dynamic and hierarchical support-based clustering, Voronoi cell-based clustering using a kernel support, Multi-basin kernels for dynamic pattern denoising.

• [J Lee, D Lee, 2005], [J Lee, D Lee, 2006], [HC Kim, J Lee, 2007], [D Lee, J Lee, 2010], [KH Jung, D Lee, J Lee, 2010], [KH Jung, N Kim, J Lee, 2011], [K Kim, Y Son, J Lee, 2014], [Y Son, S Lee, S Park, J Lee, 2018]

Stable Manifold Learning

• Many practical high-dimensional real data such as images are often confined to a region of the space having lower effective dimension

• The algorithms aim to find effective and stable low-dimensional structures in high-dimensional data spaces: Sequential manifold learning, Semi-supervised nonlinear dimensionality reduction, Nonlinear dynamic projection for noise reduction of dispersed manifolds.

• [K Kim, J Lee, 2014], [S Park, W Lee, J Lee, 2019], [S Park, J Lee, K Kim*, 2019], [S Park, J Lee, 2020]

Dynamical Systems

• Study of the long-term behavior of evolutionary nonlinear systems.

• Deterministic Differential Equation

The laws of Nature are expressed by differential equations, so it is useful to solve differential equations - Isaac Newton

Stochastic Differential Equation 

The laws of artificial systems (financial systems & artificial intelligence systems) can be expressed by (stochastic) differential equations, so it is useful to apply (stochastic) dynamical systems approach to analyze and stabilize artificial systems – J. Lee.

Convergence Analysis for Nonlinear Optimization (1999-2007)

• Convergence analysis for nonlinear optimization := Stability analysis for nonlinear systems

• The construction of the multi-basin systems (MBS) ,i.e. completely stable dynamical systems on manifolds, associated with objective function and/or constraint functions can be applied to developing efficient numerical methods towards global optimization as well as to establishing theoretical foundations of them.
  [J Lee, HD Chiang, 2001b], [J Lee, HD Chiang, 2002], [J Lee, HD Chiang, 2004], [J Lee, 2005]

• Develop novel deterministic methods for systematically computing multiple optimal solutions of general nonconvex optimization problems.
  [J Lee, HD Chiang, 2001a], [J Lee, HD Chiang, 2004], [J Lee, 2007]

Stability Analysis for Nonlinear Systems (1997-2005)

• Study of the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.