SAFE AI: Stability Analysis for Financial Engineering & Artificial Intelligence

▶ SAFE AI aims at designing truly safe AI systems that are ethically fair, privacy & security assured, algorithmically stable, and interpretable to humans.

AI Safety (2005-)

Stable Machine Learning (2005-)

– Machine Learning is the study of designing and implementing algorithms that is able to extract knowledge or hypothesis from data and to make predictions on data. Such algorithms operate by building a statistical model trained from data in order to make data-driven predictions or decisions, rather than following a given static program instructions.

▶ Multi-basin systems(MBS) for Stable Machine Learning

– Stability analysis of multi-basin systems (MBS) with toolkits from differential/algebraic topology and differential geometry can be applied to developing efficient and stable machine learning models.
-Our algorithms for unsupervised, supervised, and semi-supervise learning: 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-support vector domain description, Ranking-SVDD, Equilibrium-based SVM for semi-supervised classification, Multi-basin kernels for dynamic pattern denoising, Sparse kernel machines using attractors, and etc.

▶ 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
-Our algorithms to find an effective and stable low-dimensional structure in high-dimensional space: Sequential manifold learning, Semi-supervised nonlinear dimensionality reduction, Nonlinear dynamic projection for noise reduction of dispersed manifolds.

▶ Complexity Analysis for Machine Learning (2005- )

– Study of designing and analyzing stable machine learning algorithms that can lead to a better generalization:

  • empirical risk minimization is prone to overfitting, a trade-off between the sample size and the model complexity .

– Generalization Error =Random Error + Training Error + Model Instability + Domain Error

– Generalization error bound under the PAC (Probably Approximately Correct) learning framework

Finance and Blockchain (2007-)

-Financial Technology (or Financial Engineering)  is the design, development and implementation of innovative financial products, processes, or business models in the financial services such as derivatives  markets, cryptocurrency markets, and blockchain.
-Computational Finance/ Financial technology provides tractable solutions to problems in financial technology using a wide variety of advanced computing technologies and financial modeling techniques.

▶ Stable Model Calibration in Asset Pricing

– Stability analysis for nonlinear optimization can be applied to developing efficient and stable calibration methods of financial models with jumps and machine learning models in asset pricing
– Financial Models (with jumps): Black-Sholes Models, Affine Jump Diffusion Models, Infinite Activity Levy Process Models, Local Volatility Models, GARCH models, and etc.
– Option pricing of financial models with a given parameter set using FDM, MC, FFT, and etc.
– Stable calibration of the financial option model to market data under risk-neutral measure Q,
– Machine learning models for predicting European/ American options, volatilities, and credit derivatives.
– Filtering under real-world measure P, and risk management

▶ AI Strategies for Stable Asset Management

– Many traders use non-economic numeric data such as new, blogs, sentiments more to forecast their portfolio and predict various economic and financial variables.
– Machine learning models construct a financial predictor from the large structured financial data and non-structured data.
– Our research focus is on developing AI strategies for stable asset management under Black–Litterman framework.

▶ AI applications to Blockchain and Cyptocurrency Markets

-The cryptocurrency market refers to the decentralized cryptocurrency market produced by the entire cryptocurrency system collectively, based on the Blockchain technical system.
– Our research focus is on the AI applications to Blockchain and cryptocurrency markets.

▶ Data Mining Applications

-Data mining is the automatic or semi-automatic process of large volumes data to extract previously unknown, interesting patterns and knowledge.
-Our applications focus on: Churn prediction, Sentiment analysis, Collaborative filtering, Image recognition, Text mining, and etc.

Stability Analysis (1999-)

▶ Stability Analysis for Nonlinear Systems ( -2005)
– Study of the long-term behavior of evolutionary nonlinear systems.
– Determine stability regions (basins of attraction) of nonlinear dynamical systems.
– Transient Stability Analysis (TSA): The problem of determining whether or not the current operating point is lying inside the stability region of a desired stable equilibrium point.

▶ Stability Analysis for Nonlinear Optimization ( -2007)

– Develop novel deterministic methods for systematically computing multiple optimal solutions of general nonconvex optimization problems.

–  Convergence analysis for 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.