I develop and study universal deep learning models that leverage the infinite-dimensional curved geometries arising in stochastic finance.
A. Kratsios and L. Papon: Universal Approximation Theorems for Differentiable Geometric Deep Learning, JMLR - Journal of Machine Learning Research, 2022.
A. Kratsios, B. Zamanlooy, I. Dokmanic, T. Liu: Universal Approximation Under Constraints is Possible with Transformers, ICLR - International Conference on Learning Representations, 2022 Spotlight.
A. Kratsios and C. Hyndman: NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation, JMLR - Journal of Machine Learning Research, 2021.
A. Kratsios, S. Hou, P. Kassraie, J. Rothfuss, A. Krause: Instance-Dependent Generalization Bounds via Optimal Transport, 2022.
L. Galimberti, G. Livieri, A. Kratsios: Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis, 2022.
A. Acciaio, A. Kratsios, G. Pammer: Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer, (small revision), Mathematical Finance, 2022.
Primary Areas: Geometric deep learning, Approximation theory of neural networks. Applied Areas: Deep Learning in for Stochastic Analysis and in Finance.
A Kratsios, V Debarnot, I Dokmanić, 2022
A. Accaio, A. Kratsios and G. Pammer, (small revision) Mathematical Finance, 2022.
A. Kratsios and B. Zamanlooy, TMLR, 2022.
P. Casgrain and A. Kratsios, COLT, 2021.
L Galimberti, G Livieri, A Kratsios, 2022.
A. Kratsios and C. Hyndman, JMLR, 2021.
A. Kratsios, B. Zamanlooy, I. Dokmanic, T. Liu, ICLR (Spotlight), 2022
A. Kratsios and B. Zamanlooy, Neurocomputing, 2022.
S Hou, P Kassraie, A Kratsios, J Rothfuss, A Krause, 2022.
A. Kratsios, 2021.
LC Herrera, F Krach, A Kratsios, P Ruyssen, J Teichmann, 2021.
A. Kratsios, V. Debarnot, I. Dokmanić: Small Transformers Compute Universal Metric Embeddings, Submitted, 2022.
A. Kratsios and L. Papon: Universal Approximation Theorems for Differentiable Geometric Deep Learning, JMLR - Journal of Machine Learning Research, 2022.
A. Kratsios, B. Zamanlooy, I. Dokmanic, T. Liu: Universal Approximation Under Constraints is Possible with Transformers, ICLR - International Conference on Learning Representations, 2022 Spotlight.
T. Liu, C. Shi, A. Kratsios, I. Dokmanic: SinkGAT: Doubly-Stochastic Graph Attention, SLowDNN, 2022.
A. Kratsios and C. Hyndman: NEU: A Meta-Algorithm for Universal UAP-Invariant Feature Representation, JMLR - Journal of Machine Learning Research, 2021.
A. Kratsios: Universal Regular Conditional Distributions, Submitted, 2021.
A. Kratsios and E. Bilokopytov: Non-Euclidean Universal Approximation, NeurIPS - 33rd Conference on Neural Information Processing Systems, 2020.
C. Herrera, F. Krach, A. Kratsios, P. Ruyssen, J. Teichmann Denise: Deep Robust Principal Component Analysis for Positive Semidefinite Matrices, Submittted, 2020.
Approximation Theory of (Euclidean) Deep Neural NetworksA. Kratsios and B. Zamanlooy: Do ReLU Networks Have An Edge When Approximating Compactly-Supported Functions?, Transactions on Machine Learning Research, 2022.
A. Kratsios and B. Zamanlooy: Learning Sub-Patterns in Piece-Wise Continuous Functions, Neurocomputing, 2022.
A. Kratsios: The Universal Approximation Property, Annals of Mathematics and Artificial Intelligence, 2021.
Statistical Learning TheoryA. Kratsios, S. Hou, P. Kassraie, J. Rothfuss, A. Krause Instance-Dependent Generalization Bounds via Optimal Transport, Submitted, 2022.
Foundations of Deep Learning for Stochastic FinanceA. Accaio, A. Kratsios, and G. Pammer Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer, (Revision) Mathematical Finance, 2022.
L. Galimberti, G. Livieri, A. Kratsios Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis, Submitted, 2022.
A. Kratsios and C. HyndmanDeep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization, Risks, Special Issue: Machine Learning in Finance, Insurance and Risk Management, 2020.
A. Kratsios, et al.Replication of a Real-Estate Market Index (Teranet – National Bank of Canada), Huitième Atelier De Résolution De Problèmes Industriels De Montréal, CRM, 2017.
Stochastic Control and OptimizationP. Casgrain and A. KratsiosOptimizing Optimizers: Regret-optimal gradient descent algorithms, (COLT) Conference on Learning Theory, 34, 2021.
C. Hyndman, A. Kratsios, and R. Wang. The Entropic Measure Transform, The Canadian Journal of Statistics, 2020.
Homological Algebra and Non-Commutative GeometryA. KratsiosLower-Estimates on the Hochschild (Co)Homological Dimension of Commutative Algebras and Applications to Smooth Affine Schemes and Quasi-Free Algebras, Mathematics, Special Issue: New Trends in Algebraic Geometry and Its Applications, 2021.