Authors adapt Tannakian approach to reduce equivariant principal bundles.
problem Dimensional reduction of holomorphic principal bundles over complex projective manifolds.
method Adapt Tannakian approach to equivariant principal bundles.
result Established Hitchin--Kobayashi type correspondence for dimensional reduction.
Two new approaches to Tannakian Galois groups of holonomic D-modules.
problem Understanding Tannakian Galois groups of holonomic D-modules on abelian varieties.
method Interpreting in terms of principal bundles and constructing a microlocalization functor.
result Explains the ubiquity of minuscule representations and provides bounds for decompositions.
Study of Tannakian categories for integrable connections on Kaehler manifolds.
problem Understanding Tannakian categories for integrable connections on Kaehler manifolds.
method Analyzing pairs (E, D) where E is a trivial holomorphic vector bundle and D is an integrable holomorphic connection.
result The pro-algebraic affine group scheme uniquely determines the isomorphism class of compact Riemann surfaces.
The paper uses Tannakian reconstruction to understand hyperbolic log-orbi curves.
problem Understanding the structure of hyperbolic log-orbi curves.
method Formulates hyperbolic uniformization as a Tannakian reconstruction theorem and constructs a canonical maximal parahoric PSL2-Higgs object.
result Reconstructs the absolute Galois group of a one-variable complex function field as the inverse limit of etale fundamental groups of orbifold models.
The paper classifies Lie algebroids and their connections, modulating principal objects.
problem Classifying and studying Lie algebroids and their connections.
method Classifying integrable transitive Lie algebroids, introducing Higgs bundles, and using Tannakian categories.
result Moduli spaces of principal \(G\)-bundles and Higgs bundles are semiprojective varieties.
The study constructs differential systems on Riemann surfaces and explores their monodromy properties.
problem Constructing holomorphic differential systems with specific monodromy properties.
method Exploring the monodromy of holomorphic differential systems on Riemann surfaces.
result Holomorphic maps from Riemann surfaces to quotient spaces exist without factoring through elliptic curves.
We look into a construction of principal abelian varieties attached to certain spin manifolds, due to Witten and Moore-Witten around 2000 and try to place it in a broader framework. This is related to Weil intermediate Jacobians but it also suggests to associate abelian varieties to polarized even weight Hodge structur…
Geometric approach combines asset returns and investor views for better portfolio optimization.
problem Optimizing portfolios with investor-specific views.
method Generalized Wasserstein barycenter (GWB) to integrate statistical asset returns and investor views.
result The geometric approach offers more flexibility and rewards for correct investor views.
We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…
Paper proposes an alternative method to price American options using HJM approach.
problem Price American options efficiently and accurately.
method Utilizes HJM technique to model term structure of volatility for equity markets.
result Proposes a new value function, stopping criteria, and stopping time for American options.
Quantum machine learning: Adiabatic quantum SVM outperforms classical methods.
problem Training support vector machines efficiently on large datasets.
method Adiabatic quantum computing for SVM training.
result Quantum approach outperforms classical methods in accuracy and scalability.
Develops a semi-analytic method for auto-callable accrual notes valuation.
problem Valuation of auto-callable structures with accrual features subject to barrier conditions.
method Extends recent studies of multi-assessed binaries to time-dependent parameters, using a semi-analytic approach.
result The semi-analytic approach is more advantageous for high precision valuation compared to Monte Carlo methods.
Two ML approaches learn local volatility surfaces from option prices, with GP being arbitrage-free.
problem Interpolating European vanilla option prices to create a local volatility surface.
method Gaussian process regression and neural net with arbitrage penalties.
result GP approach is arbitrage-free and yields best out-of-sample calibration error.
This paper critiques the Standardized Measurement Approach (SMA) for operational risk and recommends maintaining Advanced Measurement Approach (AMA).
problem Weaknesses and failures of the Standardized Measurement Approach (SMA) in operational risk.
method Critical review and analysis of SMA and AMA approaches.
result SMA is unstable, insensitive to risk, and implicitly related to systemic risk in the banking sector.
A new Euclidean approach reveals the pentagram map's beauty.
problem Exploring the pentagram map through classical geometry.
method Introducing an alternative Euclidean approach.
result Demonstrates the pentagram map's elegance through classical geometry.
New approach predicts credit default using machine learning and heuristics.
problem Predicting credit default in large datasets with dynamic nature.
method Combined heuristic and machine learning approaches.
result Approaches outperform existing state-of-the-art methods.
Two approaches extend knowledge distillation to Gaussian Processes, showing relationships to existing methods.
problem Applying knowledge distillation to Gaussian Processes for regression and classification.
method Data-centric and distribution-centric approaches to extend distillation to GPR and GPC.
result Distribution-centric approach for GPC approximately corresponds to data duplication and scaling.
Online boosting method improves weak to strong learner.
problem Online learning of weak to strong learner.
method Extends batch GentleAdaBoost to online approach with line search.
result Online boosting performs better than other methods.
Classical approaches to isometric embedding simplified.
problem Isometric embedding of Riemannian surfaces in Euclidean 3-space.
method Coordinate-based and moving-frames approaches, focusing on integrability of PDEs.
result The integrability of the PDE is surprisingly easy and related to moving frames approach.
Two new methods for option pricing without or with a riskless asset.
problem Traditional option pricing methods require a riskless asset and may not be market-complete.
method Develops two approaches: one without a riskless asset and one with.
result Both methods produce the same option prices as classical approaches.
An integrated and extendable approach for stress-testing loan portfolios
problem Stress-testing loan portfolios
method Simulate completed portfolios, generate uncertain cash flow history, compute credit risk metrics
result Enhanced stress-testing practices within any bank
Bayesian symbolic regression automates model discovery from data.
problem Learning closed-form mathematical models from data using heuristic methods.
method Probabilistic approach to symbolic regression, connecting to information theory and statistical physics.
result Probabilistic approach provides model plausibility and performance guarantees.
Extended Blackwell approachability to quitting games, providing conditions for weak approachability.
problem Designing strategies for repeated games with quitting actions.
method Extending Blackwell approachability to generalized quitting games and providing geometric conditions.
result Characterization of weak approachability in quitting games, proving equivalence and full characterization.
Paper compares neural network approaches to Optimal Transport.
problem Learning Optimal Maps between probability distributions.
method Two categories of approaches: heuristic and math-justified. Novel approach involves dynamic flows and supervised learning.
result Novel approach involving dynamic flows and reductions of Optimal Transport to supervised learning.
New approach interprets Nyström for kernel machines with geometric insight.
problem No comparative study over Nyström-based kernel machine approaches.
method Developed a new approach with geometric interpretation, showing equivalence to existing methods.
result Proposed approach offers insights into approximation errors and accuracy.
Common Representation Learning (CRL), wherein different descriptions (or views) of the data are embedded in a common subspace, is receiving a lot of attention recently. Two popular paradigms here are Canonical Correlation Analysis (CCA) based approaches and Autoencoder (AE) based approaches. CCA based approaches learn …
Two approaches detect EV charging patterns at stations.
problem Identify charging patterns at electric vehicle charging stations.
method Two approaches: rule-based and hierarchical clustering.
result Hierarchical clustering revealed unexpected charging patterns.
The paper critiques the Standardized Measurement Approach for operational risk and advocates for maintaining the Advanced Measurement Approach.
problem The weaknesses and pitfalls of the Standardized Measurement Approach for operational risk.
method Discussion and study of the weaknesses and pitfalls of the Standardized Measurement Approach.
result Advocates for maintaining the Advanced Measurement Approach and suggests standardization recommendations.
Deep learning outperforms classic machine learning in DAS event detection.
problem Event detection in Distributed Acoustic Sensing (DAS).
method Comparison of classic machine learning and image-based deep learning approaches.
result Image-based deep learning offers significantly faster event detection and execution times.
Survey on methods to learn graph data representations.
problem Designing optimal Neural Network architectures for arbitrary graphs.
method Review of graph kernel methods, convolutional approaches, graph neural networks, graph embedding, and probabilistic approaches.
result Discussion of various methods for learning graph data representations.
Proposes ACP for efficient inference in noisy-or models.
problem Efficient inference in noisy-or models.
method Hybrid approach combining classical and modern variational inference.
result ACP outperforms or matches other approaches in noisy-or models.
Paper evaluates CNN-based facial landmark detection methods.
problem Evaluate characteristics and performance of CNN-based facial landmark detection methods.
method Divided into regression and heatmap approaches, investigated using a hybrid loss function and discrimination network.
result Proposed model outperforms other models in all tested datasets.
This paper provides a comprehensive benchmark and taxonomy for certifiably robust DNN defenses.
problem Certifiably robust defenses against adversarial attacks for deep neural networks.
method Taxonomy and benchmark of certifiably robust approaches.
result First comprehensive benchmark of certifiably robust approaches on different datasets.
Unified approach for Bayesian optimal experiment design using stochastic gradients.
problem Designing optimal experiments in high-dimensional settings.
method Stochastic gradient ascent to optimize variational lower bounds on expected information gain.
result Unified approach outperforms existing methods in higher dimensions.
VB approach for dynamic network models improves efficiency and accuracy.
problem Estimating dynamic network models in large-scale systems.
method Variational Bayesian inference for network autoregression.
result VB approach detects proper active structures and achieves similar or better accuracy.
Randomized exploration methods are more statistically efficient than optimistic methods in reinforcement learning.
problem Comparing and contrasting optimistic and randomized exploration methods in reinforcement learning.
method Analytic examples to compare optimistic and randomized approaches.
result Randomized approaches are more statistically efficient than optimistic approaches.
FSMJ selects features with JS-divergence for text categorization.
problem Feature selection for text categorization.
method Greedy feature selection based on Jensen-Shannon divergence for real-valued features.
result FSMJ outperforms state-of-the-art methods in text categorization experiments.
The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
New approach for prudent risk evaluation using model aggregation.
problem Risk evaluation and optimization under uncertainty.
method Model Aggregation (MA) approach based on stochastic dominance.
result Produces robust risk evaluation and distributional models.
Study examines the scenario approach for robust optimization, focusing on nonconvex cases.
problem Robust optimization with nonconvex uncertainty sets.
method Scenario approach via i.i.d sampling, analysis of concentration of measures, asymptotic and finite sample guarantees.
result Obstruction to consistency in noncompact decision sets, finite sample guarantees for nonconvex problems.
Study proposes a new approach for deep hedging using artificial market simulations.
problem Challenges in selecting the best model for underlying asset simulations in deep hedging.
method Proposes artificial market simulations to replicate financial market stylized facts.
result Achieves similar performance to traditional approaches without mathematical finance models.
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, …
This paper examines how optimization methods affect the reliability of detecting inputs outside a model's training distribution.
problem The unreliability of deep neural networks on out-of-distribution inputs.
method Analysis of optimization methods' impact on OOD detection approaches.
result Optimization methods significantly influence the robustness of OOD detection approaches.
In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is guaranteed to be unique. The proposed approaches can automatically estimate the numb…
Optimal sample complexity analysis for plug-in approach in average-reward MDPs.
problem Learning optimal policies in average-reward MDPs with a generative model.
method Plug-in approach that constructs a model estimate and computes an optimal policy.
result Optimal sample complexities for the plug-in approach without prior knowledge of problem parameters.
New approach for structured prediction problems using regularization.
problem Structured prediction problems with embedded outputs in linear space.
method Surrogate loss approach and regularization techniques.
result Universal consistency and finite sample bounds for the proposed methods.
We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long as the dataset is not split across too many machines. We also extend the approach…
Study systemic risk measures and capital allocation rules, showing commonalities.
problem Systemic risk measures and capital allocation in financial systems.
method Developed a general framework to embed axiomatic and injective capital approaches, introduced Aumann-Shapley CAR.
result Aumann-Shapley CAR provides a universal method for capital allocation regardless of risk measurement.