Paper uses Chebyshev Tensors for accurate dynamic sensitivities and ISDA SIMM computation.
problem Computing dynamic sensitivities and initial margin for financial instruments.
method Uses Chebyshev Tensors in Monte Carlo simulations to compute dynamic sensitivities and ISDA SIMM.
result High accuracy and computational gains for FX swaps and Spread Options.
Study on neuron dynamics for XOR classification with zero-margin.
problem Understanding neural network training dynamics in zero-margin classification problems.
method Analysis of Gaussian XOR problem, focusing on neuron block dynamics and generalization without margin assumptions.
result Neurons cluster into four directions and block-level signals evolve coherently, essential for reliable prediction in the Gaussian setting.
Margin enlargement over training data has been an important strategy since perceptrons in machine learning for the purpose of boosting the robustness of classifiers toward a good generalization ability. Yet Breiman (1999) showed a dilemma that a uniform improvement on margin distribution does NOT necessarily reduces ge…
Algorithm learns dynamics from past observations.
problem Learning a nonlinear dynamical system.
method Spectral filtering, online convex optimization.
result Vanishing prediction error for marginally stable systems.
DGNN predicts financial margin calls under stress tests.
problem Forecasting margin calls in dynamic financial networks.
method Dynamic Graph Neural Network (DGNN) architecture.
result DGNN produces accurate forecasts up to 21 days.
Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose both theoretical and practical challenges to statistical machine learning algori…
Study of marginally trapped surfaces in a perturbed Schwarzschild spacetime.
problem Understanding marginally trapped surfaces in perturbed Schwarzschild spacetime.
method Developed a method to study spacelike surfaces in a double null coordinate system.
result For every incoming null hypersurface nearly spherically symmetric, there exists a unique embedded marginally trapped surface.
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
New insights into using IPF for inferring dynamic networks from marginals.
problem Inferring dynamic networks from time-aggregated adjacency matrices and time-varying marginals.
method Identifying a generative network model and establishing its maximum likelihood estimates via IPF, with convergence guarantees for sparse data.
result IPF provides principled estimation of dynamic networks from marginals under certain conditions, with structure-dependent error bounds and guaranteed convergence for sparse data.
ITF improves DSR but inflates curvature, while marginal likelihood reduces it, affecting QoIs.
problem Curvature mismatch between teacher forcing and marginal likelihood in chaotic dynamical systems.
method Comparing objective-induced curvatures of ITF and marginal likelihood in a probabilistic switching augmentation of AL-RNNs.
result Curvature inflation by ITF and reduction by marginal likelihood affect dynamical quantities of interest.
Both in practice and in the academic literature, models for setting margin requirements in futures markets classically use daily closing price changes. However, as well documented by research on high-frequency data, financial markets have recently shown high intraday volatility, which could bring more risk than expecte…
3MSBM learns smooth trajectories from multiple snapshots.
problem Capturing long-range temporal dependencies in complex systems.
method Lifts dynamics to phase space, generalizes stochastic bridges to multi-marginal conditional problems, learns transport maps preserving intermediate marginals.
result Significantly improves convergence and scalability in capturing complex dynamics.
MSBM extends SB for multi-marginal trajectory inference.
problem Trajectory inference from multiple discrete snapshots.
method Multi-Marginal Schrödinger Bridge Matching (MSBM) using iterative Markovian fitting (IMF).
result MSBM effectively captures complex trajectories and respects intermediate distributions.
The paper defines marginal tubes and proves their null nature.
problem Understanding the geometry of spacelike surfaces in spacetimes.
method Introducing marginal tubes and studying spacelike surfaces with double null coordinates.
result If every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null.
SGD converges to critical points of normalized margin in late-stage training for homogeneous neural networks.
problem Analyzing the implicit bias of SGD on homogeneous neural networks.
method Interpreting SGD dynamics as an Euler-like discretization of a conservative field flow associated with the normalized classification margin.
result Normalized SGD iterates converge to the set of critical points of the normalized margin at late-stage training.
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature of a slice containing the surface. These estimates are well adapted to situatio…
Framework learns stochastic dynamics from endpoint and intermediate distributions using soft energy constraints.
problem Learning stochastic dynamics from endpoint and intermediate distributional observations.
method Formulates generation as a McKean-Vlasov control problem with soft energy constraints, solving it through FBSDE.
result Model learns coherent stochastic trajectories matching prescribed marginal laws.
We present two methods, based on Chebyshev tensors, to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. These methods are implemented and run in a Monte Carlo engine to compute Dynamic Initial Margin as defined by ISDA (SIMM). We show that the levels of accuracy, speed and impleme…
A new algorithm reconstructs population dynamics from coarse samples.
problem Reconstructing population dynamics from unlabeled samples at coarse time intervals.
method Deep Momentum Multi-Marginal Schrödinger Bridge (DMSB) framework.
result Significantly outperforms baselines in synthetic and real-world datasets.
AIS uses a suboptimal extended target distribution, which this paper improves using SGM.
problem Improving the efficiency of Annealed Importance Sampling for marginal likelihood estimation.
method Leveraging score-based generative modeling to approximate the optimal extended target distribution.
result Demonstrated novel, differentiable AIS procedures on synthetic and real-world data.
Proposes a new distance metric for multi-marginal optimal transport.
problem Computational scalability in multi-marginal optimal transport.
method Random one-dimensional projections to construct sliced multi-marginal Wasserstein distance.
result Sliced multi-marginal Wasserstein distance is a metric with dimension-free sample complexity.
This work reduces DIM computation costs by training neural networks on single MC paths.
problem Training neural networks for Dynamic Initial Margin (DIM) computation in counterparty credit risk.
method Constructing a training dataset with noisy but unbiased DIM samples from single MC paths, employing a multi-output neural network structure.
result The approach reduces dataset generation cost to a single MC execution and validates its general applicability and efficiency.
New method identifies drift and diffusivity from SDE marginals.
problem Challenging task to identify drift and diffusion from SDE population dynamics.
method Proposes nn-APPEX, a Schrodinger Bridge-based inference method.
result Gradient-flow drift and Brownian diffusivity jointly identifiable from marginals.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
New insights into deep learning: reducing training data significantly improves performance.
problem Understanding and improving generalization in deep learning models.
method Analyzing the distribution of classification margins and dynamically reducing the training set.
result The area under the curve of the margin distribution is a good measure of generalization.
New method detects metastable basins in high dimensions using trajectory sampling.
problem Identifying distinct basins in high-dimensional Markov processes.
method Discriminative approach based on marginal trajectory distribution comparison.
result Bayes-optimal classifier achieves high accuracy distinguishing between basins.
New method learns flows between multiple distributions efficiently.
problem Learning dynamic transport maps between multiple empirical distributions.
method Combining flow matching and dynamic optimal transport with potential terms.
result OTP-FM achieves state-of-the-art performance on various datasets.
NDDV estimates data point value from a single stochastic trajectory.
problem Estimating marginal contributions of data points over stochastic training paths.
method Introduces Neural Dynamic Data Valuation (NDDV) using stochastic state and adjoint equations.
result NDDV provides a one-run, trajectory-conditioned estimator of data point value.
We analyze the counterparty risk embedded in CDS contracts, in presence of a bilateral margin agreement. First, we investigate the pricing of collateralized counterparty risk and we derive the bilateral Credit Valuation Adjustment (CVA), unilateral Credit Valuation Adjustment (UCVA) and Debt Valuation Adjustment (DVA).…
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theor…
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
problem Understanding the convergence of marginal distributions in mean field dynamics.
method Assumed functional convexity of energy, used Lp-convergence and Wasserstein metrics. result Uniform-in-time propagation of chaos proved in both L2-Wasserstein and relative entropy. The study tests a functional-form restriction on risk exposure dynamics using margin debt data.
problem Understanding risk exposure dynamics under capital constraints and slack.
method Testing a regime-conditional functional-form restriction on aggregate risk-exposure dynamics implied by VaR-constrained intermediary models.
result The contraction and growth of exposures under capital constraints and slack are observed and tested.
Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important anytime properties such as: 1) providing accurate and consistent mar…
Transfer learning aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Since the source and the target domains are usually from different distributions, existing methods mainly focus on adapting the cross-domain marginal or conditional distributions. However, in real appl…
We obtain bounds on the distribution of the maximum of a martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to n-marginal Skorokhod embedding problem in Obłój and Spoida [An iterated Azéma-Yor type embedding for finitely many marginals (2013) Preprint]…
A new algorithm estimates aggregate marginals from noisy data in an online manner.
problem Estimating aggregate marginals of a Markov chain from noisy aggregate observations.
method Sliding window Sinkhorn belief propagation (SW-SBP) algorithm.
result Demonstrated improved performance on inferring population flow.
Paper tackles dynamic label shift in online learning, achieving optimal performance.
problem Adapting to changing class marginals in online supervised and unsupervised learning.
method Develops novel algorithms reducing adaptation to online regression, achieving optimal dynamic regret.
result Achieves superior performance in various online label shift scenarios.
Generative adversarial network for probabilistic forecasting of random systems.
problem Forecasting random dynamical systems without distributional assumptions.
method Recurrent neural network and generative adversarial network (GAN) with regularization based on maximum mean discrepancy (MMD).
result The proposed model successfully forecasts complex stochastic processes with multiple-step predictions.
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an initial condition and view the problem as a stochastic control problem; we esta…
TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.
problem Optimal transport with multiple marginals and tree-structured quadratic costs.
method Tree-based Diffusion Schrödinger Bridge (TreeDSB) for continuous and dynamic solutions.
result TreeDSB efficiently computes Wasserstein barycenters in high dimensions.
Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework, the dimension of the target distribution grows with each time step, thus it is nec…
Improved forecasting of financial risk using Diffusion-Copula framework.
problem Capturing complex, asymmetric dependence structures in financial markets.
method Explicitly decouples marginal distribution learning from dependence structure using Mixture Density Networks and Classification-Diffusion Copula.
result Superior performance in forecasting systemic extremes of marginal and joint events.
The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that a classical form of norm control -- but kind of hidden -- is present in deep net…
This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize…
Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field approaches have been used. However, mean field approximations assume a factorized di…
This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equa- tion, while the latter exploits a suitable kernel function. We provide an extensive comparison …
New method controls linear systems with partial info and disturbances.
problem Controlling linear dynamical systems under partial observation and adversarial disturbances.
method Double Spectral Control (DSC) using two-level spectral approximation strategy.
result Matches best known regret guarantees with exponential runtime improvement.
We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replicatio…