The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice mod…
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48 results for “path choice”
The study compares different game-theoretic attribution methods and finds that interventional Shapley values yield less consistent results than Aumann-Shapley due to path symmetry.
problem Investigating the influence of path choice on game-theoretic attribution algorithms.
method Comparative analysis of interventional Shapley values and Generalized Integrated Gradients (GIG) methods.
result Interventional Shapley values yield less consistent attributions than Aumann-Shapley due to path symmetry and extended away from the training data manifold.
New methods improve Monte Carlo estimation of partition functions.
problem Estimating the normalization constant of complex distributions.
method Annealing through paths of distributions to estimate partition functions.
result Optimal path for estimation is arithmetic, improving efficiency.
New probability path model improves flow matching forecasting performance.
problem Impact of probability path model selection on flow matching forecasting performance.
method Proposed a novel probability path model designed to improve forecasting performance.
result Our model achieves faster convergence during training and improved predictive performance compared to existing models.
A large GPS dataset reveals that a single route often covers 60% of travel observations.
problem Limited insights from small GPS datasets on route choice behavior.
method Evaluation of path generation algorithms including link penalty, link elimination, simulation, and via-node methods.
result Modified link penalty method achieves 97% coverage, significantly higher than previous studies.
Simultaneously estimates travel times and route choice model parameters.
problem Interdependent estimation of arc travel times and route choice model parameters.
method Maximum likelihood estimation for any differentiable route choice model.
result Strong performance in real-world data, even compared to arc travel time estimation methods.
We revisit the choice of SGD for training deep neural networks by reconsidering the appropriate geometry in which to optimize the weights. We argue for a geometry invariant to rescaling of weights that does not affect the output of the network, and suggest Path-SGD, which is an approximate steepest descent method with …
Solves infinite horizon portfolio problem with path-dependent labor income.
problem Infinite horizon portfolio choice with path-dependent labor income.
method Solves an infinite dimensional stochastic optimal control problem using explicit solutions to the HJB equation.
result Explicit solutions to the optimal controls in feedback form are found.
Develops Weyl structures for path geometries, simplifying their study.
problem Complexity in studying path geometries using traditional differential geometry methods.
method Defines distinguished connections and Schouten tensor, proving their dependence on line bundle sections.
result Shows a smaller subclass of Weyl structures for path geometries, with interesting connections to BGG sequences.
Signature Isolation Foreststat.ML
Signature Isolation Forest removes constraints from FIF by using rough path theory's signature transform.
problem Challenges in FIF's linear inner product and dictionary choices leading to unreliable results.
method Introduces Signature Isolation Forest using rough path theory's signature transform to remove linearity constraints.
result Demonstrates relevance of methods through numerical experiments and real-world applications.
Researchers calculate the Ray-Singer Torsion for bundles.
problem Few explicit evaluations of path integrals in higher dimensions.
method Algebraic choice of gauge leading to factorization of path integral.
result Explicit calculation of Ray-Singer Torsion for bundles.
The study proves unique path lifting properties and their implications on quotient spaces and covering maps.
problem Understanding unique path lifting properties and their implications on quotient spaces and covering maps.
method The study uses group actions on -trees and path lifting properties to prove the main results.
result Every map of manifolds with the unique path lifting property is a covering map.
New control methods improve dynamic measure transport paths.
problem Improving paths for dynamic measure transport.
method Connecting mean-field games to optimization problems for learning paths, advocating for smoothness of velocities.
result Our method recovers more efficient and smooth transport models compared to untilted paths.
This paper proposes new get-rich-quick schemes that involve trading in a financial security with a non-degenerate price path. For simplicity the interest rate is assumed zero. If the price path is assumed continuous, the trader can become infinitely rich immediately after it becomes non-constant (if it ever does). If i…
Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatilityq-fin.PR
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the path integral method, proposed B. Baaquie, and generalized it to the case of path…
New method for learning on heterogeneous graphs without meta-paths.
problem Learning on heterogeneous graphs is sensitive to meta-paths choice, leading to poor performance.
method Decompose heterogeneous graph into homogeneous relation-type graphs, combine higher-order representations, use attention mechanisms.
result Our model outperforms state-of-the-art baselines in vertex classification tasks on heterogeneous graph datasets.
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately calculate distances. When data points are real-valued vectors, by far the most common c…
New MCMC method improves sampling from multimodal distributions.
problem Sampling from multimodal distributions is challenging for classical MCMC methods.
method Interpolating along the diffusion path, preserving mode weights and mixing properties.
result MAD-Path sampler improves global exploration and mode-weight estimation.
The phase of the scattering operator from the geometry of certain infinite-dimensional groupsmath-ph
We revisit the computation of the phase of the Dirac fermion scattering operator in external gauge fields. The computation is through a parallel transport along the path of time evolution operators. The novelty of the present paper compared with the earlier geometric approach by Langmann and Mickelsson, [LM], is that w…
Optimal transport semi-supervised learning improves GNSS multi-path detection.
problem GNSS multi-path interference detection.
method Wasserstein distance based semi-supervised manifold learning.
result Significant improvement in classification accuracy over fully supervised training.
Two constructions link path geometries to almost Grassmann structures.
problem Linking path geometries to almost Grassmann structures.
method Introducing two Fefferman-type constructions.
result Characterizing conditions for almost Grassmann structures arising from these constructions.
Comparison results for conjugate and focal points in semi-Riemannian geometry via Maslov indexmath.DG
We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.
Study topological twists of massive SQCD with gauge group SU(2) and 3 or fewer fundamental hypermultiplets.
problem Evaluate topological partition functions of massive SQCD with arbitrary gauge bundles and hypermultiplet masses.
method Develop techniques for evaluating low-energy path integrals on the Coulomb branch.
result Formulate theories for arbitrary gauge bundles on compact four-manifolds.
The estimation of advantage is crucial for a number of reinforcement learning algorithms, as it directly influences the choices of future paths. In this work, we propose a family of estimates based on the order statistics over the path ensemble, which allows one to flexibly drive the learning process, towards or agains…
Study proves existence, uniqueness, and positivity of solutions to a complex volatility model.
problem Modeling equity index and spot volatility with path-dependent features and general kernels.
method Proved existence and uniqueness of a continuous solution to a Stochastic Volterra Equation (SVE) with non-convolutional, non-bounded kernels and non-Lipschitz coefficients.
result Positivity of the volatility process under certain conditions on the kernels.
A new method uses string method to explore diffusion models.
problem Understanding the geometry of learned distributions in diffusion models.
method String method to compute continuous paths between samples.
result The string method identifies realistic morphing sequences and transition pathways.
Introduces a massive variant of Ray-Singer Torsion to avoid zero modes in topological field theories.
problem Avoiding zero modes in the evaluation of path integrals for topological field theories.
method Introduces a massive variant of the Ray-Singer Torsion, involving determinants of the twisted Laplacian with mass but without zero modes.
result Explicitly evaluates the massive Ray-Singer Torsion on product manifolds and mapping tori.
Can we reduce the search cost of Neural Architecture Search (NAS) from days down to only few hours? NAS methods automate the design of Convolutional Networks (ConvNets) under hardware constraints and they have emerged as key components of AutoML frameworks. However, the NAS problem remains challenging due to the combin…
We introduce a new method to calculate the credit exposure of European and path-dependent options. The proposed method is able to calculate accurate expected exposure and potential future exposure profiles under the risk-neutral and the real-world measure. Key advantage of is that it delivers an accuracy comparable to …
A Bayesian framework models dynamic probability predictions over time.
problem Dynamic probability predictions over time in various settings.
method Gaussian latent information martingale (GLIM) framework.
result GLIM outperforms baseline methods in predicting future uncertainties.
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. S…
Paper studies CLO with partial feedback, improving decision-making in uncertain contexts.
problem Improving decision-making in contexts with uncertain cost coefficients using partial feedback.
method Unified class of offline learning algorithms for CLO with different types of feedback, using IERM framework.
result Fast-rate regret bound for IERM with partial feedback and misspecified model classes.
New imputation strategies improve signature models for irregular time series.
problem Applying signature models to irregular time series requires continuous path construction.
method Characterized imputation as a problem, evaluated various strategies, proposed GP-PoM.
result Gaussian process adapters improve predictive performance and robustness.
Synthetic tabular data synthesis models balance utility and risk.
problem Generating synthetic tabular data for regulated domains.
method Latent flow models with various learning targets, paths, and sampling methods.
result Velocity and posterior matching objectives yield higher utility, while score and noise matching achieve lower risk.
In this paper we tackle the issue of clustering trajectories of geolocalized observations. Using clustering technics based on the choice of a distance between the observations, we first provide a comprehensive review of the different distances used in the literature to compare trajectories. Then based on the limitation…
New method uses neural networks to solve complex PDEs from optimal control theory.
problem Solving high-dimensional Hamilton-Jacobi-Bellman PDEs.
method Iterative diffusion optimization techniques, focusing on path measures and divergences.
result Favourable properties of log-variance divergence for Monte Carlo estimators.
Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolationq-fin.CP
We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev method delivers a closed form approximation of the option prices along the paths…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level zero. We show that, under a proper choice of control variates, one can reduce t…
This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.
problem Expensive and unstable computation of hedge ratios from pathwise sensitivities.
method Develops reduced stochastic hedge ratios of the form φ_j^r = Σ_j^r ξ_j^q X_q, retaining sensitivity tensor through empirical averages.
result Two coefficient criteria are introduced to minimize pathwise residuals and satisfy moment equations.
Improved analysis of gradual domain adaptation with better generalization bounds.
problem Improving generalization in target domain through intermediate unlabeled domains.
method Analyzed gradual self-training under more general assumptions, proving a new generalization bound.
result Proved a significantly improved generalization bound of ε0 + O(TΔ + T/√n) + ˜O(1/√nT).
Given a point (the "spider") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the "fly" - the reflection of the spider across the center of the box). Without loss of generality, we can assume that the box has dimensions with the spider on one …
This paper improves probabilistic latent models on hyperbolic spaces.
problem Uncertainty in predictions due to geodesics crossing low-data regions.
method Augmenting hyperbolic manifold with a pullback metric for probabilistic pullback metrics.
result Geodesics on pullback metric respect both geometry and data distribution, reducing uncertainty.
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We obtain the duality of results for the sub- and super-hedging prices. For the sub…
Rethinking Test-time Likelihood: The Likelihood Path Principle and Its Application to OOD Detectioncs.LG
A new principle and method improve out-of-distribution detection in generative models.
problem Out-of-distribution detection in deep generative models often fails due to poor likelihood estimates.
method Introducing the Likelihood Path (LPath) principle and new theoretical tools for OOD detection.
result Non-asymptotic provable OOD detection guarantees for variational autoencoders (VAEs).
Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be need…
Trading in Complex Networksq-fin.GN
Global supply networks in agriculture, manufacturing, and services are a defining feature of the modern world. The efficiency and the distribution of surpluses across different parts of these networks depend on choices of intermediaries. This paper conducts price formation experiments with human subjects located in lar…
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete Itô processes market. The investor chooses his consumption under the addictive habits constraint while only observing the market stock prices but not the instantaneous rate of return. Applying the …
EBM model for functional data using path measure tilting.
problem Modeling distributions of functions from irregularly sampled data.
method Spectral decomposition of an energy-based model with a Gaussian Process path measure to reweight the distribution.
result Effective approach to up-scaling functional data.