arXiv research

Path-independent equilibrium models improve network performance on harder problems.

Closed-form formulas for path-independent options in a specific Lévy model.

Overlay framework simplifies exotic derivative pricing.

Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…

New method identifies causal relationships in presence of hidden variables.

Develops a model for causal discovery in path spaces.

Extends PD-NJ-ODE to noisy observations and dependent observation times.

In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent deriv…

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been adjusted for. We introduce a novel approach for estimating causal effects that explo…

We solve the paradox of score-based methods by minimizing path variance.

Paper presents a copula-based method to efficiently generate correlated sample paths from multi-step time series models.

We prove that the model-free typical (in the sense of Vovk) càdlàg price paths with mildly restricted downward jumps possess quadratic variation which does not depend on the specific sequence of partitions as long as these partitions are obtained from stopping times such that the oscillations of a path on the consecuti…

A positive path in the linear symplectic group $\Sp(2n)$ is a smooth path which is everywhere tangent to the positive cone. These paths are generated by negative definite (time-dependent) quadratic Hamiltonian functions on Euclidean space. A special case are autonomous positive paths, which are generated by time-indepe…

Optimizes diffusion processes for target distributions.

Solves complex equation for specific geometric solitons.

The paper proposes using path signatures for better inference in time series data.

This work develops a generic framework, called the bag-of-paths (BoP), for link and network data analysis. The central idea is to assign a probability distribution on the set of all paths in a network. More precisely, a Gibbs-Boltzmann distribution is defined over a bag of paths in a network, that is, on a representati…

Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is equivalent to the graphs in the space of independent and depedent variables of …

New proof confirms rolling objects can follow any path.

We introduce a new deep convolutional neural network, CrescendoNet, by stacking simple building blocks without residual connections. Each Crescendo block contains independent convolution paths with increased depths. The numbers of convolution layers and parameters are only increased linearly in Crescendo blocks. In exp…

The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature $T$) controlling the entropic level of the distribution. This formalism enables…

Study shows how feature weighting affects neural network regularization.

Tensor-based method simplifies causal skeleton discovery.

Study rough volatility models using path-dependent PDEs and fractional Brownian motions.

Many model selection algorithms produce a path of fits specifying a sequence of increasingly complex models. Given such a sequence and the data used to produce them, we consider the problem of choosing the least complex model that is not falsified by the data. Extending the selected-model tests of Fithian et al. (2014)…

Temporal aggregation reveals latent default correlation from monthly data.

In this paper, we provide a model-independent extension of the paradigm of dynamic hedging of derivative claims. We relate model-independent replication strategies to local martingales having a closed form which we can characterise via solutions of coupled PDEs. We provide a general framework and then apply it to a mar…

Two constructions link path geometries to almost Grassmann structures.

A new method detects anomalies in multivariate streams without unit dependence.

Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.

We establish causal semantics for SDEs and develop methods to reason about them.

A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff can be replicated exact…

Study bounds financial path expectations using martingale distributions.

Study shows saddle connection graph's geometry and quasi-isometry properties.

Develops a new causal model for path-dependent link prediction.

New approach tackles nonidentifiability in nonlinear blind source separation.

New method identifies causal structure in count data using cumulants and path analysis.

A new method for portfolio allocation in continuous-time markets.

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial couplin…

Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in Let $M$be a complete Riemnnian manifold and$μ$the distribution of the diffusion process generated by$\ff 1 2\DD+Z$where$Z$…

Geometric framework for inverse problems using foliations and dual connections.

Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity …

Enhances interpolation paths in latent space using particle filters.

New framework for fairness in continuous protected attributes.

BWFlow improves graph generation by smoothly interpolating graph components.

The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the $β$-mixing rate based on a single stationary sample…

Efficient algorithms decide algebraic constraints of causal graphs.

New methods estimate causal effects through mediators, handling confounding without strict assumptions.