A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
SGLRW improves robustness of stochastic gradient MCMC methods.
We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of after queries for a convex bounded function . The method is based on a random walk (the \emph{Ball Walk}) on the epigraph of the function. Th…
Estimates social network structure from random walk subgraphs.
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-kno…
We relate some basic constructions of stochastic analysis to differential geometry, via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either geodesics or integral curves associated to orthonormal frames, and we give particular at…
Data-driven methods link graphon limits to random walks and spectral clustering.
Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and Hierarchical Dirichlet Process, for community extraction. In RW-HDP, random walks c…
We introduce the geodesic walk for sampling Riemannian manifolds and apply it to the problem of generating uniform random points from polytopes in R^n specified by m inequalities. The walk is a discrete-time simulation of a stochastic differential equation (SDE) on the Riemannian manifold equipped with the metric induc…
NWoS solves high-dimensional Poisson equations using neural networks.
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as no…
Quantum stochastic walks optimize portfolios by leveraging financial networks, improving Sharpe ratios and reducing turnover.
The paper corrects for node degree in spectral clustering using random walk Laplacian.
New graph embedding method improves link prediction and node classification.
The Dirichlet random walk on manifolds has a positive escape rate if the cover is non-amenable.
New algorithm uniformly samples high-dimensional convex bodies efficiently.
Study on a pinning model with random walk increments, showing convergence to a critical disordered pinning measure.
Study local exploration on dynamic graphs with time-varying edges.
Online learners track optimal solutions with constant step-size.
ESPD improves learning efficiency in sparse reward reinforcement learning.
Finding the reduced-dimensional structure is critical to understanding complex networks. Existing approaches such as spectral clustering are applicable only when the full network is explicitly observed. In this paper, we focus on the online factorization and partition of implicit large-scale networks based on observati…
We introduce tools for inference in the multifractal random walk introduced by Bacry et al. (2001). These tools include formulas for smoothing, filtering and volatility forecasting. In addition, we present methods for computing conditional densities for one- and multi-step returns. The inference techniques presented in…
This paper studies node embeddings of networks, revealing their geometric properties.
This paper considers a sequence of discrete-time random walk markets with a safe and a single risky investment opportunity, and gives conditions for the existence of arbitrages or free lunches with vanishing risk, of the form of waiting to buy and selling the next period, with no shorting, and furthermore for weak conv…
Algorithm samples constrained stochastic differential equations.
Training very deep networks is an important open problem in machine learning. One of many difficulties is that the norm of the back-propagated error gradient can grow or decay exponentially. Here we show that training very deep feed-forward networks (FFNs) is not as difficult as previously thought. Unlike when back-pro…
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that includes the Ito and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is…
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Levy-like distribution, and the cross-correla…
We construct a new type of quantum walks on simplicial complexes as a natural extension of the well-known Szegedy walk on graphs. One can numerically observe that our proposing quantum walks possess linear spreading and localization as in the case of the Grover walk on lattices. Moreover, our numerical simulation sugge…
Online minimization of an unknown convex function over the interval is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing the distribution of the random gradients, a learning algorithm sequentially choo…
We propose NetGAN - the first implicit generative model for graphs able to mimic real-world networks. We pose the problem of graph generation as learning the distribution of biased random walks over the input graph. The proposed model is based on a stochastic neural network that generates discrete output samples and is…
A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a characterization of stochastic models of stock price returns which is appropriat…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization o…
Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…
Simulates financial market orders using anomalous diffusion models.
Loss-guided training accelerates node embedding methods on graphs.
A novel version of the Continuous-Time Random Walk (CTRW) model with memory is developed. This memory means the dependence between arbitrary number of successive jumps of the process, while waiting times between jumps are considered as i.i.d. random variables. The dependence was found by analysis of empirical histogram…
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
DeepWalk embeddings converge on SBM graphs, recovering cluster structure.
This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-of-the-art word2vec model to embed a graph in Euclidean space via random walks on the n…
In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the Continuous Time Random Walk (CTRW). Despite the popularity of this type of stochastic pr…
We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya wher…
Study large deviations in random walks on Lie groups.
The paper introduces walks with jumps for modeling neuron activity in hyperbolic space.
Quantum walks blend patterns into splines when averaged.
Unified view on random walk and Weisfeiler-Leman kernels, improving accuracy.
Local limit theorem for random walks on hyperbolic groups with parabolic subgroups.
We consider a generalization of the Heath Jarrow Morton model for the term structure of interest rates where the forward rate is driven by Paretian fluctuations. We derive a generalization of Itô's lemma for the calculation of a differential of a Paretian stochastic variable and use it to derive a Stochastic Differenti…
We review recent advances on the record statistics of strongly correlated time series, whose entries denote the positions of a random walk or a Lévy flight on a line. After a brief survey of the theory of records for independent and identically distributed random variables, we focus on random walks. During the last few…