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.
A new sampling algorithm speeds up Langevin sampling for multimodal distributions.
We propose a general method to obtain approximation of the first passage time distribution for the birth-death processes. We rely on the general properties of birth-death processes, Keilson's theorem and the concept of Riemann sum to obtain closed-form expressions. We apply the method to the three selected birth-death …
Decision trees are flexible models that are well suited for many statistical regression problems. In a Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree models according to their posterior probabilities. The critical component of such an …
FS&P uses birth-death process to ensure global convergence of stochastic conic particle gradient descent.
Study birth-death dynamics for sampling Gibbs measures with nonconvex potentials.
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDE…
Neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for the favorable training properties of "overparameterized" models. In this regime, gradient descent obeys a deterministic partial differential equation (PDE) that converges to a glo…
New method uses birth-death process and exploration component to accelerate sampling from multimodal distributions.
Paper proposes scalable method for analyzing multi-omic data.
New method improves phylogenetic model inference by 30x.
Near a birth-death critical point in a one-parameter family of gradient flows, there are precisely two Morse critical points of index difference one on the birth side. This paper gives a self-contained proof of the folklore theorem that these two critical points are joined by a unique gradient trajectory up to time-shi…
Paper disproves conjecture about log-Sobolev constants.
Unified framework for analyzing gradient flows of measures with exponential decay of entropy.
This work develops sampling methods for differential privacy using SHK geometry.
In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half line. We give a combinatorial characterization of Bakry and Émery's condition for linear graphs and prove the triviality of edge w…
Flow Matching for count data improves sample quality and efficiency.
The surgery technique of Gromov and Lawson may be used to construct families of positive scalar curvature metrics which are parameterised by Morse functions. This has played an important role in the study of the space of metrics of positive scalar curvature on a smooth manifold and its corresponding moduli spaces. In t…
New RL algorithm reduces regret in birth-death queueing problems.
The paper develops a stationary-distribution theory for Random Forest ensemble size selection.
Paper compares higher torsions and removes fiberwise Morse function assumption.
USD algorithm transports distributions with or without mass conservation.
New method optimizes multiple objectives using particle dynamics and gradient flow.
A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth-death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is nu…
According to Kiyoshi Igusa a generalized Morse function on an n-dimensional manifold M is a smooth function with only Morse and birth-death singularities and a framed function is a generalized Morse function with an additional structure: a framing of the negative eigenspace at each critical point of the function f. In …
We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that saddle cobordisms can be computed in terms of maps in a decorated skein exact triangle that extends the oriented skein exact triangle in knot…
Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics' distribution and popularity are time-evolving. Several mode…
Bayesian nonparametric models improve multi-object tracking robustness and flexibility.
We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simpl…
Floer theory constructs filtrations on quantum cohomology for symplectic manifolds.
New model assesses risks of staking and borrowing in smart contracts.
The study establishes a curvature-dimension condition for discrete Markov chains.
Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the drift and diffusion depends on the volume present on both sides of the spread. "J…
Stein transport improves Bayesian inference with faster convergence and reduced variance.
Bayesian method learns graph structures from Gaussian data efficiently.
Neural models learn continuous-time Markov chain transition rates from data.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricin…
A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the ca…
This study investigates self-organizing dynamics in a stochastic exponential DAM model using Temporal Complexity.
New mechanics on non-associative octonions discovered.
A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present the \emph{dual mechanical systems} called by use, \emph{dual mechanical}$(ρ,η) …
This paper assesses Gaussian and Exponential mechanisms for certifying adversarial robustness.
We propose a new input perturbation mechanism for publishing a covariance matrix to achieve -differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…
New mechanisms improve differential privacy for scalar queries.
We design two mechanisms for the recommender system to collect user ratings. One is modified Laplace mechanism, and the other is randomized response mechanism. We prove that they are both differentially private and preserve the data utility.
Quantum mechanics models for financial Black-Scholes model.
Expands differential privacy mechanisms to include the Generalized Gaussian mechanism for improved private machine learning.
Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…