arXiv research

We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-…

Study refracted skew Brownian motion, find densities and asymptotics.

We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…

Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, includi…

We consider uncorrelated Stein-Stein, Heston, and Hull-White models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Similar perturbations of the Black-Scholes model were studied by S. Kou. For perturbed stochastic volatility models, we obtain…

Improved probabilistic forecasts using behavioral transformations.

Paper uses DBSCAN variation to detect ship anomalies.

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-diffusion mode…

Research shows deep generative models' likelihoods are unreliable for anomaly detection.

Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…

We prove that capillary surfaces converge to a specific energy density as the angle approaches zero.

High density clusters can be characterized by the connected components of a level set $L(λ) = \{x:\ p(x)>λ\}$ of the underlying probability density function $p$ generating the data, at some appropriate level $λ\geq 0$. The complete hierarchical clustering can be characterized by a cluster tree ${\cal T}= \bigcup_λ L(λ)…

Study improves vehicle motion prediction by incorporating traffic density.

Study chaotic behavior in homeomorphism groups of countable products of spaces.

New method trains neural samplers to sample from multi-modal distributions efficiently.

This paper presents a method for efficient density estimation in nonlinear systems.

Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two step…

The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the p…

We study the strong predictable representation property in filtrations initially enlarged with a random variable L. We prove that the strong predictable representation property can always be transferred to the enlarged filtration as long as the classical density hypothesis of Jacod (1985) holds. This generalizes the ex…

Hierarchical VAEs detect out-of-distribution data by identifying low-level in-distribution features.

New models explain heavy-tailed behavior in neural networks.

We study the phase transition of dynamical herd behaviors for the yen-dollar exchange rate in the Japanese financial market. It is obtained that the probability distribution of returns satisfies the power-law behavior with three different values of the scaling exponent 3.11 (one time lag $τ$ = 1 minute), 2.81 (30 minut…

Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.

We present a dual-view mixture model to cluster users based on their features and latent behavioral functions. Every component of the mixture model represents a probability density over a feature view for observed user attributes and a behavior view for latent behavioral functions that are indirectly observed through u…

Proposes a method to partition univariate data into unimodal subsets.

New method extrapolates spectral densities from smaller models to larger ones.

New insights into the top-K sparse softmax gating function for deep learning.

Nanowire field-effect sensors have recently been developed for label-free detection of biomolecules. In this work, we introduce a computational technique based on Bayesian estimation to determine the physical parameters of the sensor and, more importantly, the properties of the analyte molecules. To that end, we first …

LLMs learn probability density functions in-context, showing distinct learning trajectories.

Defines foliation criterion for dense isoperiodic leaves in rank 1 affine orbifolds.

The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.

In this paper, we prove the long-time existence and uniqueness of the conical Kähler-Ricci flow with weak initial data which admits $L^{p}$ density for some $p>1$ on Fano manifold. Furthermore, we study the convergence behavior of this kind of flow.

Machine learning often needs to model density from a multidimensional data sample, including correlations between coordinates. Additionally, we often have missing data case: that data points can miss values for some of coordinates. This article adapts rapid parametric density estimation approach for this purpose: model…

CNFs model conditional densities efficiently and avoid mode collapse.

A neural network deployed in the wild may be asked to make predictions for inputs that were drawn from a different distribution than that of the training data. A plethora of work has demonstrated that it is easy to find or synthesize inputs for which a neural network is highly confident yet wrong. Generative models are…

DIF extends NF with stochastic discrete latent variables for better density estimation.

We study the dynamical behaviors of degenerate stochastic differential equations (SDEs). We select an auxiliary Fisher information functional as the Lyapunov functional. Using generalized Fisher information, we conduct the Lyapunov exponential convergence analysis of degenerate SDEs. We derive the convergence rate cond…

A new model simulates non-linear adsorption using Gaussian KDEs.

In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] and financial herd behavior model. Combining these approaches allows us to propose a mo…

We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small…

Study on evolving interfaces with complex curvature and density effects.

Fast, fully-automated histograms for large data sets.

The paper analyzes geometric densities and compression radii for knot types.

MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.

GBOC detects anomalies in time series data using granular-ball vectors.

New method improves uncertainty calibration in deep learning.

Fold maps associated to geodesic random walks on curved spaces.

We consider the Cauchy problem for doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume, or in $\R^N$. The equation contains a weight function as a capacitary coefficient which we assume to decay at infinity. We connect the behavior of non-negative solutions to the interplay betwe…