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.
New MC simulation methods use classifiers to estimate pdf ratios without explicit pdfs.
We report the proof that the expression of extended Gibrat's law is unique and the probability distribution function (pdf) is also uniquely derived from the law of detailed balance and the extended Gibrat's law. In the proof, two approximations are employed that the pdf of growth rate is described as tent-shaped expone…
We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-…
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pd…
Physics-informed neural networks approximate diffusion process pdfs efficiently.
In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a …
Many interesting machine learning problems are best posed by considering instances that are distributions, or sample sets drawn from distributions. Previous work devoted to machine learning tasks with distributional inputs has done so through pairwise kernel evaluations between pdfs (or sample sets). While such an appr…
The article derives a novel Gram-Charlier A (GCA) Series based Extended Rule-of-Thumb (ExROT) for bandwidth selection in Kernel Density Estimation (KDE). There are existing various bandwidth selection rules achieving minimization of the Asymptotic Mean Integrated Square Error (AMISE) between the estimated probability d…
Proposes a deep learning method for uncertainty propagation in complex systems.
CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. However, SIC requires additional hyper-parameter tunning, and no algorithms for computing higher order derivative from a trained NN are provided in [1]. CDF2PDF improves SIC by avoiding the tim…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically acquired modality. Inferring data pdf is of prime importance, allowing to analyze …
Paper proposes using generalized lambda distributions for stochastic simulators.
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
In this paper, a nonparametric maximum likelihood (ML) estimator for band-limited (BL) probability density functions (pdfs) is proposed. The BLML estimator is consistent and computationally efficient. To compute the BLML estimator, three approximate algorithms are presented: a binary quadratic programming (BQP) algorit…
Four new methods for computing generalized chi-square distribution.
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the 'next-best' data point (set of parameters) that when evaluated results in improv…
New methods for uncertainty in neural networks with leaky ReLU activations.
Density destructors simplify complex PDFs to maximize entropy, linking to information theory.
Channel modeling is a critical topic when considering designing, learning, or evaluating the performance of any communications system. Most prior work in designing or learning new modulation schemes has focused on using highly simplified analytic channel models such as additive white Gaussian noise (AWGN), Rayleigh fad…
New method calibrates photometric redshift PDFs more accurately.
This work improves density estimation by characterizing pdf complexity using NL-spectrum.
We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that kernel herding decreases the error of expectations of functions in the Hilbert …
SINF models transform arbitrary PDFs to target PDFs using 1D slices.
Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.
This paper improves parameter estimation in cardiac models using Gaussian process-based MH sampling.
CT compares two distributions using Bayes' theorem and chain rule.
The paper introduces flat-topped PDFs for better fitting machine learning models.
Researchers develop methods to learn neuron dynamics from colored noise.
We analyze the probability density function (PDF) of waiting times between financial loss exceedances. The empirical PDFs are fitted with the self-excited Hawkes conditional Poisson process with a long power law memory kernel. The Hawkes process is the simplest extension of the Poisson process that takes into account h…
Report presents analysis of empirical distribution of future returns of bitcoin (BTC) from BTUSD inverse option prices. Logistic pdf is chosen as underlying distribution to fit option prices. The result is satisfactory and suggests that these prices can be described with just three or even one parameter. Fitted Logisti…
In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is possible to get a new f…
The paper proposes a new framework for accurate uncertainty representation and propagation.
As the Portable Document Format (PDF) file format increases in popularity, research in analysing its structure for text extraction and analysis is necessary. Detecting headings can be a crucial component of classifying and extracting meaningful data. This research involves training a supervised learning model to detect…
A novel text-independent speaker identification (SI) method is proposed. This method uses the Mel-frequency Cepstral coefficients (MFCCs) and the dynamic information among adjacent frames as feature sets to capture speaker's characteristics. In order to utilize dynamic information, we design super-MFCCs features by cas…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
In this letter, we present a novel exponentially embedded families (EEF) based classification method, in which the probability density function (PDF) on raw data is estimated from the PDF on features. With the PDF construction, we show that class-specific features can be used in the proposed classification method, inst…
Deep adaptive sampling improves surrogate modeling for complex systems.
New variational inference approach using Hilbert space for robotic state estimation.
Deep learning reduces noise in weak lensing mass maps using GANs.
Independent component analysis (ICA) is the most popular method for blind source separation (BSS) with a diverse set of applications, such as biomedical signal processing, video and image analysis, and communications. Maximum likelihood (ML), an optimal theoretical framework for ICA, requires knowledge of the true unde…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into the evolution of the PDF, e.g., allowing the calculation of its relaxation time…
The paper compares three option pricing models with varying volatility dynamics.
Develops a neural network approach to solve inverse stochastic problems from particle observations.
New framework quantifies uncertainty in data and models using RKHS.
One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need to be assessed. Of particular interest is the question of whether the data orig…
Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the d…
Adaptive neural network approximates stochastic system densities.
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to some lower dimensional Euclidean space, as many manifold learning methods have b…