arXiv research

New method models MTPP without predefined intensity functions.

Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.

The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the $k^{th}$ order differentiable multivariate functions with equal hyper-volumes (region bounded by hyper-surfaces) and with a constraint of bounded support for $k>1$, it proves that equality …

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few uncertain variables or require large amounts of simulation data. In this paper, we…

CT compares two distributions using Bayes' theorem and chain rule.

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…

Researchers develop methods to learn neuron dynamics from colored noise.

Unified framework for PDF estimation using MDL-based binning and tensor factorization.

New methods for uncertainty in neural networks with leaky ReLU activations.

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…

We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…

We propose a deep-learning approach based on generative adversarial networks (GANs) to reduce noise in weak lensing mass maps under realistic conditions. We apply image-to-image translation using conditional GANs to the mass map obtained from the first-year data of Subaru Hyper Suprime-Cam (HSC) survey. We train the co…

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 …

New MC simulation methods use classifiers to estimate pdf ratios without explicit pdfs.

This work tackles multivariate CDFs and copulas using tensor factorization.

We investigate the statistics of the gap, G_n, between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration, L_n, which separates the occurrence of these two extremal positions. The distribution of the jumps η_i's of the RW, f(η), is symmetric and its Four…

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…

Density destructors simplify complex PDFs to maximize entropy, linking to information theory.

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…

New method calibrates photometric redshift PDFs more accurately.

This work improves density estimation by characterizing pdf complexity using NL-spectrum.

SINF models transform arbitrary PDFs to target PDFs using 1D slices.

The minute-by-minute move of the Hang Seng Index (HSI) data over a four-year period is analysed and shown to possess similar statistical features as those of other markets. Based on a mathematical theorem [S. B. Pope and E. S. C. Ching, Phys. Fluids A {\bf 5}, 1529 (1993)], we derive an analytic form for the probabilit…

A theory which describes the share price evolution at financial markets as a continuous-time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function (pdf) which uses the concept of a Lévy stable distribution is worked out.…

The paper introduces flat-topped PDFs for better fitting machine learning models.

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…

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 …

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…

The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algori…

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…

New bounds on continuous random variables' right-tail probabilities.

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…

Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.

Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random vari…

Bayesian method estimates QTEs from observational data.

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-…

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…

In this paper we describe a 1-dimensional family of initial conditions Σthat provides reduced periodic solution of the three body problem. This family Σcontains a bifurcation point and extend the periodic solution described in (Perdomo, http://arxiv.org/pdf/1507.01100.pdf). This 1-dimensional family is the union of two…

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…

This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density function (PDF) in a way that quantifies the flow of its gradient as a topological…

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…

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 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…

Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media,…

Develops a neural network approach to solve inverse stochastic problems from particle observations.

In this paper we explore the applicability of the unsupervised machine learning technique of Self Organizing Maps (SOM) to estimate galaxy photometric redshift probability density functions (PDFs). This technique takes a spectroscopic training set, and maps the photometric attributes, but not the redshifts, to a two di…

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…