New ICA algorithm improves source PDF estimation for better performance.
problem Inaccurate estimation of source PDFs leads to poor ICA performance.
method Entropy maximization with kernels, using global and local constraints.
result ICA-EMK outperforms competing algorithms in simulations and real-world data.
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…
The article derives some novel independence measures and contrast functions for Blind Source Separation (BSS) application. For the kth 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 …
CT compares two distributions using Bayes' theorem and chain rule.
problem Measuring the difference between two probability distributions.
method Conditional transport (CT) using chain rule and Bayes' theorem.
result CT strikes a good balance between mode-covering and mode-seeking behaviors.
This paper improves parameter estimation in cardiac models using Gaussian process-based MH sampling.
problem Uncertainty in estimating patient-specific model parameters from sparse and noisy clinical data.
method Integrates surrogate modeling into Metropolis-Hastings sampling to improve computational efficiency and accuracy.
result Significant gain in computational efficiency without compromising accuracy, and insights into tissue heterogeneity.
New MC simulation methods use classifiers to estimate pdf ratios without explicit pdfs.
problem Estimating ratios of probability density functions (pdfs) without explicit pdfs.
method Proposes classifier-based pdf-free versions of MC simulation algorithms.
result Enables pdf-free simulation algorithms using surrogate functions computed by classifiers.
Develops flexible ICA and IVA algorithms for medical image analysis.
problem Improper estimation of PDF leads to deviation from theoretical optimality.
method Flexible ICA and IVA algorithms using effective PDF estimation and sparsity.
result Unified mathematical framework for statistical independence and sparsity.
This work improves density estimation by characterizing pdf complexity using NL-spectrum.
problem Improving density estimation rates for general probability densities.
method Introducing NL-spectrum to characterize pdf complexity and deriving dimension-independent rates of convergence.
result Dimension-independent rates of convergence for fast density estimation.
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 …
CDF2PDF improves SIC for high-dimensional data estimation.
problem Estimating PDF from CDF in high-dimensional data.
method CDF2PDF approximates PDF by approximating CDF, avoiding hyper-parameter tuning and enabling polynomial time higher order derivative computation.
result CDF2PDF shows promising results in one-dimensional data experiments.
DeepPDF uses neural networks to estimate complex data distributions efficiently.
problem Efficiently estimating complex data distributions with high accuracy.
method DeepPDF uses a neural network to approximate a target pdf given samples, employing Probabilistic Surface Optimization (PSO) for stochastic optimization.
result DeepPDF achieves high inference accuracy for a wide range of target pdfs using a simple network structure.
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…
New method calibrates photometric redshift PDFs more accurately.
problem Inaccurate photometric redshift uncertainties lead to systematic errors.
method Local re-calibration using feature-space regression of Probability Integral Transform (PIT) distributions.
result Calibrated PDFs are more accurate at all locations in feature space.
Density destructors simplify complex PDFs to maximize entropy, linking to information theory.
problem Complex multivariate PDFs are hard to analyze.
method Invertible transforms that progressively remove structure from PDFs.
result Density destructors can improve estimates of information theoretic quantities.
A new filter estimates complex system states more accurately.
problem Non-Gaussian features in nonlinear systems violate Kalman-type filters.
method Adaptive split-combine Gaussian mixture filter (AMF) that splits and combines Gaussian particles.
result AMF consistently outperforms other filters across diverse benchmarks.
Four new methods for computing generalized chi-square distribution.
problem Computing the generalized chi-square distribution accurately and efficiently.
method Two exact and two approximate methods, with software for cdf, pdf, and inverse cdf.
result Comparison of methods' accuracy and speed, identifying best for different cases.
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM require estimating the probability distribution function (PDF), or its parameters…
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…
The paper introduces tools for nonparametric conditional density estimation in astronomy.
problem Estimating photometric redshifts and likelihood-free cosmological inference with uncertainty quantification.
method Nonparametric conditional density estimation (CDE) tools in Python and R.
result Comprehensive statistical tools and software for CDE in astronomy.
A new method uses histogram transform for better speaker identification.
problem Improving text-independent speaker identification.
method Uses Mel-frequency Cepstral coefficients and dynamic information among adjacent frames. Designs super-MFCCs features by cascading three neighboring MFCCs frames. Estimates PDF using histogram transform to generate more training data and reduce discontinuity.
result The histogram transform method shows improvement in speaker identification performance compared to conventional methods.
Unified framework for PDF estimation using MDL-based binning and tensor factorization.
problem Challenges in estimating PDFs for non-uniform, multimodal data.
method MDL-based binning with quantile cuts, tensor factorization (CPD).
result Effective PDF estimation on synthetic and real data.
Model predicts stock price volatility using stochastic differential equations.
problem Predicting stock price volatility in financial markets.
method Continuous cascade model using stochastic differential equations with two independent Brownian motions.
result The model accurately reproduces empirical volatility and multifractality.
SINF models transform arbitrary PDFs to target PDFs using 1D slices.
problem Transforming arbitrary probability distributions to target distributions efficiently.
method Iterative Optimal Transport of 1D slices, maximizing Wasserstein distance.
result SINF models generate high-quality samples and competitive density estimates.
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 introduces flat-topped PDFs for better fitting machine learning models.
problem Improving goodness of fit in machine learning models.
method Developed a new PDF based on the Fermi-Dirac or logistic function for adaptability.
result Flat-topped PDFs enhance model simplicity and fit quality.
A new visualization tool MD plot discovers interesting structures in continuous features.
problem Identifying interesting structures in data distributions, especially with skewed, clipped, or multimodal distributions.
method Proposes a new visualization tool called the mirrored density plot (MD plot) that does not require adjusting density estimation parameters.
result The MD plot outperforms conventional methods in identifying structures in complex distributions.
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential applicatio…
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…
Graph-based LRE estimates likelihood-ratios collaboratively for nodes.
problem Comparing unknown pdfs at graph nodes with graph structure.
method Graph-based Relative Unconstrained Least-squares Importance Fitting (GRULSIF).
result Collaborative estimation improves performance compared to independent methods.
Bayesian method estimates QTEs from observational data.
problem Estimating nuanced characteristics of counterfactual distributions.
method Bayesian semiparametric conditional distribution regression model with double balancing score.
result Proposed method provides more accurate QTE estimates than other methods.
Estimates class posterior probabilities without using scores from classifiers.
problem Estimating class posterior probabilities for new points in classification tasks.
method Varying prior probabilities to derive the ratio of pdf's at point x, directly determining class posterior probabilities.
result A method to estimate posterior probabilities without relying on classification scores.
Develops a method to estimate extreme event statistics in high-dimensional systems with few samples.
problem Estimating extreme event statistics in high-dimensional nonlinear systems with limited data.
method Sequential sampling strategy using Gaussian process regression and Bayesian inference.
result Accurately estimates extreme event statistics in a high-dimensional system with limited samples.
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…
Researchers develop methods to learn neuron dynamics from colored noise.
problem Learning nonlocal stochastic neuron dynamics from colored noise.
method Proposed two methods for closing Fokker-Planck equations: nonlocal large-eddy-diffusivity closure and data-driven sparse regression.
result Mutual information and total correlation between stimulus and neuron states calculated for FHN neuron.
Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.
problem Estimating joint probability densities of mixed discrete and continuous variables.
method Low-rank tensor decomposition combined with dictionary learning.
result Better classification and lower error rates compared to existing methods.
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…
This research trains a supervised model to accurately detect PDF headings.
problem Detecting headings in PDFs for text extraction.
method Supervised learning with recursive feature elimination.
result Best classifier achieved 96.95% accuracy, 0.986 sensitivity, and 0.953 specificity.
Develops a neural network approach to solve inverse stochastic problems from particle observations.
problem Inference of Fokker-Planck equation coefficients from sparse particle data.
method Physics-informed neural networks (PINNs) with Kullback-Leibler divergence loss.
result Simultaneous inference of Fokker-Planck equation and multi-dimensional PDF from few particle observations.
Autoencoder optimizes data embedding for accurate PDF reproduction.
problem Inaccurate PDF reproduction in latent space of VAEs.
method Rate-Distortion Optimization guided autoencoder with isometric property.
result Our method achieves isometric data embedding and tractable PDF relations.
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-…
Financial losses follow earthquake-like patterns, study finds.
problem Analyzing the timing between financial market losses.
method Fitting empirical interevent times with a Hawkes process.
result Financial market losses exhibit long-term memory similar to earthquakes.
We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) …
Deep learning reduces noise in weak lensing mass maps using GANs.
problem Noise reduction in weak lensing mass maps.
method Generative adversarial networks (GANs) applied to Subaru Hyper Suprime-Cam data.
result GANs successfully reproduce non-Gaussian information in denoised maps, showing stronger cosmological dependence.
Study fits BTC future returns from inverse options using logistic distribution.
problem Modeling future price distribution of Bitcoin.
method Fits empirical BTC future returns with logistic distribution using inverse options prices.
result BTC future returns can be described with a logistic distribution, but not stochastically.
Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robust…
Paper proposes using generalized lambda distributions for stochastic simulators.
problem Uncertainty quantification with complex stochastic models is computationally challenging.
method Flexible generalized lambda distribution approximates response PDF, parameters are sparse polynomial chaos expansions.
result Local inference of response PDF at each point of experimental design using replicated model evaluations.
DeepGDL models create realistic power grids from confidential data.
problem Creating realistic power grids from confidential data.
method Graph distribution learning (GDL) with a deep nonlinear recurrent structure.
result DeepGDL models accurately create synthetic power grids.