An adaptive filter improves state estimation for complex systems.
problem Estimating non-Gaussian, multimodal PDFs in nonlinear systems.
method Adaptive split-combine Gaussian mixture filter (AMF) that splits and combines Gaussian particles adaptively.
result AMF consistently outperforms other filters across diverse benchmarks.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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…
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…
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.
Bayesian method estimates line frequencies with uncertainty.
problem Bayesian estimation of continuous frequencies.
method Variational Bayesian inference with von Mises mixtures.
result Significantly improved performance over point estimates.
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.
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…
New polynomial convergence guarantees for SGM on general data distributions.
problem Efficient guarantees for multimodal and non-smooth distributions in SGM.
method Polynomial convergence guarantees for denoising diffusion models on general data distributions, with no assumptions on functional inequalities or smoothness.
result Wasserstein distance guarantees for distributions of bounded support or decaying tails, and TV guarantees for further smoothness assumptions.
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.
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.
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…
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.
New framework quantifies uncertainty in data and models using RKHS.
problem Quantifying uncertainty in data and models.
method Projecting data into RKHS, transforming PDF, decomposing gradient flow.
result Decomposes uncertainty moments, providing discriminative resolution.
Physics-informed neural networks approximate diffusion process pdfs efficiently.
problem Approximating the probability density function of diffusion processes.
method Physics-informed neural networks solving Fokker-Planck or integro-differential equations.
result Neural network solutions approximate target solutions for various types of differential equations.
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.
A new classification method using class-specific features for improved text categorization.
problem Improving text categorization accuracy by leveraging class-specific features.
method EEF classifier based on class-specific features and optimal Bayesian classification rule.
result The proposed EEF classifier outperforms conventional methods on real-life data sets.
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…
Proposes a deep learning method for uncertainty propagation in complex systems.
problem Uncertainty propagation in nonlinear dynamic systems with many uncertain variables.
method Data-driven approach using deep learning to approximate PDFs of uncertain systems.
result Demonstrates robustness evaluation of a feedback controller for a six-dimensional system.
I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
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…
Unified framework for portfolio optimization using gain PDF.
problem Optimizing portfolios with control over high profits.
method Unified approach incorporating various PO methods using gain PDF.
result Directly matching target PDF for maximal control over PO.
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…
Paper proposes Seq2Seq models for multimodal sentiment analysis.
problem Learning representations from multiple modalities in machine learning.
method Two unsupervised Seq2Seq models for multimodal sentiment analysis.
result Seq2Seq models improve F1 Score by twelve points in Bimodal sentiment analysis.
Paper proposes a method to preserve multimodal sentiment analysis fidelity.
problem Lack of fidelity in multimodal fusion for sentiment analysis.
method Variational autoencoder-based approach for modality fusion.
result Empirically shows superior performance over state-of-the-art methods.
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…
DocParser parses document structures from renderings like PDFs and scans.
problem Parsing complete hierarchical document structures from renderings.
method End-to-end system with novel weak supervision approach.
result Significant improvement in document structure parsing performance.
Deep learning models predict chaotic Lorenz 96 system accurately.
problem Predicting short-term and long-term statistics of a multi-scale chaotic system.
method Reservoir computing (RC-ESN), ANN, RNN-LSTM.
result RC-ESN outperforms ANN and RNN-LSTM for short-term prediction.
TCT learns multimodal sequence representations by translating from related sequences.
problem Challenges in learning semantic representations from multimodalities.
method Transformer based Cross-modal Translator (TCT) combined with Multimodal Transformer Network (MTN).
result Proposed method achieves new state-of-the-art performance on video-grounded dialogue.
Efficient multimodal fusion reduces complexity and improves performance.
problem Multimodal data fusion with tensor transformations.
method Low-rank Multimodal Fusion using tensors.
result Significant reduction in computational complexity with competitive performance.