This paper improves machine learning density modeling with missing data.
problem Missing data in multidimensional data samples.
method Hierarchical correlation reconstruction using orthonormal functions and L2 optimization.
result Improved imputation and prediction of missing coordinates.
UAPCA projects uncertain data to low dimensions using GMMs.
problem Uncertain multidimensional data not well described by normal distributions.
method Model data with Gaussian mixture models, derive UAPCA projection from general formulation.
result Low-dimensional projections better represent multidimensional distributions.
Proposes a new method for PDF estimation using RBIG transforms.
problem Challenging task of multidimensional PDF estimation.
method Rotation-based Iterative Gaussianization (RBIG) transforms.
result RBIG transforms can be used to estimate unknown PDFs efficiently.
A neural network method estimates densities from characteristic functions.
problem Estimating fixed-horizon probability densities from empirical characteristic functions.
method Data-driven Fourier-mixture neural-network method trained in Fourier space.
result Competitive performance and clear gains on heavy-tailed targets.
Bayesian geoacoustic inversion improved using MDN.
problem Efficiently solving Bayesian geoacoustic inversion problems.
method Deriving geoacoustic statistics from multidimensional posterior density using MDN, training the network on the whole parameter space.
result The network provides reliable predictions and good generalization performance, solving problems in seconds.
Unified framework for gradient-free MDS improves efficiency and accuracy.
problem Efficiently solving Multidimensional Scaling problems without derivatives.
method Bootstrapped Coordinate Search (BS CSMDS) for MDS, using a probability matrix to guide search.
result BS CSMDS achieves significant speedup and maintains error rate compared to other CSMDS methods.
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discr…
Optimizes kernel density ratios for better predictions and information measures.
problem Improving accuracy of kernel density estimates for density ratios.
method Derives an optimal weight function using calculus of variations.
result Reduces bias in kernel density estimates, leading to improved prediction posteriors and information-theoretic measures.
BMTI method estimates densities without bins, outperforming traditional estimators.
problem Nonparametric, robust, and data-efficient density estimation in high-dimensional spaces.
method BMTI integrates log-density differences between neighboring points, weighted by uncertainties, using a maximum-likelihood formulation.
result BMTI reconstructs smooth profiles in high-dimensional spaces, outperforming traditional estimators.
We link probability density functions to Fisher information metrics.
problem Constructing probability density functions from Fisher information metrics.
method Utilizing the spatially disjoint product of probability density functions and their Fisher information metric tensors.
result A method for constructing arbitrary Riemannian Fisher information metric tensors.
In this article, we consider European options of type h(XT1,XT2,…,XTn) depending on several underlying assets. We study how such options can be valued in terms of simple vanilla options in non-specified market models. We consider different approaches related to static hedging and derive several pricing f…
In this note, we consider European options of type h(XT1,XT2,…,XTn) depending on several underlying assets. We give a multidimensional version of the result of Breeden and Litzenberger \cite{Breeden} on the relation between derivatives of the call price and the risk-neutral density of the underlying asse…
Conditional probabilities modeled using Riemann-Theta Boltzmann Machines.
problem Modeling conditional probabilities in Boltzmann machines.
method Deriving conditional density functions from Riemann-Theta Boltzmann machines.
result Conditional densities can be directly inferred from Riemann-Theta Boltzmann machines.
Efficiently estimates densities of multidimensional shift-invariant distributions.
problem Density estimation for shift-invariant multidimensional distributions.
method Efficient algorithms for learning any distribution in the class from samples, using total variation distance.
result Shift-invariant distributions can be learned efficiently with a number of samples and time proportional to 1/εd+2 and 1/ε2d+2 respectively. Generative models improve image probability estimation but lack interpretability.
problem Lack of interpretability in generative models for natural image distributions.
method Extracted explicit probability density estimates from GANs and analyzed latent representations.
result Natural image density functions are difficult to interpret.
This work explores CS-RBFs as novel probability density functions.
problem Underexplored use of CS-RBFs in statistics and probability modeling.
method Derivation of statistical properties of CS-RBFs as univariate and conditional densities, analysis of mixture models, and introduction of an incremental learning algorithm.
result CS-RBF densities provide competitive results in likelihood and model complexity compared to Gaussian mixture models.
This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary likelihood estimator for classification purposes, so issues such as mis-modeling and …
Paper analyzes classical multidimensional scaling for cluster recovery.
problem Cluster recovery from noisy data.
method Classical multidimensional scaling followed by distance-based clustering.
result Scaling conditions for high probability cluster recovery.
Modified multidimensional scaling improves clustering in noisy high-dimensional data.
problem Improving clustering accuracy in noisy high-dimensional data.
method Unified framework of multidimensional scaling, modified with nonlinear transformation.
result Modified multidimensional scaling achieves exact recovery of cluster labels with high probability.
OPAA estimates probability densities using functional analysis.
problem Estimating probability density functions efficiently and accurately.
method OPAA uses a parallelizable algorithm based on functional analysis to estimate probability distributions.
result OPAA provides an efficient method to estimate probability density functions and normalizing weights.
RS-HDMR-GPR simplifies complex functions with machine-learned lower-dimensional terms.
problem Representing and understanding complex multidimensional functions with sparse data.
method Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR).
result Facilitates recovery of functional dependence and adds insight into input variable importance.
Paper connects probability density cuts to graph theory eigenfunctions.
problem Developing sparse cuts for probability densities.
method Defines sparse cuts and principal eigenfunctions for probability densities, proving Cheeger and Buser inequalities.
result No such inequalities hold for prior definitions, proving new inequalities for probability densities.
Hierarchical density embeddings capture word relationships with uncertainty.
problem Capturing semantic relationships and uncertainty in word embeddings.
method Learn hierarchical representations through probability density encapsulation, using simple loss functions and distance metrics.
result State-of-the-art performance on WordNet and Hyperlex datasets.
This research improves demand forecasting by predicting complete probability density functions using machine learning.
problem Forecasting complete probability density functions for better operational decision making.
method Supervised machine learning method 'Cyclic Boosting' for explainable predictions.
result Predicted probability density functions are fully explainable and avoid 'black-box' models.
Proposes a method to estimate time-dependent probability density functions using binary classifiers.
problem Estimating time-dependent probability density functions of stochastic processes.
method Trains a time-dependent binary classifier to discriminate between realizations of a stochastic process at two nearby time instants.
result Explicitly models and accurately reconstructs complex time-dependent, multi-modal, and near-degenerate densities.
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…
Simplified derivation and simulation of Feller Diffusion.
problem Deriving the probability density function of Feller Diffusion.
method Fourier Transform and Method of Characteristics for derivation; simulation algorithms for validation.
result Confirmation of hitting time probabilities via simulation.
New estimators for probability density functions, minimizing bias and variance.
problem Lack of practical estimators for Sobolev quantities of unknown probability density functions.
method Proposed and analyzed a family of estimators for Sobolev quantities of unknown probability density functions.
result Our estimators are minimax rate-optimal and computationally tractable, adapting to computational constraints.
Global minima found for multidimensional scaling with penalties.
problem Finding global minima in multidimensional scaling.
method Combining stress loss function with a quadratic penalty term to find minimizers.
result Trajectory of minimizers leads to global minima.
VI approximates complex densities faster than classical methods.
problem Approximating complex probability densities.
method Optimization of a family of probability density functions using KL divergence.
result VI converges faster than Markov Chain Monte Carlo.
A novel hyperplane classifier minimizes probability density.
problem Clustering and semi-supervised classification of unlabelled data.
method Minimum density hyperplane that minimizes the integral of empirical probability density.
result The minimum density hyperplane is asymptotically equivalent to maximum margin hyperplane.
Quantum computing speeds up option pricing for multiple assets.
problem High-dimensional integration bottleneck in option pricing.
method Calibrated marginal distributions, Gaussian copula, QAMC with QAE.
result QAMC reduces integration queries by 10-100 times for similar precision.
We develop a new statistical test for comparing variables with varying scales.
problem Comparing variables with different scales in multidimensional spaces.
method Order based on expectations of random variables, generalized stochastic dominance (GSD) order, regularized statistical test, linear optimization, imprecise probability models.
result Validated through multidimensional data from various fields.
A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.
Transformer with denoising diffusion improves probabilistic density estimation.
problem Estimating non-Gaussian and multimodal probability distributions for regression problems.
method Training a denoising diffusion head on top of a Transformer model.
result The model provides reasonable probability density estimation for high-dimensional inputs.
Develops a new method to learn kernels directly over function space.
problem Learning kernels for flexible function approximators.
method Functional Kernel Learning (FKL) using transformed Gaussian processes over spectral densities.
result Direct inference of functional posteriors over kernels enables rich representations.
New method improves sampling from high-dimensional target densities.
problem Sampling from high-dimensional target densities using Monte Carlo algorithms.
method Extends Metropolis-Adjusted Langevin Diffusion algorithm with random precondition matrix modeling.
result Significantly improves performance and computational efficiency over standard MCMC methods.
The paper analyzes kNN density estimation's convergence rates under different conditions.
problem Analyzing convergence rates of kNN density estimation under bounded and unbounded support conditions.
method Examined two cases: bounded support with known and unknown support sets, and unbounded support with smooth density function.
result kNN density estimation is minimax optimal under certain conditions and better than kernel density estimation in some cases.
A new machine learning model uses score matching to estimate probability densities efficiently.
problem Estimating probability density functions is challenging.
method Introduced a product Jacobi-Theta Boltzmann machine (pJTBM) and used score matching for efficient fitting.
result The pJTBM can fit probability densities more efficiently than the RTBM using score matching.
Extends Bayesian theory to handle complex interdependencies in multidimensional event spaces.
problem Complex interdependencies between events and hypotheses sets in real-world systems.
method Developed a mathematical formalism for modeling complex relationships through rigorous derivation and validated using analytical proofs, simulations, and case studies.
result MDSE theory improves prediction accuracy by 15-20% compared to standard Bayesian methods in high interdimensionality datasets.
The Riemann-Theta Boltzmann machine's visible sector is sampled using a discrete multi-variate Gaussian.
problem Sampling the visible sector of the Riemann-Theta Boltzmann machine.
method Discrete multi-variate Gaussian over the hidden state space.
result The visible sector probability density function is an infinite mixture of multi-variate Gaussians.
Researchers calculate the Laplace transform of a geometric Brownian motion integral.
problem Calculating the Laplace transform of a specific integral functional of geometric Brownian motion.
method Analytical calculation of the Laplace transform of the cumulative distribution and probability density functions.
result The Laplace transform of the integral functional of geometric Brownian motion is derived.
Bayesian inference engines improve density estimation accuracy and scalability.
problem Constructing accurate and scalable probability density functions.
method Bayesian inference engines (no-U-turn sampling and expectation propagation) with binning strategy.
result Density estimates have excellent comparative performance and scale well to large sample sizes.
PHOENICS optimizes complex functions efficiently, outperforming traditional methods.
problem Optimizing complex, non-convex functions with varying domains.
method Combines Bayesian optimization and kernel density estimation with an acquisition function.
result PHOENICS outperforms Gaussian processes and random forests in multidimensional optimization.
A new method for Monte Carlo sampling improves estimator performance.
problem Inefficient proposal densities in Monte Carlo methods lead to poor estimator performance.
method A layered importance sampling framework using multiple proposal densities and adaptive MCMC chains.
result The method ensures an appropriate equivalent proposal density and improves estimator performance.
A new model predicts crop yields with high accuracy and uncertainty.
problem Uncertainty in crop yield forecasting due to weather extremes.
method Quantile random forest and Epanechnikov kernel function.
result The model captures crop yields with high coverage probability and provides feature importance.
Sum-of-Squares flow improves autoregressive and flow-based density estimation.
problem Density estimation in high dimensions with limitations of existing methods.
method Proposes a Sum-of-Squares (SOS) flow framework based on triangular maps.
result SOS flow achieves competitive results in simulations and real-world datasets.
New method estimates density functionals using polynomial basis without full distribution knowledge.
problem Estimating quantities like information divergence functions requires complete distribution knowledge and integration.
method Introduces data-driven basis functions and develops methods for basis expansions of functionals of two distributions.
result Approximates functions of distributions as closely as desired using the new basis set.