Discussing new econophysics methods for volatility and probability density estimation.
problem Estimating volatility and probability densities in econophysics.
method Reviewing recent methods for volatility and probability density estimation.
result Pioneering methods for volatility and probability density estimation in econophysics.
Method estimates joint probability density from samples using low-rank decomposition and random projections.
problem Estimating joint probability density from limited samples.
method Low-rank tensor decomposition, dictionaries, and Radon transforms.
result Algorithm outperforms previous methods in estimating synthetic probability densities.
DoSE improves OOD detection by estimating model probability density.
problem Poor specificity of model likelihoods for OOD detection.
method DoSE uses density of states concept to avoid direct model probability comparison.
result DoSE achieves state-of-the-art performance on OOD detection benchmarks.
Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models leverage the power of neural networks to implicitly learn and represent probability …
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 …
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.
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.
Estimates copula density for complex data distributions.
problem Estimating copula density from observed data.
method Neural network-based copula density neural estimation (CODINE).
result Novel approach capable of modeling complex distributions.
A density ratio is defined by the ratio of two probability densities. We study the inference problem of density ratios and apply a semi-parametric density-ratio estimator to the two-sample homogeneity test. In the proposed test procedure, the f-divergence between two probability densities is estimated using a density-r…
Paper proposes new density estimators for high-dimensional data.
problem Prohibitive computational cost and slow convergence rate in high-dimensional density estimation.
method Adaptive hyperbolic cross density estimators in mixed smooth Sobolev spaces.
result Proposed estimators do not suffer curse of dimensionality under Integral Probability Metrics.
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 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.
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.
New tractable density models from squaring neural networks.
problem Flexible models for probability distributions in machine learning.
method Squared Neural Family (SNEFY) models formed by squaring neural network outputs and normalizing.
result SNEFYs are fully tractable with closed form normalizing constants in many cases.
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.
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
Kernel Density Machines learn probability densities without structural assumptions.
problem Learning probability densities under minimal assumptions.
method Kernel-based framework, agnostic to structural requirements.
result Consistency and functional central limit theorem for sample estimator.
We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural conditional density models and Gaussian processes. The proposed model is based on a novel …
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.
PSD models simplify probability density estimation.
problem Effective modeling of probability densities for inference.
method Positive semi-definite (PSD) models for non-negative functions.
result PSD models efficiently support product and sum rules.
LLMs learn probability density functions in-context, showing distinct learning trajectories.
problem Density estimation of time series data in LLMs.
method Intensive Principal Component Analysis (InPCA) to visualize and analyze LLMs' learning dynamics.
result LLMs follow similar learning trajectories in a low-dimensional InPCA space, distinct from traditional methods.
A new method estimates rare events using tensor trains.
problem Estimating rare event probabilities in high-dimensional problems.
method Approximating optimal importance distribution via tensor-train decompositions and compositions.
result Better variance reduction and efficient computation of rare event probabilities.
Unified view of KL-divergence and IPMs via DRE, with new DRM metrics.
problem Unified understanding of KL-divergence and IPMs.
method Unified representation via maximum likelihood density-ratio estimation (DRE).
result Unified form of IPMs and novel DRM metrics.
A new method for estimating density ratios in high dimensions.
problem Difficulty in accurately comparing probability distributions in high-dimensional settings.
method Divide-and-conquer approach via an infinite continuum of bridge distributions and time score matching.
result The proposed method effectively estimates density ratios and performs well on complex datasets.
This work assesses DNNs for estimating conditional probabilities.
problem Lack of uncertainty characterization in DNNs for probabilistic applications.
method Investigates DNNs' ability to estimate conditional probabilities using synthetic and real-world datasets.
result DNNs' precision in estimating conditional probabilities is influenced by probability density and inter-categorical sparsity.
Paper develops a consistent estimator for discrete mixture models.
problem Estimating mixing probability density in discrete mixture models.
method Develops an L 1 L_1 L 1 consistent estimator under specific conditions. result Consistent estimation of mixing probability density for every density f f f . This paper studies sparse density estimation via ℓ 1 \ell_1 ℓ 1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities an…
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of the data, namely a human-readable chart of the probability density from which t…
Study minimax rates for density estimation under Huber contamination and Besov IPM losses.
problem Minimax convergence rates of nonparametric density estimation under Huber contamination model with outliers.
method Re-scaled thresholding wavelet series estimator and GAN architectures.
result Achieves minimax optimal convergence rates under Besov IPM losses.
The article applies Occam's Razor to non-parametric model building, minimizing the number of bits for data encoding.
problem Overlooking the role of model parameters in data encoding leads to inefficient probability density estimators.
method Extends bit counting to model parameters, providing a true measure of complexity for parametric models.
result Minimizing total bit requirement leads to smoother, more efficient probability density estimates and fewer relevant parameters.
Truncated densities are probability density functions defined on truncated domains. They share the same parametric form with their non-truncated counterparts up to a normalizing constant. Since the computation of their normalizing constants is usually infeasible, Maximum Likelihood Estimation cannot be easily applied t…
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.
The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not yet been well-established for regression tasks. This paper considers the problem…
Improved manifold-adaptive dimension estimator for better data complexity assessment.
problem Estimating intrinsic dimensionality of complex data.
method Revised and improved Farahmand-Szepesvári-Audibert (FSA) estimator, incorporating probability density function and median.
result Median-FSA estimator outperforms existing methods in accuracy and robustness.
Normalizing flows improve density estimation from noisy data.
problem Estimating underlying density from noisy samples.
method Use normalizing flows for density estimation with arbitrary noise distributions, using amortized variational inference.
result Normalizing flows can outperform Gaussian mixtures for density deconvolution.
New method resolves density ratio estimation saturation issues.
problem Error saturation in density ratio estimation methods.
method Iterated regularization to improve kernel methods.
result Achieves fast error rates on regular learning problems.
A new tensor ring mixture model improves density estimation efficiency.
problem Efficient probability density estimation in statistical machine learning.
method Tensor ring decomposition with mixture model for adaptive weights.
result Enhanced expressive capability and flexibility in density estimation.
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.
Study improves density estimation for compact domains using h h h -lifted KL divergence.
problem Estimating probability density functions on compact domains.
method Introduced h h h -lifted Kullback--Leibler (KL) divergence for risk minimization. result Proved O ( 1 / n ) \mathcal{O}(1/{\sqrt{n}}) O ( 1/ n ) bound on estimation error. A new method for estimating density ratios using geodesics on statistical manifolds.
problem Stability of density ratio estimation when distributions are distant.
method Iterative sampling along generalized geodesics on the Riemannian manifold.
result The proposed method outperforms existing incremental mixture methods.
One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a lower-dimensional manifold of high probability. It has been more difficul…
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 technique for multiple-source adaptation without density estimation.
problem Multiple-source adaptation problem.
method Discriminative technique that uses conditional probabilities from unlabeled data.
result Our technique outperforms previous generative solutions and other domain adaptation baselines.
LADaR framework calibrates machine learning models for instance-wise predictions.
problem Challenges in assessing and calibrating predictive distributions for complex inputs.
method Local Amortized Diagnostics and Reshaping of Conditional Densities (LADaR) framework and e x t t t C a l − P I T exttt{Cal-PIT} e x ttt C a l − P I T algorithm. result Achieves better instance-wise calibration than existing methods in galaxy distance estimation.
New model for density estimation using tensor trains.
problem Estimation of high-dimensional probability density functions.
method Tensor train-based density estimation (TTDE) with Riemannian optimization.
result TTDE outperforms competitors in training speed and performance.
Paper introduces MoM-KDE for robust density estimation robust to anomalous data.
problem Density estimation robustness to anomalous data.
method Combines Kernel Density Estimation and Median-of-Means principle.
result Achieves competitive results with lower computational complexity compared to other robust estimators.
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.