Flexible evidential deep learning improves uncertainty quantification in machine learning.
problem Overconfident predictions in machine learning models can lead to serious consequences.
method Proposes flexible evidential deep learning (F-EDL) to model uncertainty over class probabilities using a flexible Dirichlet distribution.
result Empirically demonstrates state-of-the-art uncertainty quantification performance across diverse scenarios.
RegFlow models future states with flexible probability distributions.
problem Predicting future states under complex, non-deterministic scenarios.
method Hypernetwork architecture and continuous normalizing flow model.
result RegFlow achieves state-of-the-art results on benchmark datasets.
Combines MCTM and NF for flexible multivariate density regression with interpretable marginals.
problem Difficult interpretation of flexible NF models and limitations of MCTM in flexibility.
method Hybrid approach combining MCTM for interpretable marginals and NF for complex joint distributions.
result Demonstrates versatility and improved performance compared to MCTM and other NF models.
New distributions on manifolds for better sampling.
problem Creating flexible distributions on Riemannian manifolds.
method Area-preserving maps and isometries for constructing distributions.
result Flexibility and straightforward sampling of distributions.
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and…
Flexible copula model using implicit generative neural networks.
problem Limited flexibility of parametric copulas and curse of dimensionality in non-parametric methods.
method Implicit generative neural networks to model high-dimensional copula distributions with unspecified marginals.
result Demonstrated flexibility and performance on various datasets.
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.
Bayesian model improves classification performance with flexible uncertainty modeling.
problem Improving classification performance with flexible uncertainty modeling.
method Combines Gaussian process and Dirichlet process priors for latent function and link function, respectively.
result Outperforms standard logistic regression on simulated data.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
We implement a systematic asset allocation model using the Historical Simulation with Flexible Probabilities (HS-FP) framework developed by Meucci. The HS-FP framework is a flexible non-parametric estimation approach that considers future asset class behavior to be conditional on time and market environments, and deriv…
Modified lognormal distribution with flexible tails for skewed data.
problem Skewed and fat-tailed data in natural and engineering datasets.
method Developed a family of three-parameter non-Gaussian probability density functions based on generalized kappa-exponential and kappa-logarithm functions.
result Closed-form analytic expressions for statistical functions and maximum-likelihood estimation.
VSPS creates flexible prediction regions for multi-target regression with guaranteed coverage.
problem Uncertainty quantification in multi-target regression with complex distributions.
method Conditional normalizing flows with conformal calibration to identify dense regions.
result VSPS produces smaller, more informative prediction regions with robust coverage guarantees.
We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of con…
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete probability distributions in a Wasserstein space, endowed with an optimal transport metri…
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
problem Limited work on flexible and computationally convenient stochastic process extensions for dependent random probabilities.
method Introduces logistic-beta process with logistic transformation and beta marginals, capable of modeling dependence in discrete and continuous domains.
result Logistic-beta processes enable effective posterior inference and design of computationally tractable dependent Bayesian nonparametric models.
MEP-Net uses MEP to generate solutions from limited data.
problem Generating solutions to scientific problems with incomplete information.
method Combines MEP with neural networks to learn complex distributions from moment constraints.
result Demonstrates MEP-Net's effectiveness in modeling biochemical reaction networks and generating complex distributions.
I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward, flexible and effective. Even when working with far fewer data points than are rou…
A new method for deep Wishart processes improves kernel-based models.
problem Inference in deep Wishart processes is challenging due to the need for flexible distributions over positive semi-definite matrices.
method Developed a novel approach to flexible distributions over positive semi-definite matrices using the Bartlett decomposition of the Wishart probability density. Used this to create an approximate posterior for the DWP.
result Improved performance of inference in the DWP compared to DGP with equivalent prior.
Riemannian flows model curved spaces better.
problem Normalizing flows misspecified on curved spaces.
method Riemannian continuous normalizing flows using ODE solutions.
result Improves modeling on spheres, torii, and hyperbolic spaces.
Enhances flexibility in data reweighting with optimal transport and maximum entropy principles.
problem Adapting empirical distributions to predefined constraints on moments, tail behavior, etc.
method Nonparametric distributional constraints, maximum entropy principle, optimal transport.
result Maximum entropy weight adjusted empirical distribution close to a specified distribution in optimal transport metric.
New tests for binary classification regression functions without distribution assumptions.
problem Testing regression functions in binary classification without distributional assumptions.
method Conditional kernel mean embeddings and resampling-based framework.
result Distribution-free hypothesis tests with exact type I error control.
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing …
Flexible framework for bounding high-loss predictions using quantiles.
problem Need for rigorous guarantees in risk-sensitive applications.
method Order statistics of loss values, flexible quantile-based metrics.
result Ability to rigorously control loss quantiles on real-world datasets.
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
PH-VAE models heavy-tailed data with flexible Phase-Type distributions.
problem Standard VAEs fail to capture heavy-tailed behavior in real-world data.
method PH-VAE uses Phase-Type distributions defined by continuous-time Markov chains to adaptively model tail behavior.
result PH-VAE significantly outperforms existing heavy-tail-aware VAEs in approximating diverse heavy-tailed distributions.
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.
Quantum walks model financial returns with flexibility and asymmetry.
problem Accurate modeling of financial asset price dynamics.
method Discrete-time quantum walks to model asset price evolution.
result Quantum walk models can generate asymmetric return distributions and higher probabilities for extreme events.
With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that attaches an explicit uncertainty statement to the probabilities of classification u…
Semiparametric Bayesian networks combine parametric and nonparametric models for flexible data analysis.
problem Combining the advantages of parametric and nonparametric models for flexible data analysis.
method Semiparametric Bayesian networks combining parametric and nonparametric conditional probability distributions. Modifications of two algorithms for structure learning from data.
result Accurately learns the combination of parametric and nonparametric components, comparable to state-of-the-art methods.
Study optimizes tree-based models for better alignment of predicted scores and actual probabilities.
problem Traditional calibration metrics fail to align predicted scores with actual probabilities when score distributions deviate from the underlying data.
method Optimizes tree-based models (Random Forest, XGBoost) using Kullback-Leibler (KL) divergence to minimize the difference between predicted and true probability distributions.
result Optimized tree-based models yield superior alignment between predicted scores and actual probabilities without significant performance loss.
New framework controls statistical dispersion for high-stakes applications.
problem Understanding and controlling the dispersion of loss distributions in high-stakes applications.
method Simple yet flexible framework for distribution-free control of statistical dispersion measures.
result Proposed methods control statistical dispersion measures with societal implications.
New framework estimates treatment effects based on preferences.
problem Estimating treatment effects with flexible outcomes.
method Preference-based Conditional Treatment Effect (CPTE) framework.
result CPTE provides interpretable targets and new identifiability conditions.
New model improves inference on asset market durations.
problem Statistical artifacts in trade aggregation.
method Flexible stochastic duration model with uncertainty in related trades.
result Conditional hazard function varies less than previous studies.
This paper introduces Probability Engineering to improve deep learning models.
problem Challenges in traditional probabilistic modeling for AI applications.
method Treats learned probability distributions as engineering artifacts and actively modifies them.
result Improves robustness, efficiency, adaptability, and trustworthiness of deep learning models.
This paper introduces the Indian Chefs Process (ICP), a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes Indian Buffet Processes. As our construction shows, the proposed distribution relies on a latent Beta Process controlling both the orders and out…
The AMIDST Toolbox is a software for scalable probabilistic machine learning with a spe- cial focus on (massive) streaming data. The toolbox supports a flexible modeling language based on probabilistic graphical models with latent variables and temporal dependencies. The specified models can be learnt from large data s…
New risk class penalizes loss deviations from mean on both sides.
problem Current risks are sensitive to loss tails on the upside and ignore the downside.
method Introduces a bi-directional risk class with flexible tail sensitivity.
result Derives high-probability learning guarantees without gradient clipping.
Flexible framework for modeling predictive distributions of time series
problem Modeling predictive distributions of nonlinear time series
method Generative adversarial networks
result Direct simulation-based approximation to predictive distributions
This paper proposes a new method to solve functional minimization problems in probability distributions using sliced-Wasserstein gradient flows.
problem Solving functional minimization problems in high-dimensional probability distributions is computationally challenging.
method The paper introduces a new approach using sliced-Wasserstein gradient flows to approximate the Jordan-Kinderlehrer-Otto (JKO) scheme, parameterizing densities with generative models.
result The proposed method is more flexible and computationally tractable compared to existing methods like JKO-ICNN.
Proposes a risk parity portfolio optimization method that accounts for uncertainty in asset returns.
problem Risk parity portfolio optimization under uncertainty.
method Distributionally robust optimization with ambiguity set for worst-case scenario analysis.
result Distributionally robust risk parity portfolios can yield higher risk-adjusted returns.
GPDFlow models extreme threshold exceedance with flexible dependence using normalizing flows.
problem Challenges in modeling multivariate threshold exceedance probabilities due to infinite parametrizations.
method GPDFlow uses normalizing flows to flexibly represent dependence without explicit parametric assumptions.
result GPDFlow significantly improves modeling accuracy and flexibility compared to traditional parametric methods.
A new tree model, GRST, improves option pricing without log-normality assumptions.
problem Limitations of CRR binomial trees in valuing securities with early exercise characteristics.
method Gaussian Recombining Split Tree (GRST) that generates a discrete probability mass function approximating a Gaussian distribution.
result Option prices from GRST align closely with market prices.
Proposes LFGP for likelihood-free Gaussian process regression.
problem Inability to set likelihood functions in unknown probability models.
method Clusters and approximates likelihood using asymptotic normality.
result Reduces assumptions and computational costs for scalable problems.
LSI enables joint learning of latent variables and generative models.
problem Joint optimization of latent variables and generative models.
method Developed a principled ELBO objective in continuous time for joint learning.
result LSI learns effective latent representations and generative transformations.
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable metho…
A new probabilistic framework for optimal transport using collective graphical models.
problem Measuring similarity between probability distributions and histograms.
method Probabilistic Optimal Transport based on Collective Graphical Models.
result OT with entropic regularization is equivalent to maximizing a posterior probability of a CGM.
New framework transforms labeled datasets for various machine learning tasks.
problem Lack of principled methods to transform labeled datasets.
method Wasserstein gradient flows in probability space for optimization of data-generating distributions.
result Framework can impose constraints, adapt for transfer learning, or re-purpose models.
New method uses machine learning to estimate sensitivity without binning.
problem Estimating sensitivity of high-dimensional data sets without binning.
method Combines machine-learning classification with likelihood-based inference tests using Kernel Density Estimators.
result Significance estimation is not sensitive to non-smooth probability distributions.