This work tackles multivariate CDFs and copulas using tensor factorization.
problem Learning multivariate distributions, especially for mixed random variables, is challenging.
method Introducing a low-rank model for efficient sampling, inference, and uncertainty quantification.
result The proposed model outperforms traditional methods in various applications.
We leverage neural networks as universal approximators of monotonic functions to build a parameterization of conditional cumulative distribution functions (CDFs). By the application of automatic differentiation with respect to response variables and then to parameters of this CDF representation, we are able to build bl…
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.
Algorithm infers sampling distribution from i.i.d. samples without supervision.
problem Learning probability distributions from unlabeled data.
method Unsupervised tree boosting using additive tree ensembles and new distributional operations.
result Algorithm outperforms deep learning in multivariate density estimation.
BOtied optimizes multiple objectives using copulas and CDF indicators.
problem Joint optimization of multiple competing objectives.
method Proposes BOtied, a new acquisition function based on the CDF.
result BOtied outperforms state-of-the-art MOBO acquisition functions.
One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some a…
New method combines score lists using joint CDFs, improving computation.
problem Combining non-comparable score lists over a common index set.
method New algorithm for computing joint CDF values, linear runtime.
result Improved computation of joint CDF values for N-dimensional order statistics.
CDF uses centroids to split features for high-dimensional classification.
problem High-dimensional classification problems with complex class structures.
method CDF introduces a centroid-driven splitting strategy in decision trees.
result CDF outperforms conventional methods in high-dimensional classification.
We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We t…
New method for learning multidimensional CDFs using Archimedean copulas.
problem Learning multidimensional CDFs in high dimensions.
method Generative modeling technique using Archimedean copulas as mixture models with latent variables from neural networks.
result Efficacy and computational efficiency compared to existing methods.
This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches…
The paper provides bounds on the CDF of a variable under nonstationary conditions.
problem Estimating the complete distribution of a random variable under nonstationary conditions.
method Time-uniform and value-uniform bounds on the CDF of the running averaged conditional distribution.
result Presented computationally efficient bounds that are always valid and sometimes trivial.
Estimates CDF over complex regions using normalizing flows.
problem Challenges in estimating CDF over complex regions using traditional methods.
method Leverages diffeomorphic properties of normalizing flows and divergence theorem.
result Improves sample efficiency in estimating CDF over complex regions.
SURF steers scalarization weights to uniformly traverse the Pareto front.
problem Non-uniform coverage of the Pareto front when using scalarization weights.
method Geometric analysis and CDF mapping to select weights for uniform coverage.
result SURF converges to uniform Pareto front coverage under provable conditions.
Paper develops a new estimator for MDPs' risk functionals with lower variance and bias.
problem Estimating the distribution of returns in MDPs with high variance and bias.
method Developed a doubly robust (DR) estimator for the CDF of returns in MDPs, incorporating model-based estimation to mitigate variance issues.
result The DR estimator achieves lower variance and bias compared to IS estimators, and matches minimax lower bounds.
A new pseudo-metric uses data depth to compare probability distributions.
problem Designing a metric between probability distributions for machine learning applications.
method Extension of univariate quantiles to multivariate spaces, using data depth and Hausdorff distance.
result The pseudo-metric is robust, factorizes translations, and has good behavior under transformations.
The paper proposes a method to construct well-calibrated prediction sets for correlated target variables.
problem Constructing well-calibrated prediction sets for correlated target variables.
method The method uses vine copulas to estimate the joint cumulative distribution function of non-conformity scores and improves the asymptotic efficiency of the quantile estimate.
result The method guarantees asymptotically exact coverage and competitive efficiency on real-world regression problems.
Maximizing trading volume in online learning framework between traders.
problem Maximizing the total number of trades between traders with unknown valuations.
method Developed algorithms for brokers to maximize trading volume under different feedback scenarios.
result Achieved logarithmic and poly-logarithmic regret rates for different feedback models.
New method estimates SW distance using CDFs for scalable data parallelism.
problem Estimating SW distance efficiently for large datasets.
method Estimators based on CDFs of projected measures, avoiding sorting.
result Efficient estimation for large datasets and federated learning.
Proposes a method to create shorter, more accurate prediction intervals.
problem Challenges in achieving both conditional validity and interval efficiency in complex settings.
method Uses a conformal-style calibration method for neural network responses, adjusting to empirical PIT distribution.
result Demonstrates better conditional calibration and shorter intervals than existing methods.
CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. However, SIC requires additional hyper-parameter tunning, and no algorithms for computing higher order derivative from a trained NN are provided in [1]. CDF2PDF improves SIC by avoiding the tim…
Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is however piece-wise constant (the sorting permutation of a vector does not change if th…
Exact bounds derived for neural network outputs with noisy inputs.
problem Bounding the output distribution of neural networks with random inputs.
method Applying ReLU NNs to derive bounds for general NNs, then using these to find exact error guarantees.
result Exact upper and lower bounds for the output distribution of neural networks with random inputs.
Paper introduces risk assessment for contextual bandits without experiments.
problem Evaluate policies using logged data in context bandits.
method Lipschitz risk functionals and Off-Policy Risk Assessment (OPRA) framework.
result OPRA provides finite sample guarantees for various risk estimates.
Introduces CuFun model for more accurate TPPs using CDF.
problem Challenges in forecasting future events in TPPs.
method Uses Cumulative Distribution Function (CDF) and monotonic neural network.
result Significantly improves adaptability and precision in TPPs.
This paper tests the multivariate normality of node degrees in Erdős-Rényi graphs.
problem Testing the multivariate normality of node degrees in Erdős-Rényi graphs.
method Chi-square goodness of fit test, Anderson-Darling test, CDF comparison, maximum likelihood estimation.
result The degrees of nodes in Erdős-Rényi graphs do not follow a multivariate normal distribution, but the approximation is valid for large values of n and p.
Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.
problem Bounding generalization gaps for various risk functionals beyond the expectation.
method Establishes uniform convergence for Hölder risk functionals, providing guarantees for empirical risk minimization.
result First uniform convergence results for estimating the CDF of loss distributions, applicable to various risk functionals.
Generative AutoEncoders require a chosen probability distribution in latent space, usually multivariate Gaussian. The original Variational AutoEncoder (VAE) uses randomness in encoder - causing problematic distortion, and overlaps in latent space for distinct inputs. It turned out unnecessary: we can instead use determ…
The paper examines bounds for stop-loss payoffs using transformed random variables.
problem Bounding stop-loss payoffs for a difference of two random variables.
method Analyzes crossing points of cdfs of original and transformed random variables.
result Unique pairwise crossing points for mortality-linked securities under symmetric copulas.
We stabilize the Kumaraswamy distribution for efficient sampling and differentiation.
problem Numerical instabilities in the Kumaraswamy distribution's inverse CDF and log-pdf.
method Identified and resolved numerical issues, introduced a stabilized KS distribution.
result Stabilized Kumaraswamy distribution supports efficient sampling and differentiation.
AI learns to classify and represent univariate distributions in a 2D latent space.
problem Classifying and representing univariate empirical distributions.
method Unsupervised beta variational autoencoder (beta-VAE) to separate and represent distributions in a 2D latent space.
result The latent space representation separates distributions of different shapes while overlapping similar ones.
A method uses neural networks to approximate sampling distributions of test statistics.
problem Accurate modeling of p-value functions or cdfs for correct confidence set coverage.
method Uses neural networks to model the cdf of test statistics, approximating sampling distributions.
result Neural network approximations of sampling distributions are effective and simple.
We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure μ. We show that the Sobolev IPM compares two distributions in hig…
Deep conditional transformation models unify interpretable and complex predictors.
problem Challenging to learn conditional CDFs in high-dimensional settings.
method Unified deep learning framework for interpretable and complex predictors.
result Efficacy demonstrated through numerical experiments and applications.
Fast, reliable, and error-bounded option pricing with neural networks
problem Fast, reliable, and error-bounded option pricing
method Mixture Density Network
result Out-of-sample CDF error of 1.4imes10−4 The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.
problem Challenges of classical statistical models in heavy-tailed distributions.
method Theoretical study of quantile contribution statistic and its relationship with order statistics. Derivation of closed-form expression for joint CDF of order statistics and quantile contributions.
result Established asymptotic normality of quantile contributions and characterized their limiting distribution.
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…
A new distribution family extends the α-stable distribution with a degree of freedom parameter.
problem Lack of moments in the α-stable distribution. method Wright function framework to combine and extend distribution families.
result Generalized α-stable distribution with valid moments. Paper simplifies data carving inference with a parametric distribution.
problem Valid inference after selection with data carving.
method Developed a parametric distribution for data carving inference.
result Exact inference for data carving can be computed trivially.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
We relax demographic parity in regression by enforcing parity at quantile levels and score thresholds.
problem Enforcing full distributional fairness in regression can lead to substantial accuracy loss.
method Introduce (ℓ, Z)-fair predictor, derive closed-form solutions, and develop post-processing algorithm. result The risk gap to the continuous optimum vanishes as the grid is refined, and we enable targeted fairness corrections.
This paper combines and improves probabilistic forecasts of wind speeds using advanced statistical methods.
problem Improving accuracy and reliability of probabilistic forecasts in wind speed prediction.
method Adapting prediction with expert advice theory to probabilistic forecasts, combining raw or post-processed ensembles, and using CRPS and Jolliffe-Primo tests.
result Combining probabilistic forecasts can lead to more reliable and skillful predictions, as shown by the Jolliffe-Primo test.
Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis …
We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for c…
A fast regime-split Black-Scholes implied volatility solver
problem Fast computation of implied volatility
method Analytical and numerical expansions
result Achieves near-machine precision with minimal iterations
Universal algorithm learns unknown distribution for various decision-making problems.
problem Various statistical measures in contextual sequential decision-making.
method Infinite-dimensional functional regression oracle for cumulative distribution functions.
result Utility regret rate bounded by polynomial decay of eigenvalue sequence.
The cost-benefit analysis formulates the holy trinity of objectives of project management - cost, schedule, and benefits. As our previous research has shown, ICT projects deviate from their initial cost estimate by more than 10% in 8 out of 10 cases. Academic research has argued that Optimism Bias and Black Swan Blindn…
Paper addresses generalization error bounds for learning with censored feedback.
problem Impact of censored feedback on generalization error bounds.
method Derives an extension of DKW inequality for non-IID data due to censored feedback and uses it to bound generalization error.
result Existing generalization error bounds fail to account for censored feedback, necessitating new bounds.