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.
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.
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.
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…
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.
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…
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.
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.
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.
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…
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.
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.
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.
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.
This paper deals with multidimensional dynamic risk measures induced by conditional g-expectations. A notion of multidimensional g-expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…
This paper improves conditional multidimensional scaling for incomplete data.
problem Handling missing data in known features for multidimensional scaling.
method Proposes a method to learn low-dimensional configurations with missing known feature values.
result Can learn low-dimensional configurations and impute missing values.
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.
The paper explores multidimensional critic output in GANs, improving convergence and diversity.
problem Underexplored in GANs literature, multidimensional critic output.
method Generalized Wasserstein GAN framework, SRVT block, maximal p-centrality discrepancy.
result High-dimensional critic output improves GAN performance in convergence and diversity.
Improved algorithm for multidimensional scaling reduces stress.
problem Stress in multidimensional scaling.
method Proposed modifications of the smacof algorithm.
result Convergent majorization algorithm for Kruskal's stress formula two.
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 to visualize multidimensional local subspaces using implicit differentiation.
problem Understanding the effect of multidimensional projection on local subspaces.
method Implicit function differentiation to analyze local subspaces shaped by multidimensional ellipses.
result Visualization of local subspaces provides insights into the global structure of data.
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.
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a unified framework that includes low, moderate and high dimensions, we study multidim…
Study uses multidimensional SE-NBD process to analyze default portfolios and identify shock amplification.
problem Analyzing interactions and shock propagation in default portfolios with multiple sectors.
method Applied multidimensional self-exciting negative binomial distribution (SE-NBD) process to 13 sectors.
result Identified upstream and downstream sectors, showing shock amplification in default portfolios.
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…
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
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…
Novel method for multiclass ROC curves using multidimensional Gini index.
problem Multiclass performance evaluation, especially for imbalanced datasets.
method Extends ROC curve methodology to multiclass settings using multidimensional Gini index.
result Validated through case studies in health care and finance.
We show that shortfall risks of American options in a sequence of multinomial approximations of the multidimensional Black--Scholes (BS) market converge to the corresponding quantities for similar American options in the multidimensional BS market with path dependent payoffs. In comparison to previous papers we conside…
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.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
Paper presents adaptive minimax risk classifiers for multidimensional concept drift.
problem Multidimensional concept drift in supervised classification.
method Adaptive minimax risk classifiers (AMRCs) tracking multivariate and high-order distribution changes.
result AMRCs provide computable tight performance guarantees and improve classification.
sWk-means clusters multidimensional financial time series into distinct market regimes.
problem Classifying distinct market regimes in multidimensional financial time series.
method Approximated multidimensional Wasserstein distance as sliced Wasserstein distance for clustering.
result sWk-means successfully identifies distinct market regimes in real financial data.
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays the foundati…
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.
New method simulates sticky boundaries in multidimensional diffusions.
problem Simulating sticky boundaries in multidimensional diffusions.
method Approximate sticky diffusion by a Markov chain, using either finite difference or matching local moments.
result Validates both construction methods for first-order simulation schemes.