arXiv subjects

Efstathia Bura

Publications and source records attributed to Efstathia Bura.

12 recordsLinked to original sources

arXiv2026

Learning sufficient low-dimensional structures through conditional optimal transport

Sufficient dimension reduction seeks a low-dimensional covariate representation that preserves the conditional law of a response. We introduce SDR-COT, which represents that law by conditional optimal transport from an independent reference response. On separable Hilbert spaces, sufficiency forces the response component of the optimal triangular map to factor through the reduction. For quadratic cost, the induced interpolation has a Borel current-state velocity on every truncated time interval, without global injectivity of the terminal map, and this velocity has the same factorisation. These results motivate a conditional-flow-matching criterion. For linear reductions, we prove consistency using a suitably tuned relaxed empirical coupling. Euclidean responses are treated through slicewise Caffarelli bounds; Hilbert-valued responses are treated through Gaussian Sobolev regularity, interpolation compression and uniqueness of a Gaussian continuity equation. Numerical studies with Euclidean and functional data show competitive performance, especially when sufficient information is not solely contained in the conditional mean.

math.ST↗

arXiv2025

Exact Upper and Lower Bounds for the Output Distribution of Neural Networks with Random Inputs

We derive exact upper and lower bounds for the cumulative distribution function (cdf) of the output of a neural network (NN) over its entire support subject to noisy (stochastic) inputs. The upper and lower bounds converge to the true cdf over its domain as the resolution increases. Our method applies to any feedforward NN using continuous monotonic piecewise twice continuously differentiable activation functions (e.g., ReLU, tanh and softmax) and convolutional NNs, which were beyond the scope of competing approaches. The novelty and instrumental tool of our approach is to bound general NNs with ReLU NNs. The ReLU NN-based bounds are then used to derive the upper and lower bounds of the cdf of the NN output. Experiments demonstrate that our method delivers guaranteed bounds of the predictive output distribution over its support, thus providing exact error guarantees, in contrast to competing approaches.

cs.LG↗

arXiv2025

Moment-based Density Elicitation with Applications in Probabilistic Loops

We propose the K-series estimation approach for the recovery of unknown univariate and multivariate distributions given knowledge of a finite number of their moments. Our method is directly applicable to the probabilistic analysis of systems that can be represented as probabilistic loops; i.e., algorithms that express and implement non-deterministic processes ranging from robotics to macroeconomics and biology to software and cyber-physical systems. K-series statically approximates the joint and marginal distributions of a vector of continuous random variables updated in a probabilistic non-nested loop with nonlinear assignments given a finite number of moments of the unknown density. Moreover, K-series automatically derives the distribution of the systems' random variables symbolically as a function of the loop iteration. K-series density estimates are accurate, easy and fast to compute. We demonstrate the feasibility and performance of our approach on multiple benchmark examples from the literature.

stat.ME↗

arXiv2025

Generalized Multi-Linear Models for Sufficient Dimension Reduction on Tensor Valued Predictors

We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the predictors given the response as a member of the quadratic exponential family. We develop estimation procedures of sufficient reductions for both continuous and binary tensor-valued predictors. We prove the consistency and asymptotic normality of the estimated sufficient reduction using manifold theory. For continuous predictors, the estimation algorithm is highly computationally efficient and is also applicable to situations where the dimension of the reduction exceeds the sample size. We demonstrate the superior performance of our approach in simulations and real-world data examples for both continuous and binary tensor-valued predictors.

stat.ME↗

arXiv2024

Exact and Approximate Moment Derivation for Probabilistic Loops With Non-Polynomial Assignments

Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art.

stat.AP↗

arXiv2022

Moment-based Invariants for Probabilistic Loops with Non-polynomial Assignments

We present a method to automatically approximate moment-based invariants of probabilistic programs with non-polynomial updates of continuous state variables to accommodate more complex dynamics. Our approach leverages polynomial chaos expansion to approximate non-linear functional updates as sums of orthogonal polynomials. We exploit this result to automatically estimate state-variable moments of all orders in Prob-solvable loops with non-polynomial updates. We showcase the accuracy of our estimation approach in several examples, such as the turning vehicle model and the Taylor rule in monetary policy.

stat.AP↗

arXiv2022

Distribution Estimation for Probabilistic Loops

We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and Gram-Charlier series, to estimate the distributions of the loop's random variables. We measure the accuracy of our distribution estimation by comparing the resulting distributions using exact and estimated moments of the probabilistic loop, and performing statistical tests. We evaluate our method on several probabilistic loops with polynomial updates over random variables drawing from common probability distributions, including examples implementing financial and biological models. For this, we leverage symbolic approaches to compute exact higher-order moments of loops as well as use sampling-based techniques to estimate moments from loop executions. Our experimental results provide practical evidence of the accuracy of our method for estimating distributions of probabilistic loop outputs.

stat.CO↗

arXiv2021

Sufficient reductions in regression with mixed predictors

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the general regression problem of inferring on a variable of interest based on high dimensional mixed continuous and binary predictors. The aim is to find a lower dimensional function of the mixed predictor vector that contains all the modeling information in the mixed predictors for the response, which can be either continuous or categorical. The approach we propose identifies sufficient reductions by reversing the regression and modeling the mixed predictors conditional on the response. We derive the maximum likelihood estimator of the sufficient reductions, asymptotic tests for dimension, and a regularized estimator, which simultaneously achieves variable (feature) selection and dimension reduction (feature extraction). We study the performance of the proposed method and compare it with other approaches through simulations and real data examples.

math.ST↗

arXiv2021

Fusing Sufficient Dimension Reduction with Neural Networks

We consider the regression problem where the dependence of the response Y on a set of predictors X is fully captured by the regression function E(Y | X)=g(B'X), for an unknown function g and low rank parameter B matrix. We combine neural networks with sufficient dimension reduction in order to remove the limitation of small p and n of the latter. We show in simulations that the proposed estimator is on par with competing sufficient dimension reduction methods in small p and n settings, such as minimum average variance estimation and conditional variance estimation. Among those, it is the only computationally applicable in large p and n problems.

stat.CO↗

arXiv2021

Ensemble Conditional Variance Estimator for Sufficient Dimension Reduction

Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. It is a semiparametric forward regression model based exhaustive sufficient dimension reduction estimation method that is shown to be consistent under mild assumptions. It is shown to outperform central subspace mean average variance estimation (csMAVE), its main competitor, under several simulation settings and in a benchmark data set analysis.

stat.ME↗

arXiv2021

Conditional Variance Estimator for Sufficient Dimension Reduction

Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for additive error regressions with continuous predictors and link function. It operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. In contrast to the majority of moment based sufficient dimension reduction methods, Conditional Variance Estimation is fully data driven, does not require the restrictive linearity and constant variance conditions, and is not based on inverse regression. CVE is shown to be consistent and its objective function to be uniformly convergent. CVE outperforms the mean average variance estimation, (MAVE), its main competitor, in several simulation settings, remains on par under others, while it always outperforms the usual inverse regression based linear SDR methods, such as Sliced Inverse Regression.

stat.ME↗

arXiv2017

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalised linear models

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalised linear models. We develop M-estimation theory for concave criterion functions that are maximised over parameters spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalised linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.

math.ST↗