FlowSDR: Sufficient Dimension Reduction via Conditional Normalizing Flows

• URL: http://arxiv.org/abs/2606.01346v1
• Date: Sun, 31 May 2026 16:54:56 GMT
• Title: FlowSDR: Sufficient Dimension Reduction via Conditional Normalizing Flows
• Abstract summary: FlowSDR is a likelihood-based framework that jointly learns the projection and the conditional density.<n>We introduce the neural Gaussian SDR, a heteroscedastic conditional Gaussian model whose mean and variance are parameterized by shared neural-network functions.
• Score: 6.1441848595952
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sufficient dimension reduction (SDR) seeks a low-dimensional linear projection of predictors that preserves the conditional distribution of the response. Existing methods target this conditional distribution indirectly, via inverse moments, local forward regression, or neural ensemble regression. We propose FlowSDR, a likelihood-based framework that jointly learns the projection and the conditional density by maximizing a conditional log-likelihood, with the density parameterized by monotone rational-quadratic spline flows. The estimator is Fisher consistent under the SDR model, and its sample objective admits a population interpretation in terms of mutual information. As a complementary model within the same likelihood framework, we introduce the neural Gaussian SDR, a heteroscedastic conditional Gaussian model whose mean and variance are parameterized by shared neural-network functions of the projected predictors. In simulations spanning Gaussian errors, heavy-tailed distributions, two-component mixtures, and settings with tail behavior not captured by mean-variance structure, FlowSDR recovers the central subspace more accurately than existing SDR methods and the neural Gaussian SDR baseline. We further validate these advantages on a face-age prediction task using the UTKFace dataset.

Related papers

• Joint Model and Data Sparsification via the Marginal Likelihood [53.29070892356214]
  We propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification.<n>This symmetric pruning of model and data offers a natural extension that preserves conjugacy.<n> Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
  arXiv  Detail & Related papers  (2026-05-28T13:26:53Z)
• Beyond Consistency: Inference for the Relative risk functional in Deep Nonparametric Cox Models [7.2275111013288535]
  It is unclear how Cox-based optimization error propagates to population risk under partial likelihood.<n>It is also unclear how pointwise bias can be controlled, and how ensemble-based uncertainty behaves under realistic variance regimes.<n>We develop an distribution theory for deep Cox estimators that addresses these issues.
  arXiv  Detail & Related papers  (2026-03-25T01:43:12Z)
• Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression [47.1405366895538]
  Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization algorithm.
  arXiv  Detail & Related papers  (2023-09-15T22:06:29Z)
• A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty [1.8416014644193066]
  We propose a data-driven, closure model for Reynolds-averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. A fully Bayesian formulation is proposed, combined with a sparsity-inducing prior in order to identify regions in the problem domain where the parametric closure is insufficient.
  arXiv  Detail & Related papers  (2023-07-05T16:53:31Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• Reliable amortized variational inference with physics-based latent distribution correction [0.4588028371034407]
  A neural network is trained to approximate the posterior distribution over existing pairs of model and data. The accuracy of this approach relies on the availability of high-fidelity training data. We show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution.
  arXiv  Detail & Related papers  (2022-07-24T02:38:54Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Diffusion Causal Models for Counterfactual Estimation [18.438307666925425]
  We consider the task of counterfactual estimation from observational imaging data given a known causal structure. We propose Diff-SCM, a deep structural causal model that builds on recent advances of generative energy-based models. We find that Diff-SCM produces more realistic and minimal counterfactuals than baselines on MNIST data and can also be applied to ImageNet data.
  arXiv  Detail & Related papers  (2022-02-21T12:23:01Z)
• On the Double Descent of Random Features Models Trained with SGD [78.0918823643911]
  We study properties of random features (RF) regression in high dimensions optimized by gradient descent (SGD) We derive precise non-asymptotic error bounds of RF regression under both constant and adaptive step-size SGD setting. We observe the double descent phenomenon both theoretically and empirically.
  arXiv  Detail & Related papers  (2021-10-13T17:47:39Z)
• Information Theoretic Structured Generative Modeling [13.117829542251188]
  A novel generative model framework called the structured generative model (SGM) is proposed that makes straightforward optimization possible. The implementation employs a single neural network driven by an orthonormal input to a single white noise source adapted to learn an infinite Gaussian mixture model. Preliminary results show that SGM significantly improves MINE estimation in terms of data efficiency and variance, conventional and variational Gaussian mixture models, as well as for training adversarial networks.
  arXiv  Detail & Related papers  (2021-10-12T07:44:18Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Unlabelled Data Improves Bayesian Uncertainty Calibration under Covariate Shift [100.52588638477862]
  We develop an approximate Bayesian inference scheme based on posterior regularisation. We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
  arXiv  Detail & Related papers  (2020-06-26T13:50:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.