The paper introduces a framework that combines deep generative models with symbolic regression to estimate symbolic expressions for unnormalized probability density functions directly from observed samples. By incorporating domain-specific priors—such as interaction ranges and a set of primitive functions—the method can factorize large distributions and remain tractable. Experiments demonstrate its effectiveness on multivariate toy distributions and on lattice models from computational physics, including the XY model and φ⁴ theory, where it produces compact symbolic approximations of the Hamiltonian across scales.
By Vikas Kanaujia, Riyansha Singh, Shashank Sharma, Vipul Arora
arXiv:2606. 01954v1 Announce Type: new Abstract: Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling.
By Luis A. Ortega, Andr\'es R. Masegosa, Thomas D. Nielsen
arXiv:2610.22763v1 Announce Type: new
Abstract: Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps...
By Tommaso Ancilli, Thomas Wedenig, Henry Moss, Robert Peharz
arXiv:2512. 04954v3 Announce Type: replace Abstract: We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling.
By Rajneil Baruah
arXiv:2608. 07648v1 Announce Type: cross Abstract: Sampling high-dimensional probability distributions is a central task in scientific computing, with applications ranging from Bayesian inference to statistical physics and molecular simulation.
By Marylou Gabri\'e
The paper introduces the transport Neural Tangent Kernel (tNTK) to enable active learning for conditional generative models that produce distributional outputs. By decomposing the Wasserstein test risk into mean and shape components, the authors show that mean‑based active learning misses distributional shape, and propose tNTK as a tractable kernel that captures sensitivity of the predicted distribution to model parameters. Using tNTK as a Gaussian process covariance, they greedily select inputs that minimize posterior variance, and demonstrate that this distribution‑aware strategy outperforms mean‑based NTK baselines across several generative model types and datasets.
By Jayoung Ryu, Kyunghyun Cho, Romain Lopez
arXiv:2610.34484v1 Announce Type: new
Abstract: Broad classes of deep generative models (DGMs) operate by learning to map a simple source distribution, such as a standard Gaussian, to a complex high-...
By Edric Tam, Qingyang Liu, Barbara Engelhardt, Ray Bai
The paper presents a theoretical framework for approximating ratio-type functionals that arise in conditional generative modeling, specifically when the target density is expressed as a ratio of two kernel-based marginal densities. It proves that deep neural networks using the SignReLU activation can approximate these ratios with established L^p(Omega) bounds and convergence rates under standard regularity assumptions. Applying the framework to Denoising Diffusion Probabilistic Models, the authors construct a SignReLU-based estimator for the reverse process and derive bounds on the excess Kullback–Leibler risk, decomposing it into approximation and estimation errors to provide generalization guarantees for finite-sample training.
By Luwei Sun, Dongrui Shen, Feng Chuanwen, Jianfe Li, Yulong Zhao, Han Feng
arXiv:2404.17763v3 Announce Type: replace-cross
Abstract: Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn...
By Yujie Chen, Anindya Bhadra, Antik Chakraborty
arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
By Xiuyuan Cheng, Yunqin Zhu, Yao Xie
Sufficiently Reduced Distributional Regression (SRDR) is a generative approach that merges conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). By framing SDR as a risk minimization problem using strictly proper scoring rules, SRDR jointly learns a dimension reduction map and a generative prediction model through minimization of the energy score, which can be estimated via sampling. The method extends to multi‑environment data and classification, and theoretical results show convergence of estimated conditional distributions in energy distance, implying asymptotic sufficiency. In experiments on CT slice localization, superconductivity data, and digit classification, SRDR recovers low‑dimensional sufficient structure and matches or surpasses state‑of‑the‑art nonlinear SDR methods in representation quality and predictive performance.
By Alexander Henzi, Tiange Liu, Xinwei Shen
arXiv:2605. 18931v2 Announce Type: replace-cross Abstract: Heavy-tailed distributions are prevalent in performance evaluation, network traffic, and risk modeling.
By Abdelhakim Ziani, Andras Horvath, Paolo Ballarini