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.
Estimating the symbolic or analytical form of probability density functions (PDFs) from observed samples is a fundamental challenge in statistical and computational modelling. This process is critical...
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.
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.
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...
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.
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.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
arXiv:2504.05161v2 Announce Type: replace-cross Abstract: Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key...
arXiv:2605. 18931v2 Announce Type: replace-cross Abstract: Heavy-tailed distributions are prevalent in performance evaluation, network traffic, and risk modeling.
arXiv:2606. 10023v1 Announce Type: cross Abstract: Accurate posterior estimation is central to scientific inference, as uncertainties determine what can be reliably learned from observational data.
arXiv:2606. 30489v1 Announce Type: cross Abstract: Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a physical effect, a calibration constant, or a source of systematic uncertainty.
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.