Furthermore, in continuous state-action settings these methods must make coarse approximations to be computationally tractable (e.g.

This paper intends to answer the three interesting questions.

SMRL uses score matching, an unnormalized density estimation technique that enables efficient estimation of the model parameter by ridge regression.

Estimating distributions from samples is a fundamental statistical task.

Causal inference is no exception.

Learning from demonstration methods usually leverage close to optimal demonstrations to accelerate training.

For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class of non-Gaussian distributions -- those derived from diagonal transformations of a Gaussian -- information about the conditional independence structure can still be inferred from the precision matrix, provided the data meet certain criteria, analogous to the Gaussian case. We call such transformations of the Gaussian as the generalized nonparanormal. The functions that define these transformations are, in a broad sense, arbitrary. We also provide a simple and computationally efficient algorithm that leverages this theory to recover conditional independence structure from the generalized nonparanormal data. The effectiveness of the proposed algorithm is demonstrated via synthetic experiments and applications to real-world data.

Learning and generating various types of data based on conditional diffusion models has been a research hotspot in recent years. Although conditional diffusion models have made considerable progress in improving acceleration algorithms and enhancing generation quality, the lack of non-asymptotic properties has hindered theoretical research. To address this gap, we focus on a conditional diffusion model within the domains of classification and regression (CARD), which aims to learn the original distribution with given input x (denoted as Y|X). It innovatively integrates a pre-trained model f_ϕ(x) into the original diffusion model framework, allowing it to precisely capture the original conditional distribution given f (expressed as Y|f_ϕ(x)). Remarkably, when f_ϕ(x) performs satisfactorily, Y|f_ϕ(x) closely approximates Y|X. Theoretically, we deduce the stochastic differential equations of CARD and establish its generalized form predicated on the Fokker-Planck equation, thereby erecting a firm theoretical foundation for analysis. Mainly under the Lipschitz assumptions, we utilize the second-order Wasserstein distance to demonstrate the upper error bound between the original and the generated conditional distributions. Additionally, by appending assumptions such as light-tailedness to the original distribution, we derive the convergence upper bound between the true value analogous to the score function and the corresponding network-estimated value.