A.4 EstimatingparameterswhenY(t)isunavailable New parameter estimators that leverage only the available data need to be derived whenY(t) is unavailable. The derivation goes as follows: first, we eliminateY(t) from the model equations. The squared error of the estimated parameters are shown in Figure 1. First, we estimated the parameters separately for each individual. Second, we performed statistical analysis to find associations between the estimated parameters and the demographic variables.

The UN estimates 2-5% of global GDP or $0.8 - $2.0 trillion dollars are laundered

The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a statistical viewpoint, illustrating that one can actually hope for improvement when models are trained on data contaminated with synthetic samples, as long as there is some amount of fresh information from the true target distribution. In particular, we consider iterative training on samples sourced from a mixture of the true target and synthetic distributions. We analyze the entire iterative evolution in a next-token prediction language model, capturing how the interplay between the mixture weights and the sample size controls the overall long-term performance. With non-trivial mixture weight of the true distribution, even if it decays over time, simply training the model in a contamination-agnostic manner with appropriate sample sizes can avoid collapse and even recover the true target distribution under certain conditions. Simulation studies support our findings and also show that such behavior is more general for other classes of models.

Training generative models with differential privacy (DP) typically involves injecting noise into gradient updates or adapting the discriminator's training procedure.

Inspired by dataset distillation (DD) [Wang et al., 2018, Zhao et al., (Corollary 1). Extensive experiments on nine datasets of D4RL benchmark [Fu et al., 2020] with multiple environments and data qualities illustrate that our Av-PBC remarkably promotes the OBD performance, Moreover, Av-PBC has a significant convergence speed and requires only a quarter of distillation steps compared to DBC and PBC.