Browsing by Author "Li, Yinong"

The thesis is about developing a new neural network-based simulation-based inference (SBI) method for performing flexible point estimation; we call this method Neural Amortization of Bayesian Point Estimation (NBPE). Firstly, using neural networks, we can achieve amortized inference so that most of the computation cost is spent on training the neural network while performing inference only costs a few milliseconds. In this thesis, we utilize an encoder-decoder architecture; we use an encoder as a summary network to extract informative features from raw data and then feed them to a decoder as an inference network to output point estimations. Moreover, with a novel training method, the utilization of a variable \( \alpha \) in the loss function \( |\theta_i - \theta_{\text{pred}}|^\alpha \) enables the prediction of different statistics (mean, median, mode) of the posterior distribution. Thus, with our method, at inference time, we can get a fast point estimation, and if we want to get different statistics of the posterior, we have to specify the value of the power of the loss $\alpha$. When $\alpha = 2$, the result will be the mean; when $\alpha = 1$, the result will be the median; and when $\alpha$ is getting closer to 0, the result will approach the mode. We conducted comprehensive experiments on both toy and simulator models to demonstrate these features. In the first part of the analysis, we focused on testing the accuracy and efficiency of our method, NBPE. We compared it to the established method called Neural Posterior Estimation (NPE) in the BayesFlow SBI software. NBPE performs with competitive accuracy compared to NPE and can perform faster inference than NPE. In the second part of the analysis, we concentrated on the flexible point estimation capabilities of NBPE. We conducted experiments on three conjugate models since most of these models' posterior mean, median, and mode have analytical expressions, which leads to more straightforward analysis. The results show that at inference time, the different choices of $\alpha$ can influence the output exactly, and the results align with our expectations. In summary, in this thesis, we propose a new neural SBI method, NBPE, that can perform fast, accurate, and flexible point estimation, broadening the application of SBI in downstream tasks of Bayesian inference.