One of the major models in causal inference is the Rubin Causal Model. In this model, treatment effect estimation is considered within the framework of missing data analysis. However, many previous studies based on this model have not adopted the framework of missing data analysis and instead have moved to discussions based on conditional probability distributions for outcome variables. In this study, we propose a framework for causal inference that does not rely on missing data analysis, using a generalized probabilistic model for treatment effect estimation and statistical decision theory. Furthermore, to verify the effectiveness of this framework, we analytically derive the optimal treatment effect estimation under the Bayesian criterion based on Bayesian decision theory by assuming a linear basis function model. In addition, we compare the proposed method for deriving the optimal estimation with conventional treatment effect estimation methods through simulations. This comparison clarifies the properties of the conventional methods.

Most previous studies on lossless image compression have focused on improving preprocessing functions to reduce the redundancy of pixel values in real images. However, we assumed stochastic generative models directly on pixel values and focused on achieving the theoretical limit of the assumed models. In this study, we proposed a stochastic model based on improper quadtrees. We theoretically derive the optimal code for the proposed model under the Bayes criterion. In general, Bayes-optimal codes require an exponential order of calculation with respect to the data lengths. However, we propose an efficient algorithm that takes a polynomial order of calculation without losing optimality by assuming a novel prior distribution.

In this paper, we propose a novel stochastic model based on the quadtree, so that our model effectively represents the variable block size segmentation of images. Then, we construct the Bayes code for the proposed stochastic model. In general, the computational cost to calculate the posterior distribution required in the Bayes code increases exponentially with respect to the data size. However, we introduce an efficient algorithm to calculate it in the polynomial order of the data size without loss of the optimality. Some experiments are performed to confirm the flexibility of the proposed stochastic model and the efficiency of the introduced algorithm.

We consider the source coding problem with side information. Especially, we consider the FV code in the case that the encoder and the decoder can see side information. We obtain the condition that there exists a FV code under the condition that the overflow probability is smaller than or equal to some constant.