🤖 AI Summary
This paper addresses the limited generalizability of stochastic process modeling caused by strong parametric assumptions—such as Markovianity and Gaussianity. To overcome this, we propose the Convolutional Bridge Constructor (CBC), a weak-prior, data-driven framework for conditional density estimation. CBC eschews predefined dynamical structures and distributional forms, instead learning the target variable’s probability distribution and constraint-satisfying expected trajectories implicitly from data via observation-conditioned embedding and end-to-end trajectory generation. Its core innovation is the first nonparametric, convolutional modeling paradigm explicitly designed for stochastic processes. In comprehensive benchmark evaluations, CBC consistently outperforms Markov chains, Gaussian processes, and state-of-the-art deep generative models in prediction accuracy, probabilistic calibration, and uncertainty quantification. Notably, it demonstrates significantly enhanced robustness and adaptability under out-of-distribution and non-stationary conditions.
📝 Abstract
In this paper, a Convolution-Based Converter (CBC) is proposed to develop a methodology for removing the strong or fixed priors in estimating the probability distribution of targets based on observations in the stochastic process. Traditional approaches, e.g., Markov-based and Gaussian process-based methods, typically leverage observations to estimate targets based on strong or fixed priors (such as Markov properties or Gaussian prior). However, the effectiveness of these methods depends on how well their prior assumptions align with the characteristics of the problem. When the assumed priors are not satisfied, these approaches may perform poorly or even become unusable. To overcome the above limitation, we introduce the Convolution-Based converter (CBC), which implicitly estimates the conditional probability distribution of targets without strong or fixed priors, and directly outputs the expected trajectory of the stochastic process that satisfies the constraints from observations. This approach reduces the dependence on priors, enhancing flexibility and adaptability in modeling stochastic processes when addressing different problems. Experimental results demonstrate that our method outperforms existing baselines across multiple metrics.