Convolution-Based Converter : A Weak-Prior Approach For Modeling Stochastic Processes Based On Conditional Density Estimation

TL;DR

This paper introduces a Convolution-Based Converter (CBC) that estimates the conditional distribution of stochastic processes without relying on strong priors, improving flexibility and performance over traditional methods.

Contribution

The novel CBC approach removes the dependence on fixed priors in modeling stochastic processes, enabling more adaptable and accurate estimations.

Findings

Outperforms baseline methods on multiple metrics

Reduces reliance on prior assumptions

Enhances flexibility in stochastic process modeling

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.