Generative modeling for high-dimensional sparse data: Probabilistic feature extraction in high-risk financial regimes

In financial data analysis, incorrect or missing data presents significant challenges, particularly in stock markets where data corruption and system errors amplify aleatoric uncertainty in high-risk scenarios. Conventional methods for imputing missing data, such as mean or regression imputation, or traditional feature extraction techniques, often fail to capture the underlying structure of financial data effectively. To address these limitations, this study employs probabilistic generative models, including Probabilistic Principal Component Analysis (PPCA) and Probabilistic Kernel Principal Component Analysis (PKPCA), to reconstruct missing values while uncovering latent features within information-driven bars data—a rare but highly informative sampling method in finance. Utilizing returns data from information-driven bars alongside event-based sampling, we extend asset vectors to a high-dimensional sparse framework, highlighting the inadequacies of traditional imputation methods. The proposed models exhibit strong performance in both in-sample and out-of-sample evaluations, identifying significant linear and non-linear asset correlations under varying market regimes. Furthermore, by leveraging the Wishart process and the kernel trick within PKPCA, we overcome the limitations of Gaussian-based models like PPCA, particularly in capturing temporal dependencies. A backtest of the reconstructed data within a portfolio optimization context demonstrated substantial improvements in cumulative returns, underscoring the potential of these probabilistic techniques in enhancing data-driven financial decision-making. This research illustrates the efficacy of probabilistic feature extraction in mitigating uncertainty and offers new insights into latent variable exploration and missing data imputation in financial contexts.